# Named Entity Normalization Model Using
Edge Weight Updating Neural Network:
Assimilation Between Knowledge-Driven Graph
and Data-Driven Graph

Sung Hwan Jeon
Department of Industrial Engineering
Seoul National University
1, Gwanak-ro, Gwanak-gu, Seoul, Republic of Korea
<EMAIL_ADDRESS>
&Sungzoon Cho
Department of Industrial Engineering and Institute for Industrial Systems
Innovation
Seoul National University
1, Gwanak-ro, Gwanak-gu, Seoul, Republic of Korea
<EMAIL_ADDRESS>

###### Abstract

Discriminating the matched named entity pairs or identifying the entities’
canonical forms are critical in text mining tasks. More precise named entity
normalization in text mining will benefit other subsequent text analytic
applications. We built the named entity normalization model with a novel Edge
Weight Updating Neural Network. Our proposed model when tested on four
different datasets achieved state-of-the-art results. We, next, verify our
model’s performance on NCBI Disease, BC5CDR Disease, and BC5CDR Chemical
databases, which are widely used named entity normalization datasets in the
bioinformatics field. We also tested our model with our own financial named
entity normalization dataset to validate the efficacy for more general
applications. Using the constructed dataset, we differentiate named entity
pairs. Our model achieved the highest named entity normalization performances
in terms of various evaluation metrics.

_Keywords_ Named Entity Normalization $\cdot$ Edge Weight Updating Neural
Network $\cdot$ Text Mining in Bioinformatics $\cdot$ Text Mining in Finance
$\cdot$ Named Entity Graph

##  1 Introduction

The text mining technology is undergoing a rapid evolution thanks to the
exponential growth in the number of text-rich documents available online, and
as a result, it is being widely applied in a range of domains such as finance
and bioinformatics. Text mining aims to extract the information from documents
to derive valuable insights. Documents subject to analysis contain many named
entities, which are proper names that denote unique objects such as
organizations, products, persons, and locations. The technique used to extract
named entities from documents is called named entity recognition (NER,
henceforth). Furthermore, named entity normalization (NEN, henceforth)
involves matching extracted named entities with homogeneous identity and is
pivotal for text mining tasks.

More specifically, in the biomedical domain, disease names and chemicals in
drugs often have different surface forms while sharing the same concept. Types
of named entities with different surface forms that share same concept can be
divided into following categories: (1) synonyms, (2) abbreviations, (3)
acronyms, (4) different combinations of punctuations and alphabets, (5)
descriptive phrases, and (6) possible NER parsing errors. For example,
“hepatomegaly" and “liver enlarged" do not have matching strings but the two
disease names have identical meanings, and thus, these two named entities are
synonyms. Biomedical named entities have a wide variety of different surface
forms compared with entities from other text sources. More accurate named
entity normalization techniques will potentially improve the quality of
downstream tasks. Moreover, matching entity pairs such as “International
Business Machines" and “IBM", which are examples of acronyms, are very
critical in financial text mining applications. Linking entities with the same
identity enables accurate sentiment analysis on firms and products.
Furthermore, evaluation of news impacts on the stock market requires the
connection between news articles and related firms. Given the wide range of
named entities in bioinformatics and finance documents, the total number of
tokens to be calculated for text clustering and classification is enormous.

The early NEN models explored knowledge-based approaches. Generating the rules
for named entity matching based on domain knowledge is valid only for the
dataset in which the corresponding rules are already created. The rule-based
models are not robust for the neologisms. In order to overcome the
disadvantage that the rule-based model is not robust, models based on machine
learning have been introduced. However, machine learning models are limited to
specific fields such as bioinformatics NEN and chemical engineering NEN due to
lack of NEN datasets in other domains. Our research aims to construct fully
automated NEN model that can be applied to various other domains. To test our
model’s robustness on different domain, we also apply the NEN dataset in
finance.

An automated named entity normalization model reduce the burden of hand-mined
information extraction tasks. Clear linkage between entities with different
forms, such as abbreviations and acronyms, aid in more accurate sentiment
analysis. The named entity normalization model also benefits the creation of
more comprehensible classifying and clustering documents. The primary
contributions of our study are (1) constructing better performing NEN model
using an Edge Weight Updating Neural Network and (2) applying our proposed
model to bioinformatics NEN and financial NEN tasks.

The proposed method, that is, the edge weight updating neural network,
consists of four parts: (1) ground truth entity graph construction, (2)
similarity-based entity graph construction, (3) edge weight updating neural
network training, and (4) edge weight updating neural network inferencing. The
main concept behind the Edge Weight Updating Neural Network is to minimize the
Ground Truth Entity Graph’s edge weight distributions and the Similarity-Based
Entity Graph’s edge weight distributions. By minimizing the edge weight
distributions on the two graphs, entity embeddings capture more accurate
information on semantic similarity between matching entities.

Our proposed model is evaluated on three widely used bioinformatics datasets
(NCBI Disease, BC5CDR Disease, and BC5CDR Chemical) and its performance is
compared with other cutting-edge models. Furthermore, to validate the efficacy
of our proposed model in general NEN tasks, we construct a financial NEN
dataset with state-of-the-art NER using BERT [1]. Using the constructed
dataset, we propose the deep learning model to solve more practical financial
NEN tasks. Out dataset incorporates major challenges in entity matching: (1)
synonyms, (2) abbreviations, (3) acronyms, (4) different combinations of
punctuations and alphabets, (5) descriptive phrases, and (6) possible NER
parsing errors. Compare with other recent NEN models, our proposed model shows
higher accuracies in all datasets used in the experiments, and our model is
tested with not only bioinformatics NEN datasets but also financial NEN
datasets, which verifies the efficacy in general NEN tasks.

The remainder of this paper is organized as follows. Section 2 describes
related work. Section 4.1 presents an overview of dataset we used for
evaluations. A brief explanation of pre-constructed NEN datasets from the
bioinformatics domain is given in this section. The structure for our proposed
model is described in Section 3. Experiment settings for testing model
performances are provided in Section 4. Furthermore, 4.1 in Experiment
Settings(subsection 4) provides the overview of preprocessing for data and
financial NEN dataset construction with examples. In Section 5, we present the
details regarding the qualitative and quantitative analyses we conducted on
the models. Finally, in Section 6, we present our conclusions.

##  2 Related Work

Bioinformatics, chemical engineering, and materials science domain actively
adopt cutting-edge deep learning frameworks for NEN tasks. According to Cho et
al. [2], various products exist for recognizing and normalizing named entities
in biomedical fields such as ProMiner [3] and MetaMap [4]. DNorm [5] and
TaggerOne [6] also used machine learning models such as pairwise ranking
scoring and semi-Markov models, respectively, for NEN processing. In genetic
engineering, GenNorm [7] and GNAT [8] are used to normalize the gene names.
ChemSpot [9] uses Conditional Random Field for NER and NEN tasks in chemical
engineering. Weston et al. [10] developed MatScholar [10] python repository to
perform general NLP tasks on material science texts, which includes entity
normalization.

The above researches and products used NEN datasets concentrated on specific
domains. ShARe/CLEF [11] is one of the widely used NEN datasets for
bioinformatics that is made up of clinical notes. The NCBI [12] dataset
contains PubMed abstracts for disease name normalization tasks. TAC2017ADR
[13] aims to link identical drug labels. The BC2GM [14], BioNLP09 [15], and
BioNLP-OST19 [16] datasets deal with genes, proteins, and bacteria,
respectively. In chemical engineering, SCAI [17] and IUPAC [18] are available
for researches on chemical name matching. Similar to chemical names, Weston et
al. [10] developed a dataset for material engineering to normalize entities to
a canonical form.

Applying machine learning algorithms in the financial domain is gaining
increasing attention. One major branch is stock movement forecasting using
various deep learning mechanisms [19, 20]. Thanks to the rapid developments of
unstructured data processing techniques, researches on applying text mining
techniques to the financial fields have increased in number. In their study,
Gupta et al. [21] illustrated the trends for applying text mining in finance.
Among many related text mining applications in finance, NEN can be applied to
various financial researches and financial practices. In preprocessing for
applying text mining techniques to solve real-world problems, NER and NEN
models are performed preemptively. However, the NEN dataset for the financial
domain is scant and there is a need for developing a dataset targeting the
financial NEN.

Many researchers have developed targeted datasets for more general NEN tasks
in domains such as user comments, product description, and financial invoices.
For example, in their study, Jijkoun et al. [22] used user comments from
newspaper websites. Sun et al. [23] performed normalization of product entity
names, for which the dataset was developed by the authors. The study conducted
by Francis et al. [24] on financial invoices is the most relevant one to our
study. However, Francis et al. focused on insurance, telecommunications,
banking, and tax companies using the following entities: International Bank
Account Number (IBAN) of the beneficiary, invoice number, invoice date, and
due date [24]. The focus of our study is on more general financial entity
normalization, which covers entities from all financial sectors. Previous
studies using the datasets illustrated above used various machine learning and
deep learning models.

There are similarities between the string matching methodologies in various
other fields and NEN researches. Sun et al. [23] proposed NEN for product
names using a pre-constructed product entity linkage dictionary. In semantic
string matching, Siamese Neural Networks are widely used [25, 26, 27].
Krivosheev et al. [28] used Siamese Graph Neural Network for company name
normalization. We need to extend NEN on company names to NEN on a wide range
of product names and legal entities. Siamese RNN model successfully apprehends
the morphological similarity between strings [29]. Niu et al. [30] applied
Attention mechanisms for medical concept normalization. Furthermore, the
evolution of Transformer-based models capacitate the adoption pre-trained
language models such as BERT [1] for entity linking problems [31].

The major development in recent NEN researches is as follows. D‘Souza et al.
[32] proposed an early NEN model using a rule-based model, which requires
comparatively more human input when generating the rules. The model is static
and, thus, there is a possibility that new rules need to be created when
applying the model to other datasets. NEN models that use more advanced
machine learning and deep learning techniques can be more effective. Leaman et
al. [6] used semi-Markov model, Li et al. [33] used word-level CNN model, and
Wirght and Dustin [34] and Phan et al. [35] models based on BiGRU and BiLSTM.
However, BERT achieved state-of-the-art performance in many general text
mining and natural language processing (NLP) challenges. Compared with the
four models illustrated above, the most recent researches such as the BERT
ranking model [36] and BioSyn [37] takes full advantage of the BERT model by
training the model based on BERT embeddings. The BERT Ranking model [36] used
ranking-based objective function and BioSyn [37] used Synonym Marginalization
techniques as the objective function for training. Our proposed model
optimizes BERT embedding vectors with named entity graph’s edge weight
updating neural network. Our proposed model successfully captures the ground
truth linkage between named entity graphs, achieving the highest accuracies.
Previous NEN researches focus mainly on the NEN dataset from a specific
domain. To test the efficacy of our model in more general NEN tasks, we
evaluate our model with NEN datasets from both the bioinformatics domain and
financial domain.

Many NEN researches explore semi-supervised learning models. Our proposed
model is motivated by one of the leading semi-supervised models on images,
Edge-Labeling Graph Neural Network for Few-shot Learning [38] (EGNN). The
major difference between EGNN and our model is that EGNN labels an edge for
each round of training but our model updates edge weights for top K connected
entities. By capturing more node and edge information simultaneously for each
round of training, the proposed model shows better performance compared with
other NEN models.

##  3 Proposed Method

Our proposed model, Edge Weight Updating Neural Network, consists of four
major parts.

  1. 1.

Ground Truth Entity Graph construction

  2. 2.

Similarity-Based Entity Graph construction

  3. 3.

Edge Weight Updating Neural Network training

  4. 4.

Edge Weight Updating Neural Network inferencing

The basic idea behind Edge Weight Updating Neural Network is to minimize the
Ground Truth Entity Graph’s edge weight distributions and the Similarity-Based
Entity Graph’s edge weight distributions. Entity embeddings are trained with
Kullback-Leibler divergence [39] loss between two graphs. Detailed steps for
constructing the Ground Truth Named Entity Graph, building the Similarity-
Based Entity Graph, and training and inferencing the Edge Weight Updating
Neural Network are presented in Sections 3.1, 3.2, 3.3 and 3.4, respectively.

###  3.1 Ground Truth Entity Graph Construction

Figure 1: Ground Truth Named Entity Graph construction

Ground Truth Entity Graph constructions are based on mentions (entities) in
each dataset and their concept IDs. Figure 1 demonstrates the steps for
building the graph.

