# Comprehensive Overview of Named Entity Recognition: Models, Domain-Specific
Applications and Challenges

Kalyani Pakhale
Innover Digital
<EMAIL_ADDRESS>

###### Abstract

In the domain of Natural Language Processing (NLP), Named Entity Recognition
(NER) stands out as a pivotal mechanism for extracting structured insights
from unstructured text. This manuscript offers an exhaustive exploration into
the evolving landscape of NER methodologies, blending foundational principles
with contemporary AI advancements. Beginning with the rudimentary concepts of
NER, the study spans a spectrum of techniques from traditional rule-based
strategies to the contemporary marvels of transformer architectures,
particularly highlighting integrations such as BERT with LSTM and CNN. The
narrative accentuates domain-specific NER models, tailored for intricate areas
like finance, legal, and healthcare, emphasizing their specialized
adaptability. Additionally, the research delves into cutting-edge paradigms
including reinforcement learning, innovative constructs like E-NER, and the
interplay of Optical Character Recognition (OCR) in augmenting NER
capabilities. Grounding its insights in practical realms, the paper sheds
light on the indispensable role of NER in sectors like finance and
biomedicine, addressing the unique challenges they present. The conclusion
outlines open challenges and avenues, marking this work as a comprehensive
guide for those delving into NER research and applications.

_K_ eywords Natural Language Processing $\cdot$ Named Entity Recognition
$\cdot$ BERT $\cdot$ LLM $\cdot$ OCR

##  1 Introduction

Named Entity Recognition (NER) stands as a cornerstone task in Natural
Language Processing (NLP), possessing immense significance in information
extraction and knowledge organization. NER involves the identification and
classification of named entities, such as names of individuals, organizations,
locations, dates, and more, within textual data. Its pivotal role lies in its
capacity to disentangle structured information from unstructured text, thereby
enhancing data retrieval, analysis, and understanding. This research paper
embarks on a comprehensive survey of AI techniques applied to NER,
encompassing a spectrum of methodologies ranging from conventional to cutting-
edge. It elucidates the underlying principles of NER, shedding light on the
intricate interplay between linguistic patterns, contextual cues, and machine
learning algorithms that enable the recognition of named entities. NER’s
utility extends across various domains, including information retrieval,
question answering[1], document summarization, and language understanding. It
serves as the foundation upon which complex NLP applications are built.

The most important point of this research endeavor revolves around the
systematic examination of AI techniques for NER. The survey commences[2] with
classical rule-based approaches[3], where predefined rules guide the
identification of named entities. It subsequently explores sequence-based
methods that leverage the power of contextual information and sequential
patterns for entity recognition. The paradigm shift ushered in by transformer
models, epitomized by the groundbreaking BERT[1] architecture, has
revolutionized NER. This paper delves into the transformative impact of
transformers[1], highlighting their contextual embeddings and the innovative
fusion of BERT with Long Short-Term Memory (LSTM)[4] and Convolutional Neural
Networks (CNN)[4] architectures. These techniques harness contextual
embeddings to unravel the complexities of named entity recognition,
underscoring the potency of modern NLP architectures.

The study further extends into domain-specific NER models, tailored to the
specialized challenges of particular domains. Models such as ViBERTgrid[5],
meticulously designed for finance and legal documents, and BioBERT[6], fine-
tuned for the intricate landscape of medical NER, exemplify the adaptability
of NER techniques to context-specific requirements. Beyond traditional
approaches, this research paper delves into the realm of reinforcement
learning[7], unveiling the potential of Gaussian prior[8] and Distantly
Supervised NER techniques[9]. Deep learning initiatives, including E-NER[10]
with its evidential learning paradigm, as well as large language model
(LLM)[11, 12, 13] fine-tuned models and zero-shot mechanisms[12], showcase the
adaptability and prospects of these approaches. Additionally, the paper
explores Optical Character Recognition (OCR)[14] techniques, introducing the
role of OCR in the NER pipeline. Prominent solutions from industry leaders
such as AWS Textract, Azure, and Google AI demonstrate the synergy between OCR
and NER, enriching information extraction capabilities.

As the survey progresses, it culminates in the practical application of NER
techniques across diverse domains. The paper illuminates the significance of
NER in financial applications, emphasizing its role in parsing financial texts
and documents. It concurrently delves into the critical role of NER in
biomedical applications, where extracting knowledge from medical texts is of
paramount importance. Challenges intrinsic to these domains are dissected,
providing insights into the complexities of NER in practice. Lastly, the
research paper addresses open challenges awaiting exploration in NER. These
challenges transcend domain boundaries and serve as an invitation to
researchers and practitioners to venture into uncharted territories, unlocking
new possibilities and avenues for advancement. Hence, this comprehensive
survey of AI techniques for NER encapsulates the evolution, intricacies, and
practical implications of a foundational task within NLP. It caters to the
burgeoning interests of researchers and practitioners, elucidating the ever-
evolving landscape of NER and its indispensable role in the world of language
understanding and information extraction.

##  2 Background

###  2.1 What is NER?

Named Entity Recognition (NER)[15, 3, 6] is a part of text processing used in
tasks like extracting information and making sense of text in the Semantic
Web. It’s about spotting different types of named things in a bunch of
documents. These things can be common like names of people, places, dates, and
even web links or phone numbers. More advanced NER, called fine-grained NER
[16, 17], digs deeper into categories like specific kinds of people or things,
like actors, athletes, or musicians within the larger "PERSON" group. There’s
also NER for special fields[18, 17] like biology, where it finds things like
proteins and genes, and in manufacturing, where it identifies products and
brands.

Nested Named Entity Recognition (NER)[3] is a step ahead of regular NER[2]. It
deals with entities that have a hierarchy or parts inside them, like how
"Google India" contains both "Google" and "India." This is useful for
different languages and fields like finance, medicine, and law, where
documents have complex formatting and need special methods to understand
entity relationships and boundary positions.

###  2.2 Overview: AI Methods for NER

Named Entity Recognition (NER) [2] methods can be categorized into three
primary groups. It’s important to note that while this classification aids in
understanding the overarching technique categories, many NER systems discussed
in the literature[2, 3] employ a combination of these approaches. The first
category is Rule-based Approaches[15, 2] where experts manually devise rules
to identify specific types of named entities. These rules draw from syntactic,
linguistic, and domain-specific knowledge [15]. The second category,
Supervised Learning Approaches [2], involves creating a sizable manually
tagged dataset, where human experts explicitly label instances of the
designated entity type. Machine learning algorithms then generalize from this
labeled training data to derive NER rules[17]. The third category,
Unsupervised Approaches [18], typically involves equipping the system with a
limited set of seed instances (e.g., city names like ’New York’, ’Boston’,
’London’, ’Seoul’). The system analyzes the provided document collection and
learns rules from sentences containing these entity instances. These rules are
subsequently applied to detect new instances of named entities, leading to the
development of fresh rules. The learning process continues iteratively until
no further rules can be uncovered.

