# Band-gap engineering, magnetic behavior and Dirac-semimetal character in the
MoSi2N4 nanoribbon with armchair and zigzag edges

A. Bafekry<EMAIL_ADDRESS>Department of Physics, University
of Antwerp, Groenenborgerlaan 171, B-2020 Antwerp, Belgium  M. Faraji  Micro
and Nanotechnology Graduate Program, TOBB University of Economics and
Technology, Sogutozu Caddesi No 43 Sogutozu, 06560, Ankara, Turkey  C. Stampfl
School of Physics, The University of Sydney, New South Wales 2006, Australia
I. Abdolhosseini Sarsari<EMAIL_ADDRESS>Department of Physics,
Isfahan University of Technology, Isfahan, 84156-83111, Iran  A. Abdollahzadeh
Ziabari  Nano Research Lab, Lahijan Branch, Islamic Azad University, Lahijan,
Iran  N. N. Hieu  Institute of Research and Development, Duy Tan University,
Da Nang 550000, Viet Nam  Faculty of Natural Sciences, Duy Tan University, Da
Nang 550000, Viet Nam  S. Karbasizadeh  Department of Physics, Isfahan
University of Technology, Isfahan, 84156-83111, Iran  M. Ghergherehchi
College of Electronic and Electrical Engineering, Sungkyunkwan University,
Suwon, Korea

###### Abstract

Motivated by the recent successful formation of the MoSi2N4 monolayer [Hong et
al., Sci. 369, 670 (2020)], the structural, electronic and magnetic properties
of MoSi2N4 nanoribbons (NRs) is investigated for the first time . The band
structure calculations showed spin-polarization in zigzag edges and a non-
magnetic semiconducting character in armchair edges. For armchair-edges, we
identify an indirect to direct band gap shift compared to the MoSi2N4
monolayer, and its energy gap increases with increasing NR width. Anisotropic
electrical and magnetic behavior is observed via band structure calculations
in the zigzag and armchair edges, where, surprisingly, for the one type of
zigzag-edges configuration, we identify a Dirac-semimetal character. The
appearance of magnetism and Dirac-semimetal in MoSi2N4 ribbon can give rise to
novel physical properties, which could be useful in applications for next-
generation electronic devices.

The intense research into the properties and applications of graphene [1] has
triggered an enormous effort to discover novel two-dimensional (2D) layered
nanomaterials with peculiar physical properties leadint to new performances.
For example, a group of 2D transition metal dichalcogenides (TMDCs), including
MoS2 and WS2, has significantly influenced the world of optoelectronic,
photonic and energy devices over the last few years [2, 3, 4, 5, 6]. In
addition to 2D TMDCs, nanodimensional transition metal nitride (TMN) compounds
have been intensively investigated recently [7, 8, 9, 10, 11, 12]. As a new
class of air-stable 2D TMN semiconductors, the MoSi2N4 monolayer exhibits
unique electrical and mechanical properties. Recently, Ren et al. have managed
to synthesise an air-stable MoSi2N4 2D monolayer using chemical vapor
deposition (CVD) [13]. The experimental bandgap reported in Ref. [14] was 1.94
eV, very close to the value obtained by density functional theory (DFT)
calculations. Moreover, the intrinsi electron and hole mobilities at the K
point in the Brillouin zone were evaluated to be $\sim$270 and $\sim$1200
cm2V-1s-1, respectively; greater than those of monolayer MoS2 by factors of 4
to 6 [14]. Furthermore, a high optical transmittance was obtained, with an
average of 97.5 $\pm$ 0.2% in the visible range, comparable to that of
0.335-nm-thick monolayer graphene (97.7$\%$). These promising aspects make the
MoSi2N4 monolayer an appropriate candidate for use in nano-electronic and
optoelectronic devices.

These attractive properties pave the way not only to explore novel 2D devices
but also to investigate the structural, electrical, mechanical and optical
properties of MoSi2N4. To date, the physics behind electrically contacting
MoSi2N4 with metals is still unknown [15, 16, 17]. Nanoribbons are narrow
strips of a material with a very high length-to-width ratio.They combine the
flexibility and unidirectional properties of one-dimensional nanomaterials,
the high surface area of 2D nanomaterials and the electron-confinement and
edge effects of both. The structures of nanoribbons can thus lead to
exceptional control over electronic band structure, the emergence of novel
phenomena and unique architectures for applications [18, 19, 20, 21, 22, 23,
24]. As the flagship of nanoribbons, graphene nanoribbons (GNRs) were
initially introduced as a theoretical model to examine the edge and nanoscale
size effects in graphene [25]. The electronic states of GNRs largely depend on
the edge structures (armchair or zigzag). Meanwhile, black phosphorous has
become a strong focus of the science community owing to the synthesis of its
2D form, namely, the phosphorene [26, 27, 28]. Preliminary, but exciting
results indicate that phosphorene has potential applications in
nanoelectronics and optoelectronics. It has been found that all the
semiconducting phosphorene nanoribbons present very high values of Seebeck
coefficient and can be further enhanced by hydrogen passivation at the edge
[29]. There are also reports on nanoribbon structures of different materials
such as silicene [30], boron nitride [31], gallium oxide [32] and titanate
nanoribbons [33].