For the NEN corpus, each entity is annotated with one or more concept IDs. For
example in Figure 1, entities A, B, and C share the same concept ID, ID_1.
Then, entities A, B, and C are fully connected in the entity graph. Other
entity pairs, D - E (concept ID: ID_2) and F - G (concept ID: ID_3) are
linked. The training dataset for each NEN corpus has query entities with
corresponding concept ID. If query entity Q has a concept ID of ID_1, then,
query entity Q will be linked to entities A, B, and C in the pre-constructed
graph. As the constructed graph is the ground truth graph, each edge weight in
the graph is 1.

We iterate all the entities in training sets that include the referencing
dictionary entity table and the query entity table. Graph created by the
following steps above is the Ground Truth Entity Graph which is the reference
or the target graph the Similarity-Based Entity Graph will try to match.

###  3.2 Similarity-Based Entity Graph Construction

Figure 2: Entity Matching Graph based on Entity Similarity construction

For each query entity, Similarity-Based Entity Graph is constructed as
follows. Graph edges are calculated using BERT embedding vector similarities.
We use BioBERT [40] for bioinformatics NEN corpus’ initial BERT embeddings and
the original BERT [1] for financial NEN corpus’ initial BERT embeddings.

For example, in Figure 2, let query entity Q has size of 768 (vector length of
BERT embeddings), $Embed_{Q}=(X_{Q1}~{}~{}X_{Q2}~{}~{}\cdots~{}~{}X_{Q768})$.
Similarly, BERT-based entity embeddings in the dictionary set are also denoted
as
$Embed_{entity}=(X_{entity1}~{}~{}X_{entity2}~{}~{}\cdots~{}~{}X_{entity768})$.
The BERT embedding has a fixed length of 768, so our embedding vectors have a
vector length of 768.

To calculate the edge weights based on entity similarities, we calculate inner
products between query entities and dictionary entities. $<~{},~{}>$ is the
notation for inner product and $Sim_{Q}$ is the set of similarities between
query entity Q and all the entities in a dictionary; then the similarity
between each query entity and each dictionary entity calculation is expressed
as Equation 1,

$\displaystyle Sim_{Q}=\\{Sim|Sim=<Embed_{Q},~{}Embed_{D}>~{}for~{}D\in
DictionaryEntitySet\\}$ (1) $\displaystyle where,$ $\displaystyle Embed_{Q\in
QueryEntitySet}=(X_{Q1}~{}~{}X_{Q2}~{}~{}\cdots~{}~{}X_{Q768}),$
$\displaystyle Embed_{D\in
DictionaryEntitySet}=(X_{D1}~{}~{}X_{D2}~{}~{}\cdots~{}~{}X_{D768})$

We normalize the similarity score by dividing the maximum similarity score in
each query entity’s similarity score set, $Sim_{Q}$. For Similarity-Based
Entity Graph, top K edges based on similarity score are selected. Highlighted
blue region in entity similarity table for query entity Q in Figure 2
demonstrates the edge weight determination steps when $K=5$. Mathematically,
edge weights are calculated using Equation 2.

$\displaystyle ConnectedEdgeWeight=\\{Weight_{Edge}|Edge\in ConnectedEdge\\}$
(2) $\displaystyle where,$ $\displaystyle
ConnectedEdge=argmax_{k}\\{Weight_{Q}\\},$ $\displaystyle
Weight_{Q}=\left\\{Weight|Weight=\frac{Sim}{Max_{Q}}~{}for~{}Sim\in
Sim_{Q}\right\\},$ $\displaystyle and,Max_{Q}=max\\{Sim_{Q}\\}$

For each training epoch, which is illustrated in Section 3.3, edge weights are
updated. Updated entity embedding vectors generate new similarity scores that
alter the edge weights in the graph.

###  3.3 Edge Weight Updating Neural Network Training

Figure 3: Minimizing the Edge Weight Distributions in Edge Weight Updating
Neural Network for Query Entity Q

The main concept of Edge Weight Updating Neural Network is to minimize the
difference between the edge weights’ discrete distribution for each query
entity in the Ground Truth Entity Graph and the Similarity-Based Entity Graph.
As illustrated in Section 3.2, edge weights are calculated by entities’
embeddings. In each training epoch in Edge Weight Updating Neural Network,
baseline BERT model’s parameters are optimized to mimic the ground truth edge
weight distributions.

Figure 3 shows the training process of our proposed model for the number of
connected edges in the Similarity-Based Entity Graph is 5 ($K=5$). Following
the example in Section 3.2, query entity Q is connected to dictionary entities
A, B, C, D, and F, and edge weights are 0.8, 0.9, 0.6, 0.7, and 0.5,
respectively. Given the Ground Truth Entity Graph in Section 3.1, the truth
edge weights for connected edges between query entity Q and dictionary
entities, A, B, C, D, and F are 1, 1, 1, 0, and 0, respectively.

In training procedures, BERT parameters are tuned to make edge weights
distributions in Similarity-Based Entity Graph closer to the ground truth edge
weight distributions. We use Kullback-Leibler Divergence Loss [39](KL
divergence loss, henceforth) for training our model. As edge weight
distribution is discrete, we normalize the edge weights using the Softmax
function.

We denote graph as $G$, entity as $V$, and edge as $E$. The Ground Truth
Entity Graph and the Similarity-Based Entity Graph are denoted as
$G_{GT}=(V_{GT},E_{GT})$ and $G_{Sim}=(V_{Sim},E_{Sim})$, respectively. The
adjacency matrices for Ground Truth Entity Graph and the Similarity-Based
Entity Graph are denoted $GT\\_A$ and $Sim\\_A$. $P_{Sim\\_Edge_{Q}}$ is the
discrete distribution of edge weights of Q in Similarity-Based Entity Graph.
$P_{GT\\_Edge_{Q}}$ is the discrete distribution of edge weights of Q in the
Ground Truth Entity Graph. Our KL divergence loss is calculated using Equation
3.

$\displaystyle
Loss=KL(P_{GT\\_Edge_{Q}}||P_{Sim\\_Edge_{Q}})=P_{GT\\_Edge_{Q}}\cdot\log\left(\frac{P_{GT\\_Edge_{Q}}}{P_{Sim\\_Edge_{Q}}}\right)$
(3) $\displaystyle where,$ $\displaystyle
P_{GT\\_Edge_{Q}}=Softmax(GT\\_Edge_{Q}),$ $\displaystyle
P_{Sim\\_Edge_{Q}}=Softmax(Sim\\_Edge_{Q}),$ $\displaystyle
GT\\_Edge_{Q}=\\{GT\\_A_{query,d}|d\in argmax_{k}\\{Sim\\_A_{Q}\\}\\},$
$\displaystyle Sim\\_Edge_{Q}=\\{Sim\\_A_{query,d}|d\in
argmax_{k}\\{Sim\\_A_{Q}\\}\\},$ $\displaystyle
and,A_{Q}~{}is~{}the~{}edge~{}weight~{}vector~{}connected~{}to~{}Q~{}for~{}given~{}query~{}entity~{}node~{}Q$

We use an Adam optimizer with weight decay [41], and set the batch size to 16
and the number of connected edges in the Similarity-Based Entity Graph to 30
($K=30$) for all datasets we test. We train our model for 50 epochs. The best
scores are reported in Section 4.

###  3.4 Edge Weight Updating Neural Network Inferencing

Figure 4: Inferencing the Edge Weight Distributions in Edge Weight Updating
Neural Network for Query Entity Q

First, fine-tuned BERT embeddings illustrated in Section 3.3 are used to embed
unseen query entities in test sets. With newly computed BERT embedding
vectors, we repeat the steps in Section 3.2 to construct the new Similarity-
Based Entity Graph. For each query entity, a dictionary entity with the
highest edge weights is returned as a synonym. Figure 4 demonstrates the
inferencing process of the Edge Weight Updating Neural Network.

##  4 Experiment Settings

###  4.1 Dataset

####  4.1.1 Named Entity Normalization Datasets in Bioinformatics

Most NEN researches are from the bioinformatics domain. To test our model’s
performance with other NEN models, we select three of the most used
bioinforinmatics NEN datasets: NCBI Disease [12] and two datasets from
Biocreinative V CDR (BC5CDR, henceforth) [42].

Three datasets summarized below contains bioinformatics-related mentions
(entities) with unique concept IDs. The main goal of these datasets is to
identify the mentions that share the same concept IDs. We follow NEN
preprocessing convention for the datasets below, in which the mentions that do
not exist in the concept dictionary are eliminated [35]. Bioinformatics NEN
datasets usually consist of train, development, and test sets. Following
previous studies, we use train and development sets for training our model.
Test sets are used for evaluations.

Table 1: Data Statistics of Three Bioinformatics NEN Datasets | # of Documents | # of Mentions (Entities)
---|---|---
| Train | Dev | Test | Train | Dev | Test
NCBI Disease | 592 | 100 | 100 | 5,134 | 787 | 960
BC5CDR Disease | 500 | 500 | 500 | 4,182 | 4,244 | 4,424
BC5CDR Chemical | 500 | 500 | 500 | 5,203 | 5,347 | 5,385

##### NCBI Disease

[12]. NCBI Disease corpus provides disease mentions in different surface
forms. Disease mentions in this dataset are extracted from 793 PubMed
abstracts containing a total of 6,892 disease mentions, which are mapped to
790 unique disease concepts. Disease concepts are annotated by Medical Subject
Headings (MeSH) and Online Mendelian Inheritance in Man (OMIM). Disease
mentions sharing the same disease concept are considered synonyms. Table 1
shows detailed statistics of the NCBI Disease corpus.

##### Biocreative V CDR Disease and Biocreative V CDR Chemical

[42]. The BC5CDR corpus is organized for challenging tasks of disease named
entity recognition and chemical-induced disease relation extraction. The
BC5CDR corpus consists of 1,500 PubMed articles with 4,409 annotated
chemicals, and 5,818 disease and 3,116 chemical-disease interactions [42]. The
dataset contains disease mention corpus and chemical mention corpus. Disease
mentions are mapped into the MeSH IDs similar to the NCBI Disease corpus.
Chemical mentions are annotated using the Comparative Toxicogenomics Database
(CTD) [43]. Mentions that share the same disease concept and chemical concept
based on MeSH ID and CTD ID are considered synonyms. Detailed statistics of
both BC5CDR Disease corpus and BC5CDR Chemical corpus are illustrated in Table
1.

####  4.1.2 Named Entity Normalization Datasets in Finance

There are no publicly open financial NEN datasets available; therefore, we
constructed our own financial NEN dataset to test the performance of our
proposed model in NEN tasks other than the bioinformatics domain.

##### Overview

. We construct the dataset for the financial NEN task from the annual reports
(Form 10-K) of Standard and Poor’s 500 listed companies. We aim to build the
dataset that fulfills the need for financial NEN; the dataset includes (1)
synonyms, (2) abbreviations, (3) acronyms, (4) different combinations of
punctuations and alphabets, (5) descriptive phrases, and (6) possible NER
parsing errors. A detailed explanation of primary data sources, data
preprocessing steps, and dataset construction procedures are as follows. Fig.
5 demonstrates the overall flow diagram for NEN dataset construction.

Figure 5: Flow Diagram of the Overall Dataset construction

##### Data Source

. We gather the year 2019’s Form 10-Ks (published early 2020) of S&P500
companies from the U.S. firms and Exchange Commission (SEC)
website111https://www.sec.gov/edgar.shtml, which is open to the public. We
parse the business section of each 10-K documents from 496 companies. The
business section of 10-K is considered the self-identity of firms and presents
the information of main products, competitors, partners, and laws affecting
the business. Among the sections in 10-K, this section contains the most
number of entities. Out of 496 companies’ business section, 67,792 sentences
were parsed.

##### Data Preprocessing

. For NER in financial documents, we implement the BERT NER model [1] using
Huggingface’s222https://huggingface.co Python repository. Huggingface’s NER
model is trained using CoNLL-2003 NER dataset [44]. The outputs of the BERT
NER model are WordPiece tokens that we have to link together with specified
rules that will be circumstantially described below. There are four types of
entity types: persons (PER), organizations (ORG), locations (LOC) and
miscellaneous names (MISC), and one outside the named entity tag (O) in the
CoNLL-2003 dataset. We detect entities with ORG and MISC tags. For the year
2019 S&P500 firms’ 10-K, we parse a total of 41,593 named entities.

##### Dataset Construction

.