Modern deep learning techniques [15, 2] for Named Entity Recognition (NER)[15]
encompass a spectrum of models including recurrent neural networks (RNNs),
convolutional neural networks (CNNs)[19], Long Short-Term Memory (LSTM)[19],
and transformers[27] such as BERT[1] and GPT[12]. These techniques hold
substantial significance due to their inherent capacity to capture intricate
contextual relationships[20] and semantic features within text data. RNNs[15]
and LSTMs[19] excel in sequence modeling, capturing dependencies between
words. CNNs[4], on the other hand, can effectively capture local patterns and
are particularly useful for character-level representations. Transformers[21,
22] exemplified by BERT[21, 1], and GPT[12], revolutionize NER with their
attention mechanisms, enabling the model to consider all words in a sentence
simultaneously. BERT[1, 23, 21] for instance, offers contextualized
embeddings[20], enriching the understanding of words within their broader
linguistic context. The significance of these techniques[15] lies in their
ability to leverage massive amounts of unlabeled data through pre-training,
which enhances their performance[24] on NER[15] tasks with limited labeled
data. Moreover, the fine-tuning[16, 24, 13] of these models on domain-
specific[17] data further tailors their effectiveness[18], thus contributing
to state-of-the-art NER accuracy and advancing the field of natural language
processing.

##  3 Methodology

The below questions provide a broad overview of the concepts, techniques,
challenges, and applications related to Named Entity Recognition. Researchers
and practitioners often explore these questions to deepen their understanding
and improve NER systems.

1) What are the most effective techniques and models for Named Entity
Recognition across various domains, and how can they be adapted to address
domain-specific challenges?

2) What are the practical applications of NER in finance and biomedical
domains, and what insights can be gained from real-world implementations?

###  3.1 BERT

BERT[1], is a Bidirectional Encoder representation from Transformers, that
differentiates itself from recent models for language representation like
those introduced by Peters et al.[20] and Radford et al.[18] BERT is uniquely
designed to perform deep bidirectional representation pre-training using
unannotated text[2]. This is achieved by concurrently considering both the
left and right context across all layers. Consequently, the pre-trained
BERT[1] model can be fine-tuned with the addition of just one output layer,
resulting in the creation of cutting-edge models applicable to a wide spectrum
of tasks, including Named Entity Recognition[23] and language inference.
Notably, these enhancements are achieved without significant alterations to
the task-specific architecture. BERT’s conceptual simplicity is matched by its
empirical potency. It attains new state-of-the-art outcomes across eleven
diverse natural language processing benchmarks.

Figure 1: Architecture Overview of BERT: A Bidirectional Encoder
Representation from Transformers for NER

In the context of Named Entity Recognition (NER), BERT[21], a Bidirectional
Encoder representation from Transformers[4], offers a powerful approach. By
fine-tuning[21] the pre-trained[28] BERT model with a specific NER task, the
model can learn to understand and identify named entities within the text[22].
The process involves providing the pre-trained BERT[6] model with annotated
NER data, where entities are labeled. The model then learns to associate
contextual information around words with their corresponding entity types.
During fine-tuning[22], only the output layer of the BERT[23] model needs to
be adjusted, making it efficient for adapting to NER tasks. Once fine-tuned,
the BERT[21] model can accurately predict named entities in various documents,
even in scenarios where entities have complex relationships and contextual
dependencies. This capability makes BERT a valuable tool for achieving high-
quality named entity recognition across different languages and domains [22].

The challenges[22] in improving the detection of semantically similar but non-
identical news articles [23], and websites such detection is pivotal for
search engines and recommender systems to eliminate duplicates and combat
overspecialization[15]. [23] uses fine-tuned BERT[1, 21] with the SHAP library
insights into the model’s decision-making process and the significance of
individual words and named entities in making accurate determinations[15].

####  3.1.1 ViBERTgrid

The key-information Extraction task involves the extraction of entities from
various invoices, receipts, and bills. The deep learning[2], neural
networks[19]. ViBERTgrid[5], a multi-modal document representation technique
that fuses BERTgrid with Convolutional Neural Networks (CNNs)[4] which
collectively capture textual, layout, and visual information, improving
overall representation[25] ability over BERT[21] contextual embeddings.
strengthening of BERT contextual comprehension and CNN training together,
ViBERTgrid [5] gains the ability to interpret state-of-the-art techniques and
bridge the gap between image segmentation and traditional NLP approaches in
document analysis. It reinforces the notion that combining diverse data
sources leads to richer representations and improved results. As a result,
ViBERTgrid [5] offers a promising avenue for addressing real-world document
understanding challenges in various domains, including finance, legal, and
data processing. In comparison to competitive methods like LayoutLM,
LayoutLMv2, PICK, TRIE, and VIES, our ViBERTgrid demonstrates competitive
performance. Even with multimodal domain-specific pretraining on millions of
document images, ViBERTgrid achieves comparable results to LayoutLMv2-Base
when using BERT-Base and RoBERTa-Base[26] as text embedding models.
LayoutLMv2-Large, while slightly more accurate, has significantly more
parameters than ViBERTgrid (RoBERTa-Base).

####  3.1.2 BioBERT

BioBERT[6], is a pre-trained language representation model specifically
designed for entity recognition, relation extraction, terminology
normalization, and other relevant tasks in the field, It is a Pre-training on
large-scale corpora from different domains to learn general language
representations, which can then be fine-tuned on medical tasks. It
investigates how the pre-trained language model, BERT[1] can be adapted for
biomedical corpora and describes concepts like, self-attention, transformer
architecture, and the mechanisms behind contextual word, embeddings. By
adapting the pre-trained model to the specific task by training additional
task-specific layers while keeping the pre-trained weights fixed or partially
updating them such as fine-tuning methodology, such as learning rates,
optimizer choices, and batch sizes. Standard metrics such as precision,
recall, F1 score, or task-specific metrics has been used while, [6] It
highlights how pre-training on large-scale biomedical corpora enables the
models to learn general language representations that can be fine-tuned for
specific biomedical tasks, leading to improved performance and efficiency. It
provides insights into the comparative and highlighting advantages and
limitations of BioBERT[6] in various biomedical text-mining tasks. It enables
researchers to process and extract valuable information from biomedical
literature more efficiently, potentially accelerating discoveries and
advancements in the biomedical field. It could explore avenues for future
research, such as fine-tuning strategies, incorporating additional domain-
specific knowledge, or exploring new biomedical text-mining tasks.
PromtNER[27, 28] is combined with BERT zero-shot[12] and KNN clustering
algorithms where a group of entities has been clustered. For example,
"Google", "Apple", and "Amazon" combine in one cluster for an Organization
entity.