Motivated by the exciting experimental realization of 2D MoSi2N4, in this
study our objective is to explore the structural, electronic and magnetic
properties of MoSi2N4 nanoribbons using ab initio calculations and to
investigate the effect on these properties of changing the width of zigzag and
armchair nanoribbons. Our results show MoSi2N4 nanoribbons with armchair edge
possess a semiconducting behavior and the band gap increases with the width of
the NR, while MoSi2N4 nanoribbons with zigzag edges show magnetic metal
properties, where the magnetic moment is modified with the width of the NR.
Remarkably, half-metallic anisotropic Dirac cone is found in one of
configurations of MoSi2N4 nanoribbons which makes them worth systematically
investigating.

##  I Method

The plane-wave basis projector augmented wave, as implemented in the Vienna
ab-initio Simulation Package (VASP) [34, 35] was employed in the framework of
DFT. The generalized gradient approximation (GGA) of Perdew-Burke-Ernzerhof
form, [36, 37] were used for the exchange-correlation functional. The kinetic
energy cut-off of was 600 eV, and a $\Gamma$-centered 16$\times$16$\times$1
k-mesh for the unit cell was employed in our calculations. The tolerance of
the total energy convergence was less than 10-5 eV with forces less than 10-3
eV Å-1. The lattice constants and atomic positions were optimized without any
constraint. The vacuum space was $\sim$20 Å along the z-direction to avoid any
fictitious interactions.

##  II Monolayer

Table 1:  The structural and electronic parameters including lattice constant $a$; the bond lengths of Mo-N ($d_{1}$), Si-N ($d_{2}$) and Mo-N ($d_{3}$); the bond angles of N-Mo-N ($\theta_{1}$), N-Si-N ($\theta_{1}$) and N-Mo-N ($\theta_{1}$); the layer thickness $(t)$; the cohesive energy per atom, $(E_{coh})$; the work function ($\Phi$); the band gap $(E_{g})$ using PBE (HSE06); the VBM/CBM positions.  | a | d1 | d2 | d3 | $t$ | $\theta_{1}$ | $\theta_{2}$ | $\theta_{3}$ | $E_{coh}$ | $\Phi$ | $E_{g}$ | VBM/CBM |
---|---|---|---|---|---|---|---|---|---|---|---|---|---
| (Å) | (Å) | (Å) | (Å) | (Å) | (∘) | (∘) | (∘) | (eV/atom) | (eV) | (eV) | (eV) |
MoSi2N4 | 2.91 | - | 1.75 | 2.09 | 7.01 | - | 112.02 | 73,87 | -8.46 | 5.12 | 1.79 (2.35) |  $\Gamma$/K |
Figure 1: (a) The geometry (top and side views) and (b) band structure of the
2D MoSi2N4 nanosheet. Geometric structures of the (c) Armchair and (d) Zigzag
MoSi2N4 NRs with different widths specified according to the numbers. The
primitive unit cell is indicated by a red parallelogram (rectangle) for the
nanosheet (nanoribbon).

The atomic and electronic structures of the MoSi2N4 nanosheet are shown in
Figs. 1(a) and (b), respectively. From the atomic structure, we can see that
atoms are packed in a honeycomb lattice, forming a 2D crystal with a space
group of $P_{6m1}$. The hexagonal primitive unit cell is indicated by the red
parallelogram. After structure optimization the lattice constant is determined
to be 2.91 Å. The bond lengths of Mo-N and Si-N are determined to be 1.75 and
1.74 Å, respectively, while the bond length of Mo-Si is calculated to be 2.09
Å. The two angles of Si-N-Si are determined to be 112 and 106∘, while the two
angles of Si-Mo-Si are 87 and 73∘. The thickness of MoSi2N4 is 7.01 Å and for
the MoN2, the vertical distance of N-N is determined to be 2.99 Å and the Mo-N
bond length is 2.58 Å. These results are good agreement with a previous report
[13].