Table 2: Example of Financial Named Entity Normalization Dataset | Named Entity | Matching Named Entity
---|---|---
Synonyms | Coca-Cola ® | Coca-Cola
| COVID-19 Pandemic | COVID-19
| iPhone 11 Pro Max | iPhone ®
Abbreviations | Baker Hughes Company | Baker Hughes Co.
| Comcast Corporation | Comcast Corp.
| Qualcomm Incorporated | Qualcomm Inc.
Acronyms | Amazon Web Services | AWS
| Bank of New York Mellon | BNY Mellon
| New York Stock Exchange | NYSE
Combinations of punctuations | Apple, Inc. | Apple Inc.
| Walmart U. S. | Walmart U. S
| Booz Allen & Hamilton | Booz Allen Hamilton
Descriptive Phrases | EY ( formerly Ernst & Young ) | Ernst and Young
| Securities Exchange Act of 1934 | ( the Exchange Act )
| Facebook (including Instagram) | Facebook ®
NER Parsing Errors | Disney Channel-the | Disney Channel
| Full Throttle ®-a | Full Throttle ®)
| Keystone-our | Keystone Foods

With named entities recognized illustrated in Section 4.1.2, we construct the
financial named entity normalization dataset. As mentioned in Section 4.1.2,
our focus is to build a NEN dataset to meet the need for general text mining
in finance; the dataset includes (1) synonyms, (2) abbreviations, (3)
acronyms, (4) different combinations of punctuations and alphabets, (5)
descriptive phrases, and (6) possible NER parsing errors. We hand label a
total of 7,155 unique named entities into 2,600 groups; with each group
sharing the same identity. Table 2 shows three examples in our dataset for
types of named entities that need to be normalized.

  * •

Synonyms:

There exist entities with the suffix “®" or “™". “Coca-Cola ®" and “Coca-Cola"
are the same entity. In addition, “COVID-19 Pandemic" and “COVID-19" should be
linked. We generalize the product model numbers in which “iPhone 11 Pro Max"
and “iPhone ®" are considered identical entities.

  * •

Abbreviations:

Most abbreviations occur for abridging “Company" to “Co.", “Corporation" to
“Corp.", and “Incorporated" to “Inc.".

  * •

Acronyms:

Acronyms are one of the most challenging NEN tasks. There are multiple
abbreviations that are included in financial documents. We avoided matching
acronyms if there are multiple original entities can be assigned. For example,
“Advanced Development Programs ( ADP )" and “Automatic Data Processing, Inc. (
ADP )" both share the same acronyms, “ADP", but these should not be linked
together.

  * •

Combinations of punctuations:

The different combinations of punctuations problems can be solved using rule-
based approaches. However, there are many entities with a combination of
punctuations. “,", “.", and “&" are commonly found and used interchangeably.

  * •

Descriptive phrases:

In parsed named entity, an entity with descriptive phrases can be frequently
found. With or without descriptive phrases, the root or the identified entity
is invariable.

  * •

NER parsing errors:

No NER models and entity concatenation models are perfect. If NER is conducted
manually, there are possible human errors too. According to our dataset, one
common error model makes is appending the following token after “-" token. NER
parsing error correction is one of the important targets our NEN model aims to
achieve.

Table 3: Statistics of the Financial Named Entity Normalization Dataset | Train | Test | Total
---|---|---|---
# of Identical Entity Groups | 2,510 | 90 | 2,600
# of Positive Pairs | 7,064 | 3,761 | 10,825
# of Negative Pairs | 10,436 | 3,739 | 14,175
# of Pairs Total | 17,500 | 7,500 | 25,000

Hand-matched entity pairs are labeled positive. We also added negatively
labeled pairs in which two entities have no relationship. A total of 25,000
pairs with 10,825 positive matching pairs and 14,175 negative pairs are
created. We separate entity groups for a train set and test set in which there
are no overlapping groups. This eliminates possible training bias, especially
when training the model with entities’ graph topology. Table 3 shows the
statistics of our financial NEN dataset.

###  4.2 Experiment Settings: Named Entity Normalization in Bioinformatics

We compare our proposed model’s performance with seven different biomedical
NEN models. The accuracy score presented in this study is excerpted from
original papers. A summary of each model is illustrated in Table 4.

Table 4: Models Used in Bioinformatics NEN datasets evaluations Models |  Descriptions
---|---
Sieve-based [32] |  This is one the earliest NEN papers. The research was conducted with 10 Sieve, which is mostly a rule-based approaches. Many published post this research follow similar preprocessing steps.
Taggerone [6] |  Taggerone used the semi-Markov model for both NER and NEN tasks. Taggerone was originally validated on the NCBI Disease and BC5CDR corpus.
CNN Ranking [33] |  CNN Ranking model used a word-level deep learning approach for NEN. This research did not perform better than the previous model, Taggerone. However, it was the first study that applied deep learning to NEN tasks.
NormCo [34] |  NormCo used BiGRU, which is considered to be a better performing deep learning model with text data. NormCo achieved similar accuracy scores with significantly fewer parameters.
BNE [35] |  BNE introduced two-level BiLSTM to capture both character-level and word-level information of biomedical entities, achieving increased NEN performance.
BERT Ranking [36] |  BERT Ranking model is based on Transformer-based embeddings that use the pre-trained BERT [1], BioBERT [40], and ClinicalBERT [45] for their entity embeddings. For each entity, candidate concepts were retrieved and three different BERT models are fine-tuned to rank and to capture the ground truth concepts.
TripletNet [46] |  The concept of TripletNet [47] for semi-supervised learning was introduced for NEN tasks. This study uses CNN for entity embedding and shared CNN parameters are trained with TripletNet structure.
BioSyn [37] |  BioSyn uses BioBERT for entity embeddings and trained with Synonym Marginalization. Marginal Maximum Likelihood (MML) is the objective function for Synonym Marginalization.

###  4.3 Experiment Settings: Named Entity Normalization in Finance

The dataset we used is covered in Section 4.1.2. Table 5 shows each model used
in NEN in Finance is tested. The experiments are conducted using Intel
Core-i9-10940X CPU with 128GB memory and three NVIDIA GeForce Titan RTX GPU.
To avoid possible biases caused by exogenous variables, we use the same
setting for all models if applicable.

Table 5: Models Used in Finance NEN datasets evaluations Models |  Descriptions
---|---
Edit Distance [48] |  Edit Distance is suitable for basic NEN tasks for linking “Apple Inc" and “Apple Inc.". However, Edit Distance can only capture the superficial morphological similarity between two entities. In our experiment, we calculate the Edit Distance between two entity pairs and train a simple classifier to determine the equivalence of two entities.
BERT [1] |  BERT is a state-of-the-art model for various NLP tasks. However, for our specific tasks, the BERT model has a limitation on capturing morphological similarity between entity pairs. We use pre-trained BERT vectors with size 768 and train a simple MLP classifier with batch size 4096 to determine the linkage between entity pairs.
Siamese GCN [49] |  We use the entity graph illustrated in Section 3.2 and we use a pre-trained BERT vector for each entity node vector. 2-layer Siamese GCN is used in our experiment with 256 hidden nodes for the first GCN layer and 16 hidden nodes for the second GCN layer. GCN requires more epochs for training so we trained for 120 epochs for the full dataset (full batch: 17,500 entity pairs). The learning rate for ADAM optimizer for GCN is 0.01.
Siamese BiLSTM [50] |  For Character Level Siamese BiLSTM model training, we one-hot encoded the characters entity strings with unique 85 tokens. We stack two BiLSTM layers. The BiLSTM cells in the first layer return 64 dimension hidden states output and the BiLSTM cells in the second layer return 16 dimension hidden states output. To prevent overfitting, we train the BiLSTM model for 12 epochs. The BiLSTM model is trained with a learning rate of 0.001. Embedding dimension, 16, is the same as GCN.

##  5 Results

We conduct both quantitative and qualitative analysis. For NCBI Disease,
BC5CDR Disease, and BC5CDR Chemical datasets, we compare our proposed model’s
score with previous researches. Bioinformatics datasets are reported by top
one recommendation accuracy. Given the biomedical entity in the train set,
entities are matched with the most similar entities in datasets. If the query
entity and target entity share the same concept ID, it is considered correct.
The financial NEN dataset is a pairwise NEN matching corpus. For evaluations
on the financial NEN dataset, models that are used in evaluations distinguish
whether two named entity pairs share identical meanings or not. We also
perform the qualitative analysis to assess models’ weaknesses.

###  5.1 Quantitative Analysis: Bioinformatics

Table 6: Bioinformatics Named Entity Normalization Performance Test | NCBI Disease | BC5CDR Disease | BC5CDR Chemical
---|---|---|---
Sieve-Based [32] | 84.7 | 84.1 | 90.7
Taggerone [6] | 87.7 | 88.9 | 94.1
CNN Ranking [33] | 86.1 | - | -
NormCo [34] | 87.8 | 88.0 | -
BNE [35] | 87.7 | 90.6 | 95.8
BERT Ranking [36] | 89.1 | - | -
TripletNet [46] | 90.0 | - | -
BioSyn [37] | 91.1 | 93.2 | 96.6
Proposed Model | 91.7 | 93.4 | 96.7

Table 6 shows a performance comparison between our proposed model and previous
state-of-the-art models. For three bioinformatics datasets, our proposed model
achieved the highest accuracy. Our model showed the highest performance
increase by 0.6% in the NCBI Disease corpus. For BC5CDR Disease and BC5CDR
Chemical corpus, the performance increase compared the previous state-of-the-
art model is 0.2% and 0.1%, respectively.

The NCBI Disease corpus is a comparatively harder dataset based on the
performance of other models. We conclude that there there is a significant to
increase the accuracy in a relatively lower performing dataset. The previous
model already performs excellently on the the BC5CDR corpus with an accuracy
score increasing from 93.2% to 96.6%. Significant performance increase in
these datasets can be marginal.

###  5.2 Quantitative Analysis: Finance

Table 7: Precision, Recall, F-Score, Accuracy of Models | Precision (%) | Recall (%) | F-Score (%) | Accuracy (%)
---|---|---|---|---
Edit Distance | 43.12 | 63.35 | 51.31 | 62.60
BERT | 62.92 | 82.17 | 71.27 | 76.81
Siamese GCN | 79.00 | 82.16 | 80.55 | 82.56
Siamese BiLSTM | 75.96 | 89.98 | 82.38 | 85.15
Proposed Model | 93.43 | 82.11 | 87.40 | 88.13

Table 7 shows the performance of each model we test. The evaluation metrics
are expressed as follows

$\displaystyle precision=\frac{tp}{tp+fp}$ (4) $\displaystyle
recall=\frac{tp}{tp+fn}$ $\displaystyle F1=2\cdot\frac{precision\cdot
recall}{precision+recall}$

False positive indicates that two entities should not be matched, but our
proposed model decided to link two entities. False negative indicates that two
entities should be matched, but our proposed model failed to link two
entities.

For practical use in the NEN model in the finance domain, a model with higher
precision should be rewarded more. In practice, a model with higher precision
will reduce the burden for practitioners’ tasks by giving more reliable
entity-matching results. A model with higher precision will reduce time
double-checking the validity entity pairs marked as matched.

Edit Distance had the lowest score along with all performance evaluation
indicators. Graph Convolutional Network we use for the experiments adopts the
BERT vector as entity node features. BERT and GCN have a similar recall, but
GCN has higher precision, which brings higher F-score and accuracy compared
with BERT. Our proposed model achieved the highest precision, F-score, and
accuracy. Among all the models, our proposed model is the only model with a
precision score over 90%. Therefore, our proposed model is the most suitable
for practical use.

###  5.3 Qualitative Analysis

####  5.3.1 Error Analysis

In error analysis, entities for which accurate recommendations are not made
are reported. Through error analysis, we aim to recognize the pattern of cases
where recommendations are not properly made.

Table 8: Error Analysis on Three Biomedical NEN datasets | Query Entity | Retrieved Synonym Entity
---|---|---
| encephalopathy | aids encephalopathy
| nail dystrophy | twenty nail dystrophy
NCBI Disease | cdm | cdmd
| copper overload | copper deficient
| g m2 gangliosidosis | g m2 gangliosidosis type ii
| lung mass | liver mass
| hypoactivity | hyperactivity
BC5CDR Disease | htn | htx
| thrombocytopenia type ii | thrombocytopenia 2
| chronic liver disease | chronic hepatitis
| inorganic as | chemicals inorganic
| alcohol nicotine | alcohol nicotinyl
BC5CDR Chemical | dph | ddph
| naoh | natrolite
| myo inositol 1 phosphate | myo inositol 1 3 6 triphosphate

Table 8 lists the errors in three bioinformatics NEN datasets. Our proposed
model achieves approximately 90% accuracy for all three datasets. However,
finding the synonyms for short abbreviations such as “cdm", “htn", and “dph"
seems relatively harder. In addition, if there exist longer overlapping
strings, the performance of the model is degraded.