###  3.2 Reinforcement Learning

Reinforcement Learning (RL) is a facet of machine learning focusing on how
software agents optimize cumulative rewards through actions[2]. Agents learn
from interactions and rewards viewing an environment as a stochastic finite
state machine. This framework encompasses the environment’s state transition,
observation, and reward function. The overarching goal of Reinforcement
Learning (RL) is for agents to acquire effective state-update functions and
policies for maximizing cumulative rewards.

####  3.2.1 Gaussian Prior Reinforcement Learning

The Gaussian distribution is introduced by the need to address drawbacks in
existing approaches to solving nested Named Entity Recognition (NER) tasks.
The sequence-based, span-based, and hypergraph-based methods such as label
proliferation, exposure bias, computational costs, and ignoring dependencies
between nested entities. To overcome these challenges, the research[8]
explores structural and semantic characteristics of nested entities, including
entity triplet recognition order and boundary distance distribution that allow
the model to learn an optimal recognition order and remove the constraint of
predefined triplet orders and introduces[8] the concept of utilizing Gaussian
distribution to better capture the patterns and relationships more
effectively.

The Gaussian prior reinforcement learning model[8] for nested NER consists of
3 interconnected components. The Entity Triplet Generator (ETG) by employs a
pre-trained seq2seq model to predict entity boundaries and types in a
sentence, with an Index2Token mode converting predicted indices into practical
tokens. The Gaussian Prior Adjustment (GPA) incorporates a Gaussian
distribution to enhance entity boundary recognition by adjusting the boundary
distribution based on distances between tokens. The Entity Order Reinforcement
Learning (EORL) component optimizes the model’s performance by utilizing
Reinforcement Learning, enabling the generation of entity triplets without a
fixed order while rewarding high-quality triplets. These components
collectively contribute to an integrated framework for improved nested NER by
enhancing entity recognition, boundary adjustment, and recognition order
learning.

The effectiveness of modules in the GPRL[8] model is demonstrated through
ablation experiments. Removing the Gaussian Prior Adjustment (GPA) component
results in decreased F1 scores on ACE 2004, ACE 2005, and GENIA datasets,
highlighting GPA’s role in enhancing recognition of nested entity boundaries.
Deleting the Entity Order Reinforcement Learning (EORL) module leads to
further F1 score reduction, indicating the importance of reinforcement
learning in learning proper entity recognition order and mitigating training
inference gaps. GPA[8] is shown to improve attention to neighboring tokens and
diminish the impact of distant ones for nested boundary identification. EORL
effectively addresses labeling and error identification issues, while also
capturing dependencies and interactions between nested entities, leading to
enhanced nested named entity recognition and classification. The proposed
GPRL[8] model achieves state-of-the-art performance on nested NER tasks,
leveraging Gaussian prior adjustment and reinforcement learning mechanisms.

####  3.2.2 Distantly Supervised NER with RL

The significance of named entity recognition (NER) for extracting valuable
insights from digital libraries to advance scholarly knowledge discovery.
However, the scarcity of annotated NER datasets, particularly in scientific
literature beyond the medical domain, hinders the utilization of advanced
deep-learning models. To address this, the study[29] explores distant
supervision as an alternative to generate annotated datasets automatically
from external resources, despite introducing noise. The focus is on noisy-
labeled NER under distant supervision, with a novel Category-oriented
confidence calibration (Coca) strategy proposed to account for varying
confidence levels towards different entity categories. It integrated into a
teacher-student self-training framework, demonstrates promising performance
against advanced baseline models, offering a versatile solution for enhancing
NER accuracy and easily integrating with other confidence-based model
frameworks.

The [29] presents an innovative approach to enhancing Named Entity Recognition
(NER) by synergistically integrating Distant Supervision, Partial Annotation
Learning, and Reinforcement Learning (RL) methodologies. It addresses the
challenges posed by limited annotated data and maximize the NER model’s
performance. By combining these Reinforcement Learning techniques[8],
contributes to advancing the field of NER by demonstrating improved results in
NER tasks compared to existing methods.

###  3.3 Deep Learning

####  3.3.1 E-NER

E-NER[10], a specialized Named Entity Recognition (NER) model designed for
legal texts, has emerged as a transformative tool for enhancing legal
information extraction and understanding. Legal documents are characterized by
their complex language, unique terminology, and the presence of numerous legal
entities and references. E-NER addresses these challenges by providing a
dedicated solution for identifying and classifying legal entities such as
statutes, cases, regulations, and legal citations.

Figure 2: Architecture of the E-NER Framework with Evidential Deep Learning
Model

The architecture[10] works on two uncertainty-guided loss terms and training
strategies to handle sparse and Out-of-Vocabulary/Out-of-Domain (OOV/OOD)
entities. E-NER adapts to diverse NER paradigms and showcases enhanced
performance, including improved OOV/OOD detection and better generalization
for OOV entities, making it a promising approach for robust and reliable NER.

E-NER[10] framework introduces two uncertainty-guided loss terms in addition
to conventional Evidential deep learning, accompanied by a range of
uncertainty-guided training strategies. The experiments were conducted on 3
paradigms namely sequence labeling, span-based, and Seq2Seq demonstrates that
E-NER can be effectively applied to various NER[15] paradigms, leading to
accurate uncertainty estimation. Furthermore, in comparison to state-of-the-
art baselines, the proposed E-NER framework achieves improved OOV/OOD
detection performance and enhanced generalization capability on OOV entities.
The E-NER[10] with Evidential deep learning model aims to enhance the
reliability of NER systems in open environments by introducing a trustworthy
NER framework (E-NER) that effectively addresses challenges related to
uncertainty and entity recognition.