Table 9: Error Analysis on Financial NEN dataset False Positive
---
Entity 1 | Entity 2
HP Co. | IBM Corporation
Basel I-derived | Basel NSFR
Microsoft Corporation ( Microsoft ) | Microsoft Azure
AT & T Acquisition | AT & T Corp. ’ s ( ATTC )
Service Cloud | Cognitive Cloud Networking
False Negative
Entity 1 | Entity 2
Coca-Cola | Coca-Cola ( r )
Dodd-Frank ( Orderly Liquidation Authority ) | Dodd-Frank Act
Gramm-Leach-Bliley Act ( GLB Act ) | GLBA
Paris Climate Accords | Paris Agreement
Pfizer Inc. ( Pfizer ) | Pfizer

Financial NEN datasets are constructed using entity pairs. Our model predicts
whether two entity pairs are matched or not. Table 9 is divided into false
positive lists and false-negative lists. By examine the false-positive lists,
entities with similar meanings or with matching strings are often predicted
positive while the actual label is negative.

We also examine the false negatives. Matching named entities with parenthesis
and abbreviations is the part where our model’s prediction is relatively
unstable. Entity pairs such as “Paris Climate Accords" and “Paris Agreement"
can be more difficult to predict as positive because the intrinsic meaning of
“Paris Agreement" requires common sense. Even our model is based on BERT,
which captures the semantic meaning from the sentences where named entities
are excerpted, using the common sense beyond the information presented in
surrounding sentences can be limited.

####  5.3.2 Entity Recommendation Result According to Training Progresses

Table 10: Entity Recommendations for Epoch 0, Epoch 1, and Epoch with Highest
Accuracy

| NCBI Disease: c2 deficiency
---|---
| Epoch 0 | Epoch 1 | Epoch with Highest Accuracy
Top 1 | c2 deficiency | c2 deficiency | c2 deficiency
Top 2 | c3 deficiency | c6 deficiency | c2 deficient
Top 3 | t2 deficiency | c3 deficiency | hereditary c2 deficiency
Top 4 | c5 deficiency | c2 deficient | type ii c2 deficiency
Top 5 | cpox deficiency | c4 deficiency | type i c2 deficiency
| BC5CDR Disease: failing left ventricle
| Epoch 0 | Epoch 1 | Epoch with Highest Accuracy
Top 1 | tumor cerebral ventricle | dysfunction left ventricular | left sided heart failure
Top 2 | cerebral ventricle tumor | left sided heart failure | heart failure
Top 3 | tumors cerebral ventricle | remodeling left ventricular | cardiac failure
Top 4 | syndrome slit ventricle | hypertrophy left ventricular | heart failure left sided
Top 5 | ventricle tumor cerebral | outflow obstruction left ventricular | right sided heart failure
| BC5CDR Chemical: vincristine sulfate
| Epoch 0 | Epoch 1 | Epoch with Highest Accuracy
Top 1 | vincristine sulfate | vincristine sulfate | vincristine sulfate
Top 2 | sulfate vincristine | vincristine | vincristine
Top 3 | vinblastine sulfate | voacristine | sulfate vincristine
Top 4 | sulfate vinblastine | leurocristine | vincristin
Top 5 | riboflavin 3 sulfate | ergocristine | vincristin medac
| Financial NEN: Polo Ralph Lauren Children
| Epoch 0 | Epoch 1 | Epoch with Highest Accuracy
Top 1 | Pinky Swear Foundation | Polo Golf Ralph Lauren | Polo Ralph Lauren
Top 2 | Bath & Body Works Canada | Polo Ralph Lauren | Polo Ralph Lauren Children, Chaps
Top 3 | Ticketmaster North America | Siemens Medical Solutions USA | Polo Golf Ralph Lauren
Top 4 | LIP-BU TAN | Mojo Networks, Inc. | Lilly International
Top 5 | Coca-Cola Life | Polo Ralph Lauren Children, Chaps | Polo / Lauren Company, LP

As the training epochs increase, recommendations become more accurate. We
randomly selected entities from four datasets we tested. Top 5 recommendations
for the selected entities are provided for epoch 0, epoch 1, and epoch with
best result in Section 5.1 and Section 5.2.

Table 10 shows how recommendations change as training progress. Entities after
each dataset are the examples excerpted (c2 deficiency, failing left
ventricle, vincristine sulfate, and Polo Ralph Lauren Children), and bold-
underlined entities are the entities with the same concept ID as the query
entity. Throughout the datasets, at epoch 0, the recommended entities differ
greatly from the concept ID of the query entity. As the model is trained, the
recommendation becomes more accurate in epoch 1. At the epochs in which the
highest accuracy for the datasets is achieved, true synonyms for query
entities are successfully selected.

Based on our experiments, our proposed model has the highest precision,
recall, F1 score, and accuracy. Qualitative analysis shows that our proposed
model also gives the most robust results. Our proposed model is most suitable
for tasks such as financial named entity normalization automation and
preprocessing for various financial NLP tasks.

##  6 Conclusion

We introduce Edge Weight Updating Neural Network for NEN. NEN to match
extracted named entities with homogeneous identity is pivotal for many text
mining tasks. We tested our model on three widely used NEN datasets, NCBI
Disease, BC5CDR Disease, and BC5CDR Chemical. We also generated the NEN
dataset for the finance domain. Next, we verify our model’s performance for
general NEN applications.

The main contribution of this study are as follows. Our proposed model
successfully links named entities with the same meanings with different
surface forms. The proposed model performs best among previous NEN models. We
test our model not only for bioinformatics datasets in which NEN researches
are more active but also for financial NEN datasets. According to the
performance of the NEN corpus in two distinct fields, our proposed model
proves the efficacy for general NEN applications.

Similar to many other NEN models, the performance of linking named entities
with abbreviations is comparatively lower. Matching abbreviations more
accurately is one of the future works. The neural network model with our
proposed Edge Weight Updating objective function performs better than other
models. Providing the more general guideline for the number of training epochs
and increasing the training stability is one of the future research topics.

## acknowledgements

This work was supported by National Research Foundation of Korea
(2018R1D1A1A02045842).

## Conflict of interest

This work was supported by National Research Foundation of Korea
(2018R1D1A1A02045842). All authors certify that they have no affiliations with
or involvement in any organization or entity with any financial interest or
non-financial interest in the subject matter or materials discussed in this
manuscript.

## References

  * Devlin et al. [2018] Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova.  Bert: Pre-training of deep bidirectional transformers for language understanding.  _arXiv preprint arXiv:1810.04805_ , 2018.
  * Cho et al. [2017] Hyejin Cho, Wonjun Choi, and Hyunju Lee.  A method for named entity normalization in biomedical articles: application to diseases and plants.  _BMC bioinformatics_ , 18(1):451, 2017.
  * Hanisch et al. [2005] Daniel Hanisch, Katrin Fundel, Heinz-Theodor Mevissen, Ralf Zimmer, and Juliane Fluck.  Prominer: rule-based protein and gene entity recognition.  _BMC bioinformatics_ , 6(1):1–9, 2005.
  * Aronson [2001] Alan R Aronson.  Effective mapping of biomedical text to the umls metathesaurus: the metamap program.  In _Proceedings of the AMIA Symposium_ , page 17. American Medical Informatics Association, 2001.
  * Leaman et al. [2013] Robert Leaman, Rezarta Islamaj Doğan, and Zhiyong Lu.  Dnorm: disease name normalization with pairwise learning to rank.  _Bioinformatics_ , 29(22):2909–2917, 2013.
  * Leaman and Lu [2016] Robert Leaman and Zhiyong Lu.  Taggerone: joint named entity recognition and normalization with semi-markov models.  _Bioinformatics_ , 32(18):2839–2846, 2016.
  * Wei and Kao [2011] Chih-Hsuan Wei and Hung-Yu Kao.  Cross-species gene normalization by species inference.  _BMC bioinformatics_ , 12(S8):S5, 2011.
  * Hakenberg et al. [2011] Jörg Hakenberg, Martin Gerner, Maximilian Haeussler, Illés Solt, Conrad Plake, Michael Schroeder, Graciela Gonzalez, Goran Nenadic, and Casey M Bergman.  The gnat library for local and remote gene mention normalization.  _Bioinformatics_ , 27(19):2769–2771, 2011.
  * Rocktäschel et al. [2012] Tim Rocktäschel, Michael Weidlich, and Ulf Leser.  Chemspot: a hybrid system for chemical named entity recognition.  _Bioinformatics_ , 28(12):1633–1640, 2012.
  * Weston et al. [2019] Leigh Weston, Vahe Tshitoyan, John Dagdelen, Olga Kononova, Amalie Trewartha, Kristin A Persson, Gerbrand Ceder, and Anubhav Jain.  Named entity recognition and normalization applied to large-scale information extraction from the materials science literature.  _Journal of chemical information and modeling_ , 59(9):3692–3702, 2019.
  * Suominen et al. [2013] Hanna Suominen, Sanna Salanterä, Sumithra Velupillai, Wendy W Chapman, Guergana Savova, Noemie Elhadad, Sameer Pradhan, Brett R South, Danielle L Mowery, Gareth JF Jones, et al.  Overview of the share/clef ehealth evaluation lab 2013.  In _International Conference of the Cross-Language Evaluation Forum for European Languages_ , pages 212–231. Springer, 2013.
  * Doğan et al. [2014] Rezarta Islamaj Doğan, Robert Leaman, and Zhiyong Lu.  Ncbi disease corpus: a resource for disease name recognition and concept normalization.  _Journal of biomedical informatics_ , 47:1–10, 2014.
  * Demner-Fushman et al. [2018] Dina Demner-Fushman, Sonya E Shooshan, Laritza Rodriguez, Alan R Aronson, Francois Lang, Willie Rogers, Kirk Roberts, and Joseph Tonning.  A dataset of 200 structured product labels annotated for adverse drug reactions.  _Scientific data_ , 5:180001, 2018.
  * Smith et al. [2008] Larry Smith, Lorraine K Tanabe, Rie Johnson nee Ando, Cheng-Ju Kuo, I-Fang Chung, Chun-Nan Hsu, Yu-Shi Lin, Roman Klinger, Christoph M Friedrich, Kuzman Ganchev, et al.  Overview of biocreative ii gene mention recognition.  _Genome biology_ , 9(S2):S2, 2008.
  * Kim et al. [2009] Jin-Dong Kim, Tomoko Ohta, Sampo Pyysalo, Yoshinobu Kano, and Jun’ichi Tsujii.  Overview of bionlp’09 shared task on event extraction.  In _Proceedings of the BioNLP 2009 workshop companion volume for shared task_ , pages 1–9, 2009.
  * Bossy et al. [2019] Robert Bossy, Louise Deléger, Estelle Chaix, Mouhamadou Ba, and Claire Nédellec.  Bacteria biotope at bionlp open shared tasks 2019.  In _Proceedings of The 5th Workshop on BioNLP Open Shared Tasks_ , pages 121–131, 2019.
  * Kolárik et al. [2008] Corinna Kolárik, Roman Klinger, Christoph M Friedrich, Martin Hofmann-Apitius, and Juliane Fluck.  Chemical names: terminological resources and corpora annotation.  In _Workshop on Building and evaluating resources for biomedical text mining (6th edition of the Language Resources and Evaluation Conference)_ , 2008.
  * Klinger et al. [2008] Roman Klinger, Corinna Kolářik, Juliane Fluck, Martin Hofmann-Apitius, and Christoph M Friedrich.  Detection of iupac and iupac-like chemical names.  _Bioinformatics_ , 24(13):i268–i276, 2008.
  * Arratia et al. [2019] Argimiro Arratia, Lluís A Belanche, and Luis Fábregues.  An evaluation of equity premium prediction using multiple kernel learning with financial features.  _Neural Processing Letters_ , pages 1–18, 2019.
  * Corba et al. [2020] Burcin Seyda Corba, Erol Egrioglu, and Ali Zafer Dalar.  Ar–arch type artificial neural network for forecasting.  _Neural Processing Letters_ , 51(1):819–836, 2020\.
  * Gupta et al. [2020] Aaryan Gupta, Vinya Dengre, Hamza Abubakar Kheruwala, and Manan Shah.  Comprehensive review of text-mining applications in finance.  _Financial Innovation_ , 6(1):1–25, 2020.
  * Jijkoun et al. [2008] Valentin Jijkoun, Mahboob Alam Khalid, Maarten Marx, and Maarten De Rijke.  Named entity normalization in user generated content.  In _Proceedings of the second workshop on Analytics for noisy unstructured text data_ , pages 23–30, 2008.
  * Sun et al. [2012] Chengjie Sun, Lei Lin, Ming Liu, Bingquan Liu, and Xuejun Sha.  A product named entity normalization method based on entity relations.  In _2012 8th International Conference on Information Science and Digital Content Technology (ICIDT2012)_ , volume 1, pages 166–169. IEEE, 2012\.
  * Francis et al. [2019] Sumam Francis, Jordy Van Landeghem, and Marie-Francine Moens.  Transfer learning for named entity recognition in financial and biomedical documents.  _Information_ , 10(8):248, 2019.
  * Mueller and Thyagarajan [2016] Jonas Mueller and Aditya Thyagarajan.  Siamese recurrent architectures for learning sentence similarity.  In _Proceedings of the AAAI Conference on Artificial Intelligence_ , volume 30, 2016.
  * Ranasinghe et al. [2019] Tharindu Ranasinghe, Constantin Orasan, and Ruslan Mitkov.  Semantic textual similarity with siamese neural networks.  In _Proceedings of the International Conference on Recent Advances in Natural Language Processing (RANLP 2019)_ , pages 1004–1011, 2019\.
  * Liu et al. [2018] Bang Liu, Ting Zhang, Di Niu, Jinghong Lin, Kunfeng Lai, and Yu Xu.  Matching long text documents via graph convolutional networks.  _arXiv preprint arXiv:1802.07459_ , pages 2793–2799, 2018.
  * Krivosheev et al. [2020] Evgeny Krivosheev, Mattia Atzeni, Katsiaryna Mirylenka, Paolo Scotton, and Fabio Casati.  Siamese graph neural networks for data integration.  _arXiv preprint arXiv:2001.06543_ , 2020.
  * Neculoiu et al. [2016] Paul Neculoiu, Maarten Versteegh, and Mihai Rotaru.  Learning text similarity with siamese recurrent networks.  In _Proceedings of the 1st Workshop on Representation Learning for NLP_ , pages 148–157, 2016.
  * Niu et al. [2019] Jinghao Niu, Yehui Yang, Siheng Zhang, Zhengya Sun, and Wensheng Zhang.  Multi-task character-level attentional networks for medical concept normalization.  _Neural Processing Letters_ , 49(3):1239–1256, 2019.
  * Mulang’ et al. [2020] Isaiah Onando Mulang’, Kuldeep Singh, Chaitali Prabhu, Abhishek Nadgeri, Johannes Hoffart, and Jens Lehmann.  Evaluating the impact of knowledge graph context on entity disambiguation models.  In _Proceedings of the 29th ACM International Conference on Information & Knowledge Management_, pages 2157–2160, 2020.
  * D’Souza and Ng [2015] Jennifer D’Souza and Vincent Ng.  Sieve-based entity linking for the biomedical domain.  In _Proceedings of the 53rd Annual Meeting of the Association for Computational Linguistics and the 7th International Joint Conference on Natural Language Processing (Volume 2: Short Papers)_ , pages 297–302, 2015.
  * Li et al. [2017] Haodi Li, Qingcai Chen, Buzhou Tang, Xiaolong Wang, Hua Xu, Baohua Wang, and Dong Huang.  Cnn-based ranking for biomedical entity normalization.  _BMC bioinformatics_ , 18(11):79–86, 2017.
  * Wright [2019] Dustin Wright.  _NormCo: Deep disease normalization for biomedical knowledge base construction_.  PhD thesis, UC San Diego, 2019.
  * Phan et al. [2019] Minh C Phan, Aixin Sun, and Yi Tay.  Robust representation learning of biomedical names.  In _Proceedings of the 57th Annual Meeting of the Association for Computational Linguistics_ , pages 3275–3285, 2019.
  * Ji et al. [2020] Zongcheng Ji, Qiang Wei, and Hua Xu.  Bert-based ranking for biomedical entity normalization.  _AMIA Summits on Translational Science Proceedings_ , 2020:269, 2020.
  * Sung et al. [2020] Mujeen Sung, Hwisang Jeon, Jinhyuk Lee, and Jaewoo Kang.  Biomedical entity representations with synonym marginalization.  _arXiv preprint arXiv:2005.00239_ , 2020.
  * Kim et al. [2019] Jongmin Kim, Taesup Kim, Sungwoong Kim, and Chang D Yoo.  Edge-labeling graph neural network for few-shot learning.  In _Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition_ , pages 11–20, 2019.
  * Kullback and Leibler [1951] Solomon Kullback and Richard A Leibler.  On information and sufficiency.  _The annals of mathematical statistics_ , 22(1):79–86, 1951.
  * Lee et al. [2020] Jinhyuk Lee, Wonjin Yoon, Sungdong Kim, Donghyeon Kim, Sunkyu Kim, Chan Ho So, and Jaewoo Kang.  Biobert: a pre-trained biomedical language representation model for biomedical text mining.  _Bioinformatics_ , 36(4):1234–1240, 2020.
  * Loshchilov and Hutter [2017] Ilya Loshchilov and Frank Hutter.  Decoupled weight decay regularization.  _arXiv preprint arXiv:1711.05101_ , 2017.
  * Li et al. [2016] Jiao Li, Yueping Sun, Robin J Johnson, Daniela Sciaky, Chih-Hsuan Wei, Robert Leaman, Allan Peter Davis, Carolyn J Mattingly, Thomas C Wiegers, and Zhiyong Lu.  Biocreative v cdr task corpus: a resource for chemical disease relation extraction.  _Database_ , 2016, 2016.
  * Davis et al. [2009] Allan Peter Davis, Cynthia G Murphy, Cynthia A Saraceni-Richards, Michael C Rosenstein, Thomas C Wiegers, and Carolyn J Mattingly.  Comparative toxicogenomics database: a knowledgebase and discovery tool for chemical–gene–disease networks.  _Nucleic acids research_ , 37(suppl_1):D786–D792, 2009.
  * Sang and De Meulder [2003] Erik F Sang and Fien De Meulder.  Introduction to the conll-2003 shared task: Language-independent named entity recognition.  _arXiv preprint cs/0306050_ , 2003.
  * Si et al. [2019] Yuqi Si, Jingqi Wang, Hua Xu, and Kirk Roberts.  Enhancing clinical concept extraction with contextual embeddings.  _Journal of the American Medical Informatics Association_ , 26(11):1297–1304, 2019.
  * Mondal et al. [2020] Ishani Mondal, Sukannya Purkayastha, Sudeshna Sarkar, Pawan Goyal, Jitesh Pillai, Amitava Bhattacharyya, and Mahanandeeshwar Gattu.  Medical entity linking using triplet network.  _arXiv preprint arXiv:2012.11164_ , 2020.
  * Hoffer and Ailon [2015] Elad Hoffer and Nir Ailon.  Deep metric learning using triplet network.  In _International workshop on similarity-based pattern recognition_ , pages 84–92. Springer, 2015.
  * Levenshtein [1966] Vladimir I Levenshtein.  Binary codes capable of correcting deletions, insertions, and reversals.  In _Soviet physics doklady_ , volume 10, pages 707–710, 1966.
  * Kipf and Welling [2016] Thomas N Kipf and Max Welling.  Semi-supervised classification with graph convolutional networks.  _arXiv preprint arXiv:1609.02907_ , 2016.
  * Schuster and Paliwal [1997] Mike Schuster and Kuldip K Paliwal.  Bidirectional recurrent neural networks.  _IEEE transactions on Signal Processing_ , 45(11):2673–2681, 1997.


# Superconducting Properties of Topological Semimetal 1$T$-RhSeTe

C. Patra  Department of Physics, Indian Institute of Science Education and
Research Bhopal, Bhopal, 462066, India  T. Agarwal  Department of Physics,
Indian Institute of Science Education and Research Bhopal, Bhopal, 462066,
India  Arushi  Department of Physics, Indian Institute of Science Education
and Research Bhopal, Bhopal, 462066, India  P. Manna  Department of Physics,
Indian Institute of Science Education and Research Bhopal, Bhopal, 462066,
India  N. Bhatt  Department of Physics, Indian Institute of Science Education
and Research Bhopal, Bhopal, 462066, India  R. S. Singh  Department of
Physics, Indian Institute of Science Education and Research Bhopal, Bhopal,
462066, India  R. P. Singh<EMAIL_ADDRESS>Department of Physics, Indian
Institute of Science Education and Research Bhopal, Bhopal, 462066, India

###### Abstract

Platinum-group transition-metal dichalcogenides have emerged as a subject of
considerable interest in condensed matter physics due to their remarkable
topological properties and unconventional superconducting behavior. In this
study, we report the synthesis and superconducting characteristics of a new
Dirac-type topological semimetallic compound 1$T$-RhSeTe. It shows type-II
superconductivity with a superconducting transition temperature of 4.72 K and
a high upper critical field. The coexistence of superconductivity and
topological properties makes it a prime candidate for hosting topological
superconductivity.

##  I INTRODUCTION

Topological semimetals have emerged as a new study area in quantum materials
research. Unlike topological or crystalline insulators, semimetals have
minimal overlaps between their bulk conduction and valence bands. This unique
characteristic distinguishes them from insulating materials. Topological
semimetals are classified into types, including topological Dirac and Weyl
semimetals. More recently, this classification has been extended to include
nodal lines and non-symmorphic semimetals high_Tc_Sc ; NiS2_mott_insulator ;
topology_insulator ; Dirac_A3Bi ; VAl3_dirac ; Dirac_Cd3As2 ;
inversion_symmetry_dirac ; symetery_dirac_weyl ; symmerty_lokking . The
exploration of topological semimetals has yielded remarkable discoveries, such
as topological superconductivity, negative magnetoresistance, chiral magnetic
effects, and the quantum anomalous Hall effect. These properties hold
significant potential to develop cutting-edge technologies axial_signature ;
transport_dirac ; transport_Bi2_family . Despite these exciting findings, the
main focus of research on topological semimetals has been centered around the
discovery of new Dirac and Weyl semimetals, as well as the intricate study of
their band topology VAl3_dirac ; Dirac_Cd3As2 ; TaAs ; wte2 ; MoTe2_weyl . At
the same time, superconducting topological semimetals remain largely
unexplored territory despite their potential for direct application in quantum
computing.

Transition-metal dichalcogenides (TMDs) offer a promising avenue to achieve
topological superconductivity Theory_MoTe2 ; structure_stable ;
rhIrTe2_thermal . These materials can exist in various crystal structures,
including hexagonal (2$H$ and 4$H$), rhombohedral (3$R$), trigonal (1$T$),
cubic pyrite-type, and orthorhombic forms. The trigonal structure, in
particular, is known to host bulk Dirac type-II fermions and topological
surface states bulk_dirac_cone . Notably, the 1$T$ phases of NiTe2, PdTe2,
PtSe2, PtTe2 and IrTe2 exhibit a tilted Dirac cone in the vicinity of the
Fermi level NiTe2_dirac ; PtTe2_dirac ; PdTe2_dirac ; IrTe2_nano_flake ;
PtSe2_dirac . Among these compounds, NiTe2 and IrTe2 possess Dirac points very
near the Fermi level ($\sim$ 80 meV and 0.15 eV, respectively)
IrTe2_dirac_energy , which can be fine-tuned through application of strain,
pressure or chemical doping. This tunability has been shown to induce or
enhance superconductivity in these materials Pt_doped_sc_IrTe2 ;
IrTe2_nano_flake ; spectroscopy_IrTe2_Pt_doped ; ARPES_IrTe2 . The ability to
control the positions of Dirac points in the 1$T$ phase of chalcogenides makes
them very promising for realizing topological superconductivity
dirac_cone_IrTe2 . Therefore, searching for new 1$T$ topological semimetals is
of utmost importance to advance research in the field.

Rhodium-based dichalcogenide compounds have been relatively underexplored,
tending to stabilize in 1$T$ or pyrite-type crystal structures
structure_stable ; rhIrTe2_thermal ; layered_structure_irte2 ; Tc_IrTe2 ;
first_principle_IrTe2 ; RhSe2_IrSe2 . RhSe2 typically adopts a pyrite-type
structure, while RhTe2 can exhibit both pyrite-type and 1T structures,
depending on the Rh/Te ratio. Interestingly, in the pyrite-type structure,
RhSe2 and RhTe2 exhibit superconductivity with transition temperatures of 6 K
and 1.5 K, respectively RhSe2_sc_first ; RhSe2_paper_sc ; RhTe2_first_paper ;
RhTe_phase . Investigations on Rh substitution at the Ir site in these
compounds demonstrate the formation of a 1$T$ structure with a maximum
transition temperature ($T_{c}$) of 2.6 K when the Rh content ranges from 0 to
0.3 in standard solid-state synthesis RhSe2_IrSe2 . In the Ir${1-x}$RhxSe2
system, high-pressure synthesis leads to the formation of a pyrite-type
structure, resulting in a dome-shaped variation in $T_{c}$, with the highest
$T_{c}$ of 9.6 K achieved at $x=0.36$ RhSe2_IrSe2 . These findings suggest
that disorder/charge transfer can induce or enhance superconductivity in
1$T$/Pyrite phases of RhTe2.