###  3.4 Fine-tuned Large Language Models

In the rapidly advancing field of NLP, significant attention has been directed
toward the large language models(LLM) such as GPT-3[12], LaMDA[11], and
PaLM[13] which achieve remarkable results in zero-shot and few-shot[30]
scenarios with proper instructions or prompts, even without parameter updates.
However, OpenAI has not provided its training data so the question arises as
to whether and to what extent ChatGPT can handle information extraction(IE)
which is for applications like, question-answering and knowledge graph
construction[24] evaluates ChatGPT’s performance, evaluation criteria,
robustness, and types of errors in information extraction tasks. By [24]
ChatGPT is able to understand well the subject-object relationships in
extraction tasks by fine tunnng it. Large Language Models (LLMs) [12] and
prompt-based techniques such as PromptNER[28] is to use prompts or
instructions to guide an LLM to recognize entities in a given sentence. This
involves providing the LLM with a set of entity definitions and a few-shot
example. The LLM[12, 11] then generates a list of potential entities within
the sentences in cross-domain NER PIXIU[31].Additionally, a standardized
benchmark covering financial NLP and prediction tasks that proposed to
evaluate FinMA and existing LLMs. The advancement of large language models
(LLMs)[12, 11] in natural language processing (NLP) within the financial
domain is hindered by the absence of domain-specialized financial LLMs,
instruction datasets, and evaluation benchmarks. Addressing this gap,
PIXIU[31], is a financial-based LLM based on the LLAMA framework features the
financial LLM called FinMA[31], which is achieved by refining LLaMA[32]
through instruction data fine-tuning that introduces a substantial instruction
dataset of 136K data samples, including diverse financial tasks, document
types, and data modalities.

###  3.5 Optical Character Recognition

Optical Character Recognition (OCR) is a technology that converts printed or
handwritten text from images, scanned documents, or photographs into machine-
readable text. OCR involves several steps in its process. First, the input
image is preprocessed, which includes tasks like noise reduction, binarization
to convert it into black and white, and skew correction to align the text
properly. Next, text regions are detected through methods like layout analysis
and object detection, identifying areas containing text. The detected regions
are then segmented into individual characters or words. The segmentation step
is followed by feature extraction, where relevant characteristics of the
characters are identified, aiding in recognition. The recognition phase
involves matching extracted features with a predefined character set or
language model to convert the image text into editable text. Finally, post-
processing steps like spell-checking and grammar correction may be applied to
refine the recognized text. The goal of OCR is to enable computers to
understand and work with text data from images, enabling various applications
such as document digitization, information retrieval, and text analysis.

OCR services provided by major cloud providers like Google Cloud[33], AWS
[14], and Azure[34] offer advanced capabilities for text extraction from
images and documents. Google Cloud Vision OCR employs deep learning models to
extract text, perform document structure analysis, and recognize handwriting.
Azure Computer Vision OCR utilizes OCR technology combined with AI to extract
printed and handwritten text, supporting multiple languages and document
types. AWS Textract offers advanced features including text and form
extraction, key-value pair identification, tabular data extraction, and its
incorporation of a query answering system but it may require fine-tuning for
optimal results. Despite the advantages of these services, limitations may
include difficulties in handling handwritten text, complex layouts, and low-
resolution images. It’s important to consider specific requirements and data
characteristics when choosing an OCR service.

Despite the significant advancements in Optical Character Recognition
(OCR)[33] technology, extracting complete key-value pairs from PDFs,
particularly invoices and bills with diverse table layouts, remains a
formidable challenge. The complexity arises from the varied and often
unpredictable table formats within multi-structured invoice PDFs, which
confound traditional OCR systems. Recognizing these table layouts accurately
is an intricate task, and it is evident that there is a pressing need for more
robust and adaptable approaches to address this issue. As to overcome these
challenges by utilizing cutting-edge machine learning models, tailored OCR
methods, and advanced table recognition algorithms. The primary objective is
to facilitate accurate and thorough extraction of key-value pairs from these
intricate document layouts, ultimately boosting data extraction efficiency,
minimizing errors, and supporting the automation of vital processes. These
insights underline the importance of continuous endeavors to enhance OCR
capabilities, particularly in industries dependent on precise information
retrieval from various complex document structures.

##  4 Applications and its Challenges

The application of Named Entity Recognition (NER) research spans numerous
critical domains, each demanding tailored solutions to address distinct
challenges and extract domain-specific knowledge effectively. In the realm of
healthcare and biomedical research, NER is instrumental in unlocking insights
from a burgeoning volume of medical data, enabling advancements in patient
care, drug discovery, and disease monitoring. In the cybersecurity domain, NER
aids in swiftly identifying and classifying cybersecurity entities, bolstering
threat detection and incident response capabilities in the face of evolving
cyber threats. Furthermore, NER empowers environmental scientists to decipher
climate parameters, species data, and ecological trends, facilitating a deeper
comprehension of environmental changes and conservation efforts. In the legal
arena, NER streamlines the complex task of identifying legal entities, case
references, and legal codes within vast legal documents, enhancing document
analysis and compliance monitoring. Meanwhile, NER research in the energy
sector supports informed energy policy development and sustainable resource
management. During humanitarian crises, NER plays a pivotal role in swiftly
locating and coordinating relief efforts for affected populations. In space
exploration, NER catalogues celestial discoveries and space mission details,
while in the AI and technology sector, it identifies emerging technologies and
innovations, informing tech trend analysis and investment decisions. NER in
education aids in research, student enrollment, and content recommendation,
while in public health, it contributes to timely disease outbreak monitoring
and resource allocation during health crises. Across these domains, NER
research stands as a crucial and ever-evolving field, continuously adapting to
diverse challenges and domains to deliver specialized entity recognition
systems that enrich research, industry, and society as a whole.

###  4.1 Finance

##### Applications:

Named Entity Recognition (NER) has several applications in the finance domain,
mainly in the extraction of crucial information from various documents
Applications of NER[4] in finance involve extracting important details from
documents. For instance, it helps sort transactions by recognizing vendor
names, product descriptions, and amounts. By linking a found entities to
databases, NER provides extra info, like connecting a company’s name to its
financial data. It even helps analyze feelings by spotting entities in
financial texts, making it possible to gauge opinions about companies, stocks,
or events. Moreover, it’s used to identify risk-related entities, aiding in
evaluating potential financial risks. NER supports compliance with rules by
pinpointing entities that matter for regulations. Also, it’s handy in managing
portfolios by recognizing stock symbols, company names, and financial markers.

##### Challenges:

However, there are challenges when extracting named entity data from financial
documents like PDFs, invoices, and bills. These documents come in different
styles, making it hard to consistently find entities. Plus, some documents mix
structured info (like tables) with unstructured text, needing special methods.
Errors like typos or inconsistent naming in financial documents can affect
accurate entity detection. Poor scans could lead to errors, and similar terms
may mean different things based on context, needing smart NER models.
Financial documents often have multiple entities together (like company names
and money amounts), making it tricky to tell them apart. Also, there’s not
enough labeled data specific to finance, which makes building good models
tough. Using specialized words and linking entities to external sources can be
tough too, as can ensuring sensitive info is extracted in compliance with
rules. Overcoming these issues needs smart NER models, special data, and
methods that understand finance’s complexities.

###  4.2 Biomedical

##### Applications:

In the field of Biomedical, Named Entity Recognition (NER) has various uses.
It helps in identifying crucial information in medical texts. For instance, it
can locate and categorize medical terms like disease names, drug names, and
medical procedures. NER also supports medical research by recognizing genes,
proteins, and molecular structures mentioned in scientific literature.
Moreover, it aids in tracking patient data, linking medical terms with patient
records, and helps in managing medical databases.