Figure 1:  (a) shows the crystal structure of RhSeTe. (b) Powder XRD pattern
under ambient conditions for RhSeTe. The structural refinement was performed
using the space group of $P\bar{3}m1$. The inset shows the EDS scan that
detects Rh, Se, and Te. (c) Resistivity shows the superconducting transition
at 4.72(6) K. The inset reveals hysteresis in the normal-state resistivity
during heating and cooling cycles. (d) The Hall resistivity at 10 K exhibits a
linear behavior to the applied magnetic field variation ($\pm$ 9 T).

Although RhTe2 can stabilize in the 1T structure, superconductivity has not
been reported in this phase rhIrTe2_thermal ; RhSe2_sc_first . Sametime,
coexistence of pyrite and the 1T structure presents a challenge in obtaining a
pure 1T phase of RhTe2. However, in our current study, we achieved a pristine
1T-phase of RhSeTe by substituting selenium for tellurium in RhTe2
PdTeSe_dirac . Notably, this RhSeTe exhibits a superconducting transition
below 4.72 K. Resistivity measurements reveal significant hysteresis,
indicating the presence of a charge density wave. Density functional theory
(DFT) calculations suggest the presence of a type-II Dirac cone located 82 meV
above the Fermi level in RhSeTe. The electronic band structure closely
resembles the isostructural topological semimetal 1$T$-NiTe2. Phonon band
structure calculations indicate unstable phonon modes away from the zone
center, further supporting the potential for charge density wave formation,
possibly linked to the observed resistivity hysteresis.

##  II EXPERIMENTAL METHODS

A polycrystalline sample of RhSeTe was prepared by the standard solid-state
reaction method. The stoichiometric mixtures of Rh (4N), Se (5N) and Te (5N)
were thoroughly grounded, pelletized, and sealed in an evacuated quartz tube.
The sample was heated to 1100°C for a week, followed by quenching with ice
water to avoid the formation of unwanted impure phases. The purity of the
RhSeTe phase was determined using powder X-ray diffraction (XRD) on a
PANalytical diffractometer equipped with Cu$K_{\alpha}$ radiation ($\lambda$ =
1.54056 Å). Furthermore, magnetization measurements were performed using a
quantum interference device (MPMS3, Quantum Design). The resistivity and
specific heat of the sample were measured in the Physical Property Measurement
System (PPMS) using the conventional four-probe AC technique and the two-tau
relaxation method, respectively.

##  III RESULTS AND DISCUSSION

###  a Sample characterization

The crystal structure of 1$T$ -RhSeTe from side and top views is represented
in Fig. 1(a). The phase purity of the sample and the crystal structure were
determined from the Rietveld refinement of the powder XRD pattern using
FullProf software, shown in Fig. 1(b). It confirms that RhSeTe adapts the
trigonal structure with space group: $P\bar{3}m1$ (space group no. 164)
structure . The extracted lattice parameters are a = b = 3.798(2)Å, and c =
5.389(5)Å with $\gamma$ = 120$\degree$. EDS measurements conducted in
different regions revealed an average elemental concentration,
Rh1.01Se1.05Te0.94, as depicted in the inset of Fig. 1(b). All parameters,
including space group, atomic, and Wyckoff positions, acquired from refinement
are summarized in Table 1.

Table 1: Parameters obtained from Rietveld refinement. | Structure | Trigonal |  |
---|---|---|---|---
| space-group |  $P\bar{3}m1$ (164) |  |
| lattice parameters |  |  |
|  $a=b$ (Å) | 3.798(2) |  |
|  $c$ (Å) | 5.389(5) |  |
Atom | Wyckoff position | x | y | z
Rh1 | 1a | 0 | 0 | 0
Se1 | 2d | 0.333 | 0.667 | 0.256
Te1 | 2d | 0.333 | 0.667 | 0.256

###  b Transport measurement

The temperature dependence of the electrical resistivity $\rho(T)$ was
measured in a zero applied magnetic field over the range of 350 to 1.9 K and
is represented in Fig. 1(c). The low-temperature resistivity region is
depicted, and it abruptly reaches zero at 4.72(6) K, confirming the occurrence
of a superconducting transition structure ; RhTe2_first_paper . The
resistivity of 1$T$-RhSeTe in the normal state demonstrates a negligible
temperature dependence. In contrast, for 1$T$-RhTe2, the resistivity exhibits
a metallic-type variation with temperature rhIrTe2_thermal . This distinction
can potentially be attributed to the high disorder introduced by the
isoelectronic selenium atom within the system. Interestingly, the resistivity
of 1$T$-RhSeTe shows a notable behavior with a negative temperature
coefficient above approximately 140 K, as shown in the inset of Fig. 1(c).
Moreover, a large hysteresis is observed between the temperature-dependent
resistivity heating and cooling cycles. The hysteresis and negative
temperature coefficient may originate from a CDW transition or dimerization. A
similar hysteresis behaviour is observed in 1$T$-IrTe2 at 260 K, originating
by stripe charge ordering accompanied by the first-order structural transition
involving dimerization or depolymerization layered_rh_doped_IrTe2 ;
spin_orbit_coupling_IeTe2 .

Furthermore, to extract the carrier concentration of RhSeTe, the field-
dependent Hall resistivity $\rho_{xy}(H)$ at 10 K was measured as shown in
Fig. 1 (d). $\rho_{xy}(H)$ is well described by a straight-line fit and
provides the Hall coefficient $R_{H}$ = -4.77(4)$\times$ 10-8 $\ohm$-cm/T for
RhSeTe. The negative sign indicates the presence of electron carrier
concentration in the system, and using the relation $R_{H}=1/{ne}$ (where e is
the electronic charge), the calculated carrier concentration n =
1.31(4)$\times$ 1022 cm-3 at 10 K, which is of the same order as that reported
for 1$T$-RhTe2 rhIrTe2_thermal .

###  c Magnetization

Magnetic susceptibility was measured in zero-field-cooled-warming mode (ZFCW)
and field-cooled-cooling mode (FCC) under 1 mT magnetic field for bulk
1$T$-RhSeTe. The onset of diamagnetism confirmed the superconductivity in
RhSeTe with the appearance of a superconducting transition temperature
$T_{c}^{onset}$ = 4.65(3) K, as shown in Fig. 2(a). Fig. 2(b) displays the
full range magnetization with field ($M$-$H$) at $T$ = 1.8 K, indicating type-
II superconducting behaviour of RhSeTe, and magnetization is irreversible
below a field $H_{irr}$ = 1.1 T.

Figure 2:  (a) Magnetization data at ZFCW-FCC mode showing the superconducting
transition at 4.65(3) K for RhSeTe. (h) Magnetization vs magnetic field at 1.8
K indicates type-II superconducting behaviour and Hirr estimated 1.1 T at 1.8
K.

The lower critical field, $H_{c1}(0)$, is extracted from the low field
magnetization curves as a function of the magnetic field (0-15 mT) at
different constant temperatures, which is shown in the inset of Fig. 3(a). The
points of $H_{c1}(T)$ are deduced from the linear deviation of the Meissner
line from the initial slope of $M$-$H$ curves. The value of $H_{c1}(0)$ =
0.63(1) mT was depicted from the fit using the Ginzburg-Landau equation,

$H_{c1}(T)=H_{c1}(0)\left[1-\left(\frac{T}{T_{c}}\right)^{2}\right]$ (1)

and it is presented in Fig. 3(a). The upper critical field, $H_{c2}$(0), is
calculated from the temperature variation of the resistivity and magnetization
measurements taken at different applied magnetic fields. $T_{c}$ shifts
towards the lower temperature with an increasing magnetic field. The inset of
Fig. 3(b) shows the temperature-dependent resistivity curves for different
fields. From magnetization measurements, $T_{c}$ is considered the onset of
the diamagnetic signal. In the case of resistivity curves, the determination
of $T_{c}$ is based on the 90% value of the normal state resistivity. The
temperature variation of $H_{c2}(T)$ was well described using the Ginzburg-
Landau equation (Eq. (2)),

$H_{c2}(T)=H_{c2}(0)\left[\frac{1-\left(\frac{T}{T_{c}}\right)^{2}}{1+\left(\frac{T}{T_{c}}\right)^{2}}\right].$
(2)

Figure 3:  (a) The temperature variation of $H_{c1}$ for RhSeTe displays the
value of lower critical field 0.63(1) mT and the inset shows low field
magnetization curves as a function of applied magnetic field for different
temperatures. (b) $H_{c2}(T)$ data from magnetization and resistivity fitted
with the Ginzburg-Landau model for RhSeTe. The inset illustrates the
temperature variation of the resistivity in different fields up to 3 T.

and yielded $H_{c2}^{mag,\rho}$(0) as 2.09(1) T and 4.06(7) T respectively,
shown in Fig. 3(b). Iridium-based dichalcogenides, including pyrite- or
trigonal-typeIr0.93Te2 shows a superconducting transition temperature of 4.7
K, accompanied by an upper critical field value of 4.58 T Tc_IrTe2 .

The fundamental superconducting parameters, such as coherence length,
penetration depth, and thermodynamic critical field, are estimated by using
the values of $H_{c2}^{\rho}(0)$ and $H_{c1}(0)$. The Ginzburg-Landau
coherence length, $\xi_{GL}(0)$ and the penetration depth, $\lambda_{GL}(0)$
are calculated by using the following equations:

$H_{c2}^{\rho}(0)=\frac{\Phi_{0}}{2\pi\xi_{GL}^{2}}$ (3)

$H_{c1}(0)=\frac{\Phi_{0}}{4\pi\lambda^{2}_{GL}(0)}\left[ln\left(\frac{\lambda_{GL}(0)}{\xi_{GL}(0)}\right)+0.12\right]$
(4)

where $\Phi_{0}$ (= 2.07$\times 10^{-15}$ Tm2) is the magnetic flux quantum.
The extracted values of $\xi_{GL}(0)$ and $\lambda_{GL}(0)$ for RhSeTe are
90.1(8) Å and 1138(9) nm, respectively. Furthermore, the values of
$\xi_{GL}(0)$ and $\lambda_{GL}(0)$ were used to calculate the Ginzburg-Landau
parameter $\kappa_{GL}$ = $\frac{\lambda_{GL}(0)}{\xi_{GL}(0)}$ = 126(2). The
value of $\kappa_{GL}$ is greater than $\frac{1}{\sqrt{2}}$, indicating the
type II superconducting behaviour of the sample. The thermodynamic critical
field $H_{c}$ is obtained from the relation
$H_{c1}(0)H_{c2}(0)=H^{2}_{c}ln{\kappa_{GL}}$ and provides the value $H_{c}$ =
22 (1) mT.

Type-II superconductors exhibit two mechanisms for breaking Cooper pairs in a
magnetic field: the orbital effect and the Pauli paramagnetic effect, or
Zeeman splitting, as described in pauli_limit . In the case of orbital pair
breaking, the increased kinetic energy causes the pairs to break. On the
contrary, in the Pauli paramagnetic limiting effect, the spins of the Cooper
pair attempt to align in the direction of the magnetic field, leading to a
difference in energy between the electrons and the consequent breaking of the
Cooper pair WHH_model . The Pauli paramagnetic limit is expressed as
$H_{c2}^{P}(0)=1.86T_{c}$ = 8.78 T for RhSeTe. The orbital pair-breaking limit
is given by the Werthamer-Helfand-Hohenberg (WHH) expression:

$H_{c2}^{orbital}=-\alpha T_{c}\frac{dH_{c2}(T)}{dT}.$ (5)

The initial slope $\frac{dH_{c2}(T)}{dT}$ near $T=T_{c}$ is calculated to be
-1.03(5) T/K. When considering $\alpha$ = 0.693 for the dirty limit, the
$H_{c2}^{orbital}$ value is determined to be 3.37 T. Moreover, the Maki
parameter maki_parameter
($\alpha_{M}=\frac{\sqrt{2}H_{c2}^{orbital}}{H_{c2}^{P}}$) is 0.54. The value
of the Maki parameter is less than unity, indicating that the influence of the
paramagnetic effect is negligibly small in RhSeTe in breaking Cooper pairs
under the applied magnetic field.

###  d Specific heat

Furthermore, the superconducting gap symmetry is explored using the zero-field
specific heat measurement. Specific heat data for RhSeTe are collected from
1.9 to 10 K in a zero field, as shown in Fig. 4(a). The phononic properties of
the normal state and the electron density of the states are evaluated in Fig.
4(b) using Eq. (6).