##### Challenges:

There are challenges in NER for Biomedical texts. One challenge is the vast
number of medical terms and variations, which can make accurate recognition
tricky. Also, medical texts often have complex sentence structures and
abbreviations that can confuse NER systems. Ambiguities between common words
and medical terms pose another issue. Additionally, there’s a lack of large
annotated datasets specific to Biomedical NER, making training accurate models
challenging. Overcoming these hurdles requires advanced algorithms,
specialized training data, and methods that can navigate the intricacies of
medical language.

###  4.3 Other applications and challenges

Named Entity Recognition (NER) finds applications across various fields beyond
finance and biomedical domains. In legal texts, NER helps identify legal
terminologies, case references, and entities like names of laws and
regulations. However, challenges arise due to the diverse legal language and
context-specific entity meanings. In the news domain, NER aids in extracting
people’s names, locations, and organization names, supporting news
categorization and sentiment analysis. The ambiguity of entity references and
rapidly evolving entities pose challenges. Similarly, in the e-commerce
sector, NER assists in extracting product names, brands, and specifications.
Yet, the vast variety of product names and frequent changes in product
listings create difficulties. In social media, NER is used for sentiment
analysis, topic identification, and user profiling. However, the informal
language, abbreviations, and context-dependent entity mentions make accurate
recognition challenging. While Named Entity Recognition(NER) systems excel for
English, numerous challenges persist for other Indian and Asian languages. The
issues such as the absence of capitalization norms, linguist morphological
complexities, the ambiguity between common and proper nouns, and the overlap
of terms like person and location names. Overcoming these challenges requires
domain-specific [12] training data, context-aware models, and adaptable
algorithms.

##  5 Conclusion

In the realm of Natural Language Processing, Named Entity Recognition (NER)
stands as a monumental pillar, bridging the gap between unstructured textual
data and structured knowledge organization. This comprehensive survey of AI
techniques for NER underpins the tremendous strides made in the domain, while
also acknowledging the multifaceted challenges it continues to confront.

From the rudimentary rule-based methods to the transformative prowess of
transformer architectures, the NER landscape has witnessed a profound
metamorphosis. The dawn of domain-specific NER models accentuates the
adaptability of these techniques, demonstrating the finesse with which models
like ViBERTgrid and BioBERT cater to the nuanced requirements of specialized
domains like finance and medicine. Yet, the continuous evolution of deep
learning paradigms, like E-NER and the utilization of large language models,
indicates that the NER journey is still unfolding, with newer horizons
awaiting exploration.

The synergy between Optical Character Recognition (OCR) and NER is an exciting
testament to the interdisciplinary collaboration within AI, showcasing the
potential of integrating diverse technologies for more robust information
extraction. Such amalgamations signal the future direction of NER — a
direction characterized by holistic, multimodal information extraction that
spans not only text but also visual and auditory data.

Despite these advancements, the challenges delineated in the paper underscore
the areas awaiting deeper inquiry. The intrinsic hurdles posed by different
industries, languages, and the ever-evolving nature of information, emphasize
the dynamic terrain of NER. Adapting to low-resource languages and domains,
while enhancing the model’s ability to handle ambiguity and connect recognized
entities to expansive databases, forms the crux of the road ahead.

Moreover, as NER cements its role in pivotal applications, from parsing
intricate financial documents to deciphering the complexities of medical
texts, its societal impact becomes even more pronounced. It becomes imperative
to ensure the transparency, reliability, and ethical considerations of these
models, considering their profound implications in decision-making processes
across sectors.

In summation, while this research offers a panoramic view of the current NER
landscape, it also serves as a clarion call to the research community. The
realm of Named Entity Recognition is rife with opportunities, challenges, and
responsibilities. With the accelerating pace of innovation and the ever-
increasing significance of language understanding in the digital age, NER
stands not just as a technical endeavor but as a cornerstone in shaping the
future of information extraction and knowledge representation. The road ahead
is long, promising, and teeming with potential — a journey that beckons the
collaborative efforts of researchers, practitioners, and industry stalwarts.

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# Quantum transport of Dirac fermions in HgTe gapless quantum wells

G. M. Gusev, 1 A. D. Levin, 1 D. A. Kozlov2 Z. D. Kvon, 2,3 and N. N.
Mikhailov 2,3 1Instituto de Física da Universidade de São Paulo, 135960-170,
São Paulo, SP, Brazil  2Institute of Semiconductor Physics, Novosibirsk
630090, Russia  3Novosibirsk State University, Novosibirsk 630090, Russia

###### Abstract

We study transport properties of HgTe quantum wells with critical well
thickness, where the band gap is closed, and the low energy spectrum is
described by a single Dirac cone. In this work, we examined both macroscopic
and micron-sized (mesocopic) samples. In micron-sized samples, we observe a
magnetic field induced, quantized resistance ($\sim h/2e^{2}$) at Landau
filling factor $\nu=0$, corresponding to the formation of helical edge states
centered at the charge neutrality point (CNP). In macroscopic samples, the
resistance near zero Landau level (LL) reveals strong oscillations, which we
attribute to scattering between the edge $\nu=0$ state and bulk $\nu\neq 0$
hole LL. We provide a model taking an empirical approach to construct a LL
diagram based on a reservoir scenario, formed by the heavy holes.

##  I Introduction

The gapless helical edge states flowing along the edge of the two-dimensional
(2D) system attract the attention of many due to both fundamental and
practical motivations. First, their existence serves as a signature for 2D
topological insulators bernevig ; kane ; hasan ; qi ; moore ; moore2 . Second,
the one dimensional nature of the edge states offers the possibility to study
strongly correlated fermion systems such as the helical Tomonaga–Luttinger
liquid kainaris . Moreover, the helical edge states can be used to produce
Majorana or parafermion modes for quantum computation moore3 .

Helical edge states arise at the edges of the topological insulator (spin Hall
effect) in the absence of an external magnetic field. Particulary, the HgTe
based quantum well with inverted band spectrum can host topological helical
states zhou ; konig ; roth ; gusev ; gusev2 . It is expected that these
helical channels lead to quantized conductance with the value of $e^{2}/2h$
and nonlocal edge transport roth ; gusev2 , which has been observed only for
short distances between the measurement probes in the range of the few
micrometers. The deviation between the theoretical prediction and experimental
value has been attributed to many different effects, including effects of
Rashba spin-orbit coupling strom ; crepin , charge puddles vayrynen ;
vayrynen2  and other numerous sources of inelastic scattering loss .

Besides the insulator with a bulk gap, helical states can also exist in a
gapless system. Such a remarkable example is 2D massless Dirac fermions in the
presence of a strong perpendicular magnetic field, such as graphene sarma ;
geim  and gapless HgTe quantum wells buttner ; kozlov ; kozlov2 ; gusev3 ;
kozlov3 . It has been demonstrated that at the critical HgTe well thickness
$d_{c}$ equal to, depending on the surface orientation and the quantum well
deformation, $6.3-6.5$ nm, the band gap collapses, and single-valley Dirac
fermions can be realized. In the presence of a strong perpendicular magnetic
field, the zero Landau level of the Dirac fermions forms two counter
propagating edge states similar to 2D topological insulators gusev3 . As a
result, conductance is zero in the QHE regime and quantized in universal units
$e^{2}/2h$ in the quantum Hall (QH)-metal regime in the absence of
backscattering between spin-polarized states.

In the present work, we studied the quantum transport in both mesocopic and
macroscopic devices fabricated from HgTe zero-gap quantum structures. In the
mesoscopic samples, we observe a magnetic field induced, quantized resistance
at $\nu=0$. These experiments clearly demonstrate the existence of a robust
helical edge state in a system with single-valley Dirac cone materials. In
macrosopic sample, the resistance strongly deviates from the quantized value.
Moreover, we observe large oscilations of the resistance at $\nu=0$. We
attribute these oscillations to the elastic intersubband scattering between
the edge $\nu=0$ state and bulk $\nu\neq 0$ hole LL. We observed a
unconventional LL diagram for hole Dirac particles with several ring-like
patterns, which is attributed to LL crossing of single LL and manifold-
degenerate subband levels. We report a model taking into account the reservoir
of the sideband hole states. The model reproduces some of the key features of
the data, in particular the density dependence of the hole LL and manifold LL
crossing points. We believe that this model provides a framework for more
sophisticated theoretical tools to understand many-body phenomena, such as
spin-splitting enhancement effects.

##  II Materials and Methods.

Quantum wells $Cd_{0.65}Hg_{0.35}Te/HgTe/Cd_{0.65}Hg_{0.35}Te$ with (013)
surface orientations and a well thickness of 6.3-6.4 nm were prepared by
molecular beam epitaxy. Two different types of devices were used: macroscopic
and mesoscopic Hall bars. The mesoscopic sample is a Hall bar device with 2
current and 7 voltage probes. The bar has a width $W$ of $3,2\mu m$ and three
consecutive segments of different lengths $L$ $(2.8,8.6,33\mu m)$. The
macroscopic bar has a width W of $50\mu m$ and three consecutive segments of
different lengths L(100, 250, 100$\mu m$). A dielectric layer was deposited
(100 nm of $SiO_{2}$ and 100 nm of $Si_{3}Ni_{4}$) on the sample surface and
then covered by a TiAu gate. The density variation with gate voltage was
$1\times 10^{11}cm^{-2}V^{-1}$. The magnetotransport measurements were
performed in the temperature range $1.4-4.2K$ using a standard four point
circuit with a $1-27Hz$ ac current of $1-10nA$ through the sample, which is
sufficiently low to avoid overheating effects. 6 devices from the different
wafers were measured, all with similar results.

Figure 1: (Color online) (a) Schematic of the transistor. (b) Resistivity
$\rho_{xx}$ as a function of gate voltage measured for different devices. The
red trace-macroscopic, black line- mesocopic devices. The bottom of the figure
presents a top view of the samples.

##  III Transport measurements in micron-sized (mesoscopic) samples.

The variation of resistivity with gate voltage and lattice temperature for 6.4
nm quantum wells for mesoscopic and macroscopic devices is shown in Figure 1b.
The current flows between contacts 1,5; voltage is measured between probes 2,3
($\rho_{xx}=\frac{W}{L}R_{xx},R_{xx}=R^{2,3}_{1,5}=V_{2,3}/I_{1,5}$) for
mesoscopic device; and current is applied between contacts 1,6; voltage is
measured between probes 2,3 $R_{xx}=R^{2,3}_{1,6}=V_{2,3}/I_{1,6}$ for
macroscopic device. The resistance behaviour in zero magnetic field resembles
behaviour in other HgTe-based quantum wells, including topological insulators
konig ; gusev ; gusev2 : resistance shows a peak around the charge neutrality
point (CNP). In graphene and zero gap HgTe wells, the CNP is coincident with
the Dirac point. Transport in HgTe QWs of a critical width $d_{c}$ is expected
to be determined by the energy gap fluctuations leading to the formation of
the topological channel network entin ; gusev4 . The minimum conductivity at
the Dirac point $\sigma_{xx}=1/\rho_{xx}=\frac{e^{2}}{h}(2.5\pm 1)$ agrees
with the observations gusev4 .

In the presence of a magnetic field, the energy spectrum is organized in
Landau levels (LLs) with square root versus linear dependence on the magnetic
field and square root dependence on the Landau index $n$. Moreover, there is
an additional zero energy LL, originated from Berry phase carried by each
Dirac point, similar to graphene castro . It is worth noting that, in HgTe
quantum wells, Dirac fermions have a single cone (one valley) spectrum, which
allows the realization of edge state transport in a strong magnetic field via
counter propagating modes gusev2 , while in graphene transport depends on
which degeneracy, spin or valley, is removed first in a strong magnetic field
abanin . A symmetric LL spectrum around zero energy level is expected for low
energy.

Figure 2: (Color online) The color map of $R_{xx}(N_{s},B)$ versus $N_{s}$ and
B at T=4.2K for mesoscopic device. The arrow indicates the plateau of
resistance at $\nu=0$. The insert shows the counterpropagating spin-polarized
edge states in the presence of a strong perpendicular magnetic field. (b)The
red trace represents the longitudinal $R_{xx}$ resistance as a function of the
magnetic field (B) at the CNP. The black line shows the theoretical resistance
calculated from the model calvo . The blue line represents the B dependence of
the mean free path calculated from the model calvo .