$C/T=\gamma_{n}+\beta_{3}T^{2}$ (6)

where $\gamma_{n}$ represents the electronic contribution and $\beta_{3}$
describes the Debye constant or the phononic contribution. The fitting
parameters yield $\gamma_{n}$ = 3.89(2) mJ/mol-K2 , and $\beta_{3}$ = 0.78(3)
mJ/mol-K4. The specific heat data do not show a distinct jump in the
transition temperature, possibly due to the presence of significant disorder
in the layered structure, a characteristic of doping in polycrystalline
materials. However, it is worth noting that the superconducting jump in
single-crystal samples may be observable since single crystals generally
exhibit less disorder than polycrystalline materials. From the Debye constant
$\beta_{3}$, the Debye temperature $\theta_{D}$ is estimated to be 195(5) K
using Eq. (7). The reported Debye temperatures for Ir0.94-xRhxSe2 RhSe2_IrSe2
are closer to the value found for RhSeTe.

Figure 4:  (a) The temperature variation of specific heat. (b) $C/T$ vs
$T^{2}$ representation of specific heat is used to find the electronic and
phononic contribution at normal state.

$\theta_{D}=\left(\frac{12\pi^{4}RN}{5\beta_{3}}\right)^{\frac{1}{3}}$ (7)

where $R$ is the universal gas constant (=8.314 J mol-1 K-1) and $N$ = 3, the
number of atoms per formula unit.

The density of state, $D_{C}(E_{F})$, is calculated from the concept of the
Sommerfeld coefficient $\gamma_{n}$ via the relation
$\gamma_{n}=(\frac{\pi^{2}k_{B}^{2}}{3})D_{C}(E_{F})$, where $k_{B}$ = 1.38
$\times$ $10^{-23}$ J K-1. The estimated value $D_{C}(E_{F})$ is 1.65 states
eV-1 f.u.-1. The calculated values of the density of states and Sommerfeld
coefficient from specific heat were verified from the theoretical
calculations, as discussed in a later section. Also, the dimensionless
parameter, the electron-phonon coupling constant ($\lambda_{e-ph}$), provides
information about the strength of the electron-phonon interaction in the
system. $\lambda_{e-ph}$ is computed using the expression of $\lambda_{e-ph}$
from McMillan’s model coupling  Eq. (8)

$\lambda_{e-ph}=\frac{1.04+\mu^{*}ln(\theta_{D}/1.45T_{c})}{(1-0.62\mu^{*})ln(\theta_{D}/1.45T_{c})-1.04}$
(8)

where $\mu^{*}$ represents the Coulomb repulsion constant and is taken to be
0.13 coupling . The extracted value of $\lambda_{e-ph}$ = 0.72 for RhSeTe is
slightly higher than that reported for other weakly coupled superconductors.
Previous studies on 2$H$-TaSe2-xSx TaSexSx ; tases_2H , Ir-doped MoTe2 IrMoTe2
, and Re-doped NiTe2 Re_doped_NiTe2  have shown that increasing disorder leads
to an increase in electron-phonon coupling and, consequently, enhances the
superconducting transition temperature. Similarly, it is possible that in
1$T$-RhSeTe, disorder plays a crucial role in moderate enhancement of
$\lambda_{e-ph}$ and, in turn, may be responsible for the increase in $T_{c}$,
compared to the 1$T$-RhTe2 phase where no superconductivity has been found.

###  e Electronic properties and the Uemura plot

To explore the electronic and phononic characteristics of the system, we
conducted Density Functional Theory (DFT) calculations. Our investigation
involved employing a 2$\times$2$\times$1 supercell of bulk Rh$X_{2}$ to assess
the impact of the alloying of Te and Se at the $X$ site. To simulate the
disorder of chalcogen atoms, we utilized the special quasirandom structure
method (SQS) as described in Reference SQS ; SQS1 . The calculations were
carried out using the projector augmented wave (PAW) method implemented in the
Vienna Ab-initio Simulation Package (VASP) VASP ; PAW ; PAW1 . An energy cut-
off of 500 eV was set for the plane-wave basis. Exchange-correlation
functionals were based on the Generalized Gradient Approximation (GGA)
following the non-local vdW-DF functional optB88-vdW proposed by Klime et al.
vdW-DF , and they were employed to fully optimize the lattice structure.
During the structural optimization of the supercell, we ensured that atomic
forces remained below 0.5 meV/Å, and we sampled a $\Gamma$-centered
9$\times$9$\times$9 $k$-mesh across the Brillouin zone. The relaxed unit cell
lattice parameters ($a$ = $b$ = 3.806 Å, $c$ = 5.346 Å) closely matched the
values obtained by experimental means.

Furthermore, our DFT calculations incorporated spin-orbit coupling, and we
derived the effective band structure using the VASPKIT program VASPKIT . To
assess the phonon spectrum, we employed a 2$\times$2$\times$2 supercell of the
SQS and applied the frozen phonon approach as implemented in the PHONOPY code
PHONOPY .

Figure 5:  Electronic band structure and density of states obtained from DFT
calculations including SOC. Figure 6:  Phononic band structure and density of
states.

The calculated electronic band structure unfolded in the primitive Brillouin
zone, and the density of states is shown in Fig. 5. The band structure is very
similar to NiTe2, where two bands that appear around 0.5 eV and 1.3 eV at the
$\Gamma$ point in the unoccupied energy range disperse to form the electron
pocket centered around the M and K points. These bands cross each other to
form a type II Dirac cone while dispersing in the $\Gamma$ \- A direction. The
energy and momentum position of the Dirac cone was found to be approximately
82 meV above the Fermi level and $k_{z}$ = 0.394 $c^{*}$. The density of
states at the Fermi level is found to be about 1.61 eV-1, leading to a
Sommerfeld coefficient of about 3.8 mJ/mol-K2 in excellent agreement with the
results obtained from specific heat measurements. The density of states has an
increasing trend towards unoccupied, with a maximum of 2.25 eV-1 appearing at
the energy position of the Dirac crossing. It should be noted that 1$T$-RhTe2
exhibits type II Dirac crossing at approximately 320 meV above Fermi level at
$k_{z}$ = 0.362 $c^{*}$. The SOC-driven splitting of the Te $p_{x}$ +$p_{y}$
band at the $\Gamma$ point is approximately 0.89 eV for RhTe2. This splitting
reduces significantly for RhSeTe and becomes approximately 0.57 eV as seen in
Fig. 5. The reduction of the SOC strength in the case of RhSeTe leads to the
appearance of a Dirac crossing in the close vicinity of the Fermi level.

Fig. 6 shows the calculated phonon dispersion and phonon density of states
obtained for the SQS. Phonon dispersion, calculated with an electronic
broadening ($\sigma$) of 0.01 eV, exhibits imaginary phonon frequencies along
the $\Gamma$-M and $\Gamma$-K directions suggesting structural instability.
These unstable acoustic phonons become stable with a larger electronic
broadening of 0.1 eV, as shown in Fig. 6. The signature of a soft-phonon mode
can also be seen at the boundary of the Brillouin at the L and H points. It is
to note here that a variety of structural distortion and/or charge density
orders are observed in various TMDs, more specifically in 1T type TMDs leading
to 1T′, 1T′′ and 1T′′′ structures. The observation of imaginary phonon
frequencies away from the zone center and its stabilization with increased
electronic broadening suggests a charge density wave formation in this system
similar to other TMDs, e.g., TaS2, NbSe2, etc. The observed hysteresis in the
cooling and warming cycles in the broad temperature range of the resistivity
measurement may be related to these unstable/soft phonon modes.

To quantify the electronic parameters for RhSeTe, such as effective mass, mean
free path, and Fermi velocity, first, the Fermi wave vector, $k_{F}$, is
estimated from the carrier concentration deduced from Hall measurement using
the relation $k_{F}=(3\pi^{2}n)^{1/3}$ book_parameter . Here $n$ = 1.31
$\times$ 1022 cm-3, which yields $k_{F}$ = 0.73 (1) $\times$ 1010
$\text{\AA}^{-1}$. The Sommerfeld coefficient $\gamma_{n}$ and $k_{F}$ are
used to calculate the effective mass, $m^{*}=(\hbar
k_{F})^{2}\gamma_{n}/\pi^{2}nk_{B}$, where $k_{B}$ is the Boltzmann constant,
and $m^{*}$ becomes 2.45(3)me. The mean free path is defined as
$l_{e}=v_{F}\tau$, where $\tau$ the scattering time given by
$\tau=(ne^{2}\rho_{0}/m^{*})^{-1}$ and $v_{F}=\hbar k_{F}/m^{*}$, $\rho_{0}$
is the residual resistivity. Thus, the values of $\rho_{0}$, $\tau$, and
$m^{*}$ provide the value of the mean free path, $l_{e}$ = 1.50(2) Å. The
coherence length $\xi_{0}$ = 0.18$\hbar v_{F}$/$k_{B}T_{c}$ is calculated as
1006(2) Å. The $\frac{\xi_{0}}{l_{e}}$ ratio = 670, indicating that RhSeTe is
in the dirty limit.

Uemura et al. proposed that superconducting materials can be considered
conventional or unconventional based on the $T_{c}/T_{F}$ ratio uemra_plot_2 .
Chevrel phases, heavy fermions, Fe-based superconductors, and high $T_{c}$
superconductors are placed in the unconventional category as the $T_{c}/T_{F}$
ratio falls within 0.01 $\leq$Tc/T${{}_{F}}\leq$0.1. To classify RhSeTe, the
Fermi temperature $T_{F}$ has been evaluated by the following equation:

$k_{B}T_{F}=\frac{\hbar^{2}}{2}(3\pi^{2})^{2/3}\frac{n^{2/3}}{m^{*}}$ (9)

where $n$ = 1.31 $\times$ 1028 m-3 and m∗ = 2.45me for the sample. The
calculated Fermi temperature for RhSeTe is 9621(44) K (as shown in Fig. 7).
The obtained ratio of $T_{c}/T_{F}$ = 0.00049 places RhSeTe close to the
unconventional band, where there are a few other unconventional
superconductors tases_2H ; NbSeTe_uenra ; 1st_uemra ; uemra_equation .

Figure 7:  The Uemura plot represents the superconducting transition temperature versus the Fermi temperature for different superconducting families. The region between two dotted blue lines shows the unconventional band of superconductors. RhSeTe lies close to the unconventional band. Table 2: Parameters in the normal and superconducting state of RhSeTe Parameter | Unit | RhSeTe
---|---|---
$T_{c}$ | K | 4.72(6)
$H_{c1}(0)$ | mT | 0.63(1)
$H_{c2}^{\rho}(0)$ | T | 4.06(7)
$H_{c2}^{P}$ | T | 8.77(9)
$\xi_{GL}(0)$ | Å | 90.08(8)
$\lambda_{GL}(0)$ | nm | 1138(9)
$\gamma_{n}$ | mJ/mol-K2 | 3.89(2)
$\beta_{3}$ | mJ/mol-K4 | 0.78(3)
$\theta_{D}$ | K | 195(5)
$\lambda_{e-ph}$ |  | 0.72(1)
$n$(10 K) | 1022cm-3 | 1.31(4)
$\frac{m^{*}}{m_{e}}$ |  | 2.45(3)
$l_{e}$ | Å | 1.50(2)
$\xi_{0}$ | Å | 1006(2)
$\frac{\xi_{0}}{l_{e}}$ |  | 670(4)
$T_{F}$ | K | 9621(44)

Our findings reveal that RhSeTe exhibits the features of a type-II Dirac
semimetal, characterized by a tilted Dirac cone, and the proximity of the
Dirac point to the Fermi surface, indicating the emergence of a topological
phase. This property presents an intriguing opportunity, as the inclusion of
isoelectronic disorder in the parent compounds RhSe2 and RhTe2 allows fine-
tuning of the Dirac point to approximately 82 meV above the Fermi surface.
Notably, this proximity of the type-II Dirac point to the Fermi surface,
reminiscent of the observations in NiTe2, is of considerable interest.

Moreover, we observe an increase in the electron-phonon coupling constant,
suggesting that the introduced disorder triggers superconductivity.
Consequently, this disorder-controlled layered TMD system, 1$T$-RhSeTe, serves
as a distinctive platform for exploring topological superconductivity.

##  IV Conclusion

The study investigated the superconductivity of 1$T$-RhSeTe at 4.72 K, which
offers a unique platform to explore CDW and Dirac/Weyl semi-metals.
Substituting Te in RhSe2 resulted in a stabilized trigonal structure instead
of the expected cubic pyrite structure under ambient conditions. The results
shed light on the origin of superconductivity in Rh-based systems and show
that disorder plays a crucial role in determining the structure and
enhancement of the upper critical field and other superconducting parameters.
The superconducting and thermodynamic parameters are listed in Table 2.
Observing insulating behavior above 140 K and hysteresis in resistivity
indicates a CDW and dimerization in the system. Furthermore, density
functional theory (DFT) calculations suggest the presence of a Dirac type-II
node located approximately 82 meV above the Fermi surface, very similar to
1$T$-NiTe2 and instability in phonon spectra related to charge density wave.
Since the current study indicates that the manipulation of the Se/Te ratio can
control the location of the Dirac point on the Fermi surface, it can offer a
novel perspective on understanding the interplay between the position of Dirac
points and superconductivity in topological semimetallic compounds.