In this section we present the results for the mesoscopic sample. Longitudinal
$R_{xx}$ resistance has been measured as a function of gate voltage ($V_{g}$)
and magnetic field (B). Figure 2 shows the the resistance color plots as a
function of carrier density and B. One can see stripes corresponding to
resistance maxima and minima in the B, and the slopes of the stripes are
determined by the LL filling factor $\nu$ : $dN_{s}/dB=\nu e/h$, where $h$ is
the Plank constant. The Dirac point corresponds to the charge neutrality point
(CNP), where Hall resistance passes zero value and changes sign gusev2 . The
zero energy Landau level occurs at CNP splitting, due to Zeeman energy at the
high magnetic field, which leads to the formation of two counter propagating
states (insert in Figure 2a). Simultaneous observations of the resistance
plateaux in local and in nonlocal (not shown) transport confirms this scenario
gusev2 . The experimental consequences expected for the ballistic edge
transport resulting from the helical states is resistance quantization with
the universal value $\frac{h}{2e^{2}}$. Figure 2b shows the resistance trace
corresponding to the chemical potential position at the CNP. One can see that
the resistance plateau reaches the quantized value $\frac{h}{2e^{2}}$ in the
range of the magnetic field $0.5<B<2T$, diverging towards the insulating value
at higher B. The resistance quantization is not perfect and demonstrates
mesoscopic fluctuations similar to resistance fluctuations observed in 2D
topological insulators in zero magnetic field konig ; gusev . As was mentioned
above, the mechanism of resistance deviations in TI is still under discussion
loss . Note, however, that in the presence of a strong magnetic field and spin
orbit interaction, backscattering between different spin polarized chiral edge
channels may occur khaetskii . Adapting this model for the helical edge states
and assuming scattering by the Coulomb impurities in the presence of the spin
orbit coupling, we can obtain the equation for inverse scattering length calvo

$\frac{1}{l}=\frac{(2\pi)^{3/2}}{v_{1}v_{2}}\left[\frac{e^{2}}{\hbar\varepsilon}\right]^{2}\frac{N}{q_{s}^{2}\lambda}\left[\frac{m\delta
v\alpha g\mu H}{\delta E^{2}}\right]^{2}$

where $v_{1,2}$ are the velocities of the spin polarized edge states, $\delta
v=v_{2}-v_{1}$, N is the impurity density, $q_{s}$ is the inverse screening
length, $\lambda=\sqrt{\hbar c/eB}$ is the magnetic length, $g\mu H$ is the
Zeeman term. The energy splitting between edge states is determined by
equation

$\delta E=\sqrt{(g\mu H/2)^{2}+(mv\alpha)^{2}}$

where $v$ is the averaged edge state velocity, $\alpha$ is spin orbit coupling
constant, $m$ is the effective mass. Assuming $\delta v\approx\delta
E/\hbar\omega_{c}\ll v$, where $\omega_{c}=eB/mc$ is the cyclotron frequency,
we calculate the scattering length for our system. Figure 2b demonstrates the
magnetic field dependence of the scattering length for parameters:
$N=10^{11}cm^{-2},\alpha\approx 10^{5}m/s,v=10^{5}cm/s$. The resistance can be
calculated from equation $R=h/2e^{2}(1+L/l)$ abanin ; gusev . One can see that
the characteristic scattering length strongly decreases with the magnetic
field and becomes comparable with the distance between probes at $B_{c}\approx
2.5T$. Therefore, the transport regime is expected to be ballistic below
$B_{c}$, and resistance is quantized, while the resistance increases at
$B>B_{c}$ because the electrons experience more scattering.

##  IV Transport measurements in macrosopic samples.

In this section, we focus on the transport properties in large-sized
macroscopic samples. Figure 3a shows the the resistance (a) color plots as a
function of carrier density and B for a smaller field range. In addition we
invert the gate voltage scale in comparison with Fig.2a and demonstrate the
hole-like spectrum of the LL on the right side of the voltage sweep. One can
see a significant difference between microscopic and macroscopic sample
behaviour near the CNP: the resistance in the small sample is quantized and
shows the plateau at low field , while the resistance in the large device is
much larger than the value $h/2e^{2}$ and reveals oscillations. Fig. 3b shows
the evolution of resistance at the CNP with the magnetic field. Note, that at
the CNP Hall resistance is zero, therefore, the behaviour of the transport
coefficients in the quantum Hall effect regime and at $\nu=0$ are very
different. For example, when $\rho_{xy}\gg\rho_{xx}$ one can expect that
$\rho_{xx}\sim\sigma_{xx}$ . In contrast at $\nu=0$ we observe
$\rho_{xy}\approx 0$, and $\rho_{xx}\sim 1/\sigma_{xx}$. In Fig. 3b we plot
conductivity versus the magnetic field, and, for comparison, we also plot the
B-dependence of resistivity at $V_{g}=-2.5V$, corresponding to the quantum
Hall regime of hole-like Landau levels. One can see the coincidence between
the position of the conductivity peaks at $\nu=0$ and the resistivity (or
conductivity, because $\rho_{xx}\sim\sigma_{xx}$ ) peaks of 2D Dirac-like
holes.

To get more insight into the physics of the observed resistivity oscillations,
it is important to consider the energy spectrum of of the gapless HgTe quantum
well. The particle energy in 6.4 nm HgTe wells represents a single valley cone
and, aside from the Dirac-like holes in the center of the Brillion zone, the
valance band contains local a valley formed by the heavy holes with a
parabolic spectrum. Therefore, one can expect that LL energy in the presence
of the magnetic field is asymmetric for electrons and holes buttner ; kozlov2
; gusev3 ; kozlov3 . A previous study of the quantum Hall effect in HgTe wells
demonstrated strong asymmetry between electrons and holes, which was
attributed to the presence of a band maximum in the spectrum of the holes
kozlov . It has been found that the quantized Hall plateaux for hole-like
particles occurs in magnetic field 3 times smaller than for electron-like
carriers, and the plateaux for holes is much wider that for electrons. The
authors attributed such anomalous behaviour to the existence of sideband
holes, which may serve as reservoir and pin the Fermi level in the gap between
the Landau levels of the Dirac holes. Recently heavy hole density of the
states has been measured by the capacitance technique kuntsevich .

Figure 4a shows a two-dimensional color plot of the hole part of the spectrum.
One can see, that the resistance reveals a strikingly rich ring-like
structure. Instead of stripes, expected in a conventional LL diagram, sharp
abrupt bends occur at low magnetic field. The empirical linear fit is shown as
dashed lines in Fig.3a and basically corresponds to the Dirac-like hole LL.
The slopes of the lines decrease with the magnetic field, however, it is
always larger than $\nu e/h=2.4\times 10^{10}cm^{-2}/T$. For example, one can
see that the slope of the first LL is close to $40\times 10^{10}cm^{-2}/T$,
which is about 17 time larger than expected.

Figure 3: (Color online) (a) (a) Color map of $R_{xx}(N_{s},B)$ versus $N_{s}$
and B at T=4.2K for a macroscopic device. (b) The red trace represents the
longitudinal $R_{xx}$ resistance as a function the magnetic field (B) at the
CNP. The blue trace represents the conductivity $\sigma_{xx}$ as a function
the magnetic field (B) at the CNP. The black trace represents $R_{xx}$ in the
quantum Hall effect regime for 2D Dirac holes as a function the magnetic field
(B) at $V_{g}=-2.5V.$ Figure 4: (Color online) (a) Color map of
$R_{xx}(N_{s},B)$ versus $N_{s}$ and B at T=4.2K for a macroscopic device.
Black dashes represent the slope of the LL for Dirac-like holes. (b)
Theoretical calculations of the density of states as a function of the hole
density and magnetic field. Red dashes represent the slope of the LL for
Dirac-like holes.  Figure 5: (Color online) Calculated Landau levels for a 6.4
nm symmetric HgTe quantum well for B=0.5T and B=1T. Two sets of levels
originating from spin splitting of 2D subbands are shown. Horizontal lines
show the energy when the fermi level is pinned by the backside hole LLs.

It is worth noting that this unconventional LL pattern has never been observed
before in other 2D systems. Indeed, in the presence of two subbands, the LL
diagram shows a ring-like structure due to LL crossing zhang  with topology,
which is different from our observations. The LL crossing points become
crossing 2-folds owing to the crossing between spin-split first and second
subbands. Instead of a diamond structure, expected from a naive picture,
nonmonotonic behaviour of electrochemical potential leads to a ring-like
shape, although the electron-electron interactions may play a significant role
too. The LL spectrum in the valence band of a HgTe well becomes complicated at
high energy and LL crossing occurs. We use all relevant Kane Hamiltonian
parameters to numerically calculate the density of the states for the valence
band as a function of $P_{s}$ and $B$. The magnetic field and density
coordinates of the LL crossing in the plot of the density of the states
correspond to the energy level crossing, and comparison with the experiment
allows to determine the Kane Hamiltonian parameters. However, one can see that
the calculations show the LL crossing at high B and density, and therefore, it
is clearly insufficient to explain the ring-like pattern at low B and $P_{s}$
obtained in experiment.

The features observed in our experiment can be understood from the
consideration of the behaviour of the chemical potential $\mu$ (the Fermi
energy at T=0) in the presence of the reservoir formed by the density of the
states originated from the tails of high index valence band LLs. To account
for the key features of the model, it is important to get an idea of how the
energy spectrum is quantized in the magnetic field. Fig.5 shows the calculated
Landau level originated from the valence band for two fixed magnetic fields.
The low index levels rapidly go up with increasing B. In contrast, the high
index levels form a dense set, especially near the band extreme, and are
slowly shifted with increasing magnetic field. One can see that the number of
levels near the maximum inside of the energy interval $\Delta E\approx 5meV$
is close to 80 at B=0.5 T. As the magnetic field increases further, the level
number near the maximum decreases. The behaviour of the Fermi level in a two-
dimensional system strongly depends on the density of the states. In
conventional 2D electron gas, the Fermi level is proportional to the charge
concentration because the density of the states is constant, while in the
system with a linear Dirac-like spectrum, $E_{F}$ is proportional to the
square root of $N_{s}$. In the magnetic field, $E_{F}$ jumps from one Level to
the next lower level. Deep minima in the diagonal resistance accompanied by a
plateaux in $R_{xy}$ are attributed to the existence of localized electronic
states on the tail of the broadened LL in the presence of the disorder and
pinning of the Fermi level. Due to the big density of LL, shown in Figure 4,
the Fermi level becomes locked near $E_{c}\approx-15meV$ (the energy at the
CNP corresponds to E=-30 meV), indicated by the red line, and a further
increase of density results in the overlapp between heavy holes and Dirac-like
holes. Note that the energy $E_{c}$ corresponds to the very low density
$P_{s}=0.15\times 10^{11}cm^{-2}$.

To calculate the color map plot of the density of the states $D$ as a function
of density and B, we adapted the Lorentzian form of the density of the states
in a strong magnetic field duarte . Figure 4b shows the color map
$D(N_{s},B)$, assuming level broadening independent of the magnetic field. One
can see two parts of the spectrum: the low density part consists of the
stripes with the large slope, corresponding to the Dirac-like hole LL at
$\mu<E_{c}$, and the high density part corresponds to the overlap between
Dirak-like and heavy holes with the parabolic spectrum at $\mu>E_{c}$. We also
plot the slope of the LL for Dirac-like holes at high densities, corresponding
to the region where $\mu>E_{c}$.

Now we turn to a detailed comparison between the experimental resistance plot
of $R_{xx}(P_{s},B)$ and the theoretical DOS for the LL spectrum. In the
experimental fan chart, we don’t see the slope for the Dirac-like hole Landau
levels at $\mu<E_{c}$ because of the broadening of the zero LL. We can resolve
the LL only in a very narrow energy (density) window $0.2\times
10^{11}<P_{s}<0.2\times 10^{11}$. For higher densities, LL broadening abruptly
increases and particle motion becomes not quantized into discrete levels. Our
model is much too simple to adequately describe the slope for the Dirac-like
hole Landau levels for all densities and more advanced theory is required to
describe this behavior, which is out of the scope of our experimental paper.
However the model can qualitatively explain the difference of the LL slope
from the one expected.

As we demonstrated above, conductivity at the CNP reveals the oscillations,
which coincide with conductivity oscillations close in proximity to the CNP
(Fig.3b). We attribute this effect to the resonance scattering between helical
edge states at $\nu=0$ to the bulk LL. In such narrow band gap materials as
HgTe, potential fluctuations due to nonuniform doping play a significant role.
Such potential fluctuations lead to the formation of conducting large size
puddles or lakes in the bulk of the insulator, and carriers at the edge states
interact with these puddles vayrynen ; gusev2 . A number of puddles should be
present in the vicinity of the edge to allow for scattering between the
counter-propagating states and the bulk LL localized in each lake.

##  V Conclusions

In this paper, we present a detailed study of the transport in single cone
Dirac fermions in 6.3-6.4 nm HgTe quantum wells in mesoscopic and macroscopic
devices. We observe quantized four-terminal resistance in mesoscopic devices
which provides a stark indicator for helical edge transport at $\nu=0$ in the
presence of a magnetic field. In macroscopic samples, we observe resistance
oscillations at $\nu=0$ and an unconventional LL diagram for hole Dirac
particles with several ring-like patterns. We attribute the fan chart to LL
crossing of single LL and manifold-degenerate subband levels. We report a
model taking into account the reservoir of the sideband hole states. The model
reproduces some of the key features of the data, in particular the density
dependence of the hole LL and manifold LL crossing points. The oscillations of
resistance at the CNP may occur due to the elastic intersubband scattering
between the edge $\nu=0$ state and bulk $\nu\neq 0$ hole LL localized in the
large size puddles near the edge.

##  VI Acknowledgment

We thank O.E. Raichev for the helpful discussions and providing us with some
of the calculations of the LL.

## References

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