##  V Acknowledgments

R. P. S. acknowledges the SERB, Government of India, for the Core Research
Grant CRG/2019/001028.

## References

  * (1) J. G. Bednorz, and K. A. Muller, Rev. Mod. Phys. 60, 585 (1988).
  * (2) S. Friedemann, H. Chang, M. B.Gamza, P. Reiss, X. Chen, P.Alireza, W.A. Coniglio, D.Graf, S.Tozer, and F. M. Grosche, Sci Rep 6, 25335 (2016).
  * (3) A. A. Burkov, Nat. Mater. 15, 1145 (2016).
  * (4) Z. Wang, Y. Sun, X.-Q. Chen, C. Franchini, G. Xu, H. Weng, X. Dai, and Z. Fang, Phys. Rev. B 85, 195320 (2012).
  * (5) R. Singha, S. Roy, A. Pariari, B. Satpati, and P. Mandal, Phys. Rev. B 98, 081103(R) (2018).
  * (6) M. Neupane, S.-Y. Xu, R. Sankar, N. Alidoust, G. Bian, C. Liu, I. Belopolski, T.-R. Chang, H.-T. Jeng, H. Lin, A. Bansil, F. Chou, and M. Z. Hasan, Nat Commun 5, 3786 (2014).
  * (7) L. X. Yang, Z. K. Liu, Y. Sun, H. Peng, H. F. Yang, T. Zhang, B. Zhou, Y. Zhang, Y. F. Guo, M. Rahn, D. Prabhakaran, Z. Hussain, S. K. Mo, C. Felser, B. Yan, and Y. L. Chen, Nat. Phys. 11, 728 (2015).
  * (8) H. M. Weng, C. Fang, Z. Fang, B. A. Bernevig, and X. Dai, Phys. Rev. X 5, 011029 (2015).
  * (9) H. Zheng, S.-Y. Xu, G. Bian, C. Guo, G. Chang, D. S. Sanchez, I. Belopolski, C.-C. Lee, S.-M. Huang, X. Zhang, R. Sankar, N. Alidoust, T.-R. Chang, F. Wu, T. Neupert, F. Chou, H.-T. Jeng, N. Yao, A. Bansil, S. Jia, H. Lin, and M. Z. Hasan, ACS Nano 10, 1378 (2016).
  * (10) J. Gooth, A. C. Niemann, T. Meng, A. G. Grushin, K. Landsteiner, B. Gotsmann, F. Menges, M. Schmidt, C. Shekhar, V. Sub, R. Huhne, B. Rellinghaus, C. Felser, B. Yan, and K. Nielsch, Nature 547, 327 (2017).
  * (11) T. M. McCormick, R. C. McKay, and Nandini Trivedi, Phys. Rev. B 96, 235116 (2017).
  * (12) H. Zhang, C.-X. Liu, X.-L. Qi, X. Dai, Z. Fang, and S.-C. Zhang, Nature Phys. 5, 438 (2009).
  * (13) B. Q. Lv, H. M. Weng, B. B. Fu, X. P. Wang, H. Miao, J. Ma, P. Richard, X. C. Huang, L. X. Zhao, G. F. Chen, Z. Fang, X. Dai, T. Qian, and H. Ding, Phys. Rev. X 5, 031013 (2015).
  * (14) A. A. Soluyanov, D. Gresch, Z. Wang, Q. Wu, M. Troyer, X. Dai, and B. A. Bernevig, Nature (London) 527, 495 (2015).
  * (15) T. R. Chang, S. Y. Xu, G. Chang, C. C. Lee, S. M. Huang, B. Wang, G. Bian, H. Zheng, D. S. Sanchez, I. Belopolski, N. Alidoust, M. Neupane, A. Bansil, H.-T. Jeng, H. Lin, and M. Z. Hasan, Nat. Commun. 7, 10639 (2016).
  * (16) P. Hosur, X. Dai, Z. Fang, and X.-L. Qi, Phys. Rev. B 90, 045130 (2014).
  * (17) C.-S. Lee, and G. J. Miller, Inorg. Chem. 38, 5139 (1998).
  * (18) F. E. Lurgo, F. Pomiro, R. E. Carbonio, and R. D. Sanchez, Phys. Rev. B 105, 104104 (2022).
  * (19) M. S. Bahramy, O. J. Clark, B.-J. Yang, J. Feng, L. Bawden, J. M. Riley, I. Markovic, F. Mazzola, V. Sunko, D. Biswas, S. P. Cooil, M. Jorge, J. W. Wells, M. Leandersson, T. Balasubramanian, J. Fujii, I. Vobornik, J. E. Rault, T. K. Kim, M. Hoesch, K. Okawa, M. Asakawa, T. Sasagawa, T. Eknapakul, W. Meevasana, and P. D. C. King, Nature Mater. 17, 21 (2018).
  * (20) J. Zhang, and G. Q. Huang, J. Phys.: Condens. Matter. 32, 205702 (2020).
  * (21) M. Yan, H. Huang, K. Zhang, E. Wang, W. Yao, K. Deng, G. Wan, H. Zhang, M. Arita, H. Yang, Z. Sun, H. Yao, Y. Wu, S. Fan, W. Duan, and S. Zhou, Nat Commun 8, 257 (2017).
  * (22) Y. He, D. Yan, L. R. Ng, L. Shi, S. Wang, H. Lin, S.-H. Lin, H. Luo, and K. Yan, Mater. Chem. Front. 3, 2184 ( 2019).
  * (23) Y. Song, F. Meng, T. Ying, J. Deng, J. Wang, X. Han, Q. Zhang, Y. Huang, J-g. Guo, and X. Chen, J. Phys. Chem. Lett. 12, 12186 (2021).
  * (24) K. Zhang, M. Yan, H. Zhang, H. Huang, M. Arita, Z. Sun, W. Duan, Y. Wu, and S. Zhou, Phys. Rev. B 96, 125102 (2017).
  * (25) F. Fei, X. Bo, P. Wang, J. Ying, J. Li, K. Chen, Q. Dai, B. Chen, Z. Sun, M. Zhang, F. Qu, Y. Zhang, Q. Wang, X. Wang, L. Cao, H. Bu, F. Song, X. Wan, and B. Wang, Phys. Rev. B 96, 041201(R) (2017).
  * (26) S. Pyon, K. Kudo, and M. Nohara, J. Phys. Soc. Jpn. 81, 053701 (2012).
  * (27) F. Fei, X. Bo, P. Wang, J. Ying, J. Li, K. Chen, Q. Dai, B. Chen, Z. Sun, M. Zhang, F. Qu, Y. Zhang, Q. Wang, X. Wang, L. Cao, H. Bu, F. Song, X. Wan, and B. Wang, Adv. Mater. 30, 1801556 (2018).
  * (28) A. Vasdev, D. Rana, A. Vashist, Y. Singh, and G. Sheet, Phys. Rev. B 105, 094509 (2022).
  * (29) J. Jiang, S. Lee, F. Fei, F. Song, E. Vescovo, K. Kaznatcheev, F. J. Walker, and C. H. Ahn, APL Mater. 8, 061106 (2020).
  * (30) T. Qian, H. Miao, Z. J. Wang, X. Shi, Y. B. Huang, P. Zhang, N. Xu, L. K. Zeng, J. Z. Ma, P. Richard, M. Shi, G. Xu, X. Dai, Z. Fang, A. F. Fang, N. L. Wang, and H. Ding, New J. Phys. 16, 123038 (2014).
  * (31) Y. Qi, S. Matsuishi, J. Guo, H. Mizoguchi, and H. Hosono, Phys. Rev. Lett. 109, 217002 (2012).
  * (32) G. Saleh, and S. Artyukhin, J. Phys. Chem. Lett. 11, 2127 (2020).
  * (33) J. Guo, Y. Qi, S. Matsuishi, and H. Hosono, J. Am. Chem. Soc. 134, 20001 (2012).
  * (34) S. Geller, and B.B. Cetlin, Acta Cryst. 8, 272 (1955).
  * (35) T. E. Rummery, and R. D. Heyding, Can. J. Chem. 45, 131 (1967).
  * (36) S. Geller, and J. Am, Chem. Soc. 77, 2641 (1955).
  * (37) V. Abadiea, S. Jobica, R. Krachlerb, H. Ipserb, I. Orionc, and R. Brec, J. Alloys Compd. 268, 50 (1998).
  * (38) Amit, R. K. Singh, N. Wadehra, S. Chakraverty, and Y. Singh, Phys. Rev. Materials 2, 114202 (2018).
  * (39) F. Hulliger, Nature. 204, 644 (1964).
  * (40) Y. Liu, H. Lei, K. Wang, M. Abeykoon, J. B. Warren, E. Bozin, and C. Petrovic, Phys. Rev. B 98, 094519 (2018).
  * (41) J. J. Yang, Y. J. Choi, Y. S. Oh, A. Hogan, Y. Horibe, K. Kim, B. I. Min, and S.-W. Cheong, Phys. Rev. Lett. 108, 116402 (2012).
  * (42) B. S. Chandrasekhar, Appl. Phys. Lett. 1, 7 (1962).
  * (43) N. R. Werthamer, E. Helfand, and P. C. Hohenberg, Phys. Rev. 147, 295 (1966).
  * (44) K. Maki, Phys. Rev. 148, 362 (1966).
  * (45) W. L. McMillan, Phys. Rev. 167, 331 (1968).
  * (46) L. Li, X. Deng, Z. Wang, Y. Liu, M. Abeykoon, E. Dooryhee, A. Tomic, Y. Huang, J. B. Warren, E. S. Bozin, S. J. L. Billinge, Y. Sun, Y. Zhu, G. Kotliar, and C. Petrovic, npj Quant Mater 2, 11 (2017).
  * (47) C. Patra, T. Agarwal, R. R. Chaudhari, and R. P. Singh, Phys. Rev. B 106, 134515 (2022).
  * (48) M. Mandal, C. Patra, A. Kataria, S. Paul, S. Saha, and R. P. Singh, Supercond. Sci. Technol. 35, 025011 (2022).
  * (49) M. Mandal, and R. P. Singh, J. Phys. Condens. Matter 33 135602 (2021).
  * (50) A. Zunger, S.-H. Wei, L. G. Ferreira, and J. E. Bernard, Phys. Rev. Lett. 65, 353 (1990).
  * (51) A. van de Walle, P. Tiwary, M. de Jong, D. L. Olmsted, M. Asta, A. Dick, D. Shin, Y. Wang, L. Q. Chen, Z. K. Liu, Calphad 42, 13 (2013).
  * (52) P. E. Blochl, Phys. Rev. B 50, 17953 (1994).
  * (53) G. Kresse, and D. Joubert, Phys. Rev. B 59, 1758 (1999).
  * (54) G. Kresse and J. Hafner, Phys. Rev. B 47, 558(R) (1993).
  * (55) J. Klimeš, D. R. Bowler, and A. Michaelides, J. Phys.: Condens. Matter 22, 022201 (2010).
  * (56) V. Wang, N. Xu, J.-C. Liu, G. Tang, W.-T. Geng, Computer Physics Communications 267, 108033 (2021).
  * (57) A. Togo, and I. Tanaka, Scr. Mater. 108, 1 (2015).
  * (58) C. Kittel, Introduction to Solid-State Physics, 8th ed. (Wiley, New York, 2005).
  * (59) E. F. Talantsev, Condens. Matter 4, 83 (2019).
  * (60) C. Patra, T. Agarwal, Rajeshwari R. Chowdhury, R. P. Singh, arXiv:2304.12619
  * (61) Y. J. Uemura, V. J. Emery, A. R. Moodenbaugh, M. Suenaga, D. C. Johnston, A. J. Jacobson, J. T. Lewandowski, J. H. Brewer, R. F. Kiefl, S. R. Kreitzman, G. M. Luke, T. Riseman, C. E. Stronach, W. J. Kossler, J. R. Kempton, X. H. Yu, D. Opie, and H. E. Schone, Phys. Rev. B 38, 909(R) (1988).
  * (62) D. Singh, Sajilesh K. P., S. Marik, A. D. Hillier and R. P. Singh, Phys. Rev. B 99, 014516 (2019).