The cohesive energy ($E_{coh}$) per atom is calculated using the following
equation:

$E_{coh}=\frac{E_{tot}-E_{Mo}-2E_{Si}-4E_{N}}{n_{tot}},$ (1)

where $E_{Mo}$, $E_{Si}$ and $E_{N}$, $E_{tot}$ represent the energies of
isolated Mo, Si, N atoms and total energy of the ML, ntot is the total number
of atoms, respectively. The cohesive energy is found to be -8.46 eV/atom for
MoSi2N4, while the negative energy indicates the exothermicity of the
structure. The electronic band structure of MoSi2N4 is shown in Fig. 1(b). Our
results show that MoSi2N4 is semiconductor with an indirect band gaps of 1.79
eV (2.35), using the PBE (HSE06) [38] functional, where the VBM and CBM are
located at the $\Gamma$ and the K-point, respectively.

Figure 2: (a) Optimized structures, (b) electronic band structure of armchair
MoSi2N4 NR with different widths. (c) Variation of the band gap with respect
to the different widths. Figure 3: Charge density of valence band maximum
(VBM) and conduction band minimum (CBM) of Armchair MoSi2N4 NR for the (a)
$W=2$ and (b) $W=3$ widths (top and side views). (c) Density of states (DOS)
and projected DOS (PDOS).

##  III Armchair edge Nanoribbon

As shown in Fig. 1(c) and (d), the structure of the MoSi2N4 NRs is specified
with different widths. In the monolayer nanosheet, all atoms have the same
atomic environment which make their bands degenerate. However, in the NRs, the
existence of different environments for different rows of atoms changes the
degeneracy of the bands of the respective atoms, resulting in the presence of
numerous non-degenerate energy bands in the band structure.

The optimized atomic structure and electronic band structure for different
widths in the armchair edges are shown in Figs. 2(b-c), respectively. Notice
that the NRs are direct bandgap semiconductors, and we can see that the
bandgap with increasing increases with increasing width. Compared to the
monolayer nanosheet, formation of NRs create a change from an indirect
semiconductor behavior to direct gap. Focusing on the band structures of
MoSi2N4 NRs as illustrated in Fig. 2(b), it is found that both the valence
band maximum (VBM) and the conduction band minimum (CBM) locate at the
$\Gamma$-point in the Brillouin zone. Interestingly, the subbands near the
Fermi level get flatter as the width of NR increases. The phenomenon that
energy subbands near the Fermi level become flatter for wider nanoribbon has
also been observed in armchair graphene nanoribbons [39].

Also, as depicted in Fig. 2(c), the energy gap of MoSi2N4 NR tends to increase
more slowly over wider ribbon. The calculated band gaps are 0.7 eV (W=2), 0.88
eV (W=3) and 0.96 eV (W=4)

In Fig. 3 we show the density of states (DOS) and the electron density
distribution of the VBM and the CBM for two armchair NRs. Fig. 3(c) shows
spurious Mo-$d$/N-$p$ hybridization which because of $p$-$d$ repulsion pushes
the N-$p$ states higher in energy reducing $\Delta E$. Since the Mo-$d$/N-$p$
hybridization in armchair NR with $W=2$ is more than armchair NR with $W=3$,
energy reducing $\Delta E$ compete with effects of quantum confinement. This
effect, which can be traced to the self-interaction error, is over and above
the conventional DFT underestimation of band gaps in semiconductors[40].

The charge density of the VBM is concentrated inside the armchair MoSi2N4 NRs,
while the charge density of the CBM distributes towards the edges with
increasing width. This property suggests the potential for tailoring and
engineering of the transport by tuning the width. In the monolayer nanosheet,
the CBM and the VBM are located at the K-point and $\Gamma$-point,
respectively, while in the armchair MoSi2N4 NRs, both CBM and VBM are located
at the $\Gamma$-point. This transition from indirect to direct bandgap is the
effective consequence of quantum confinement along the $\Gamma$–K path in
armchair MoSi2N4 NRs. Regarding to the contribution of the atomic orbitals to
the formation of electronic bands of MoSi2N4 NRs, the image of the partial
density of states (PDOS) in Fog. 3(c) demonstrate that the Mo-$d$ orbitals
make a dominant contribution to the formation of electronic band, especially
the conduction band as well as the valence band close to the fermi level. In
the both cases of MoSi2N4 NRs as depicted in Fig. 3(c), the valence band is
formed from the main contributions of the Mo-$d$, Si-$p$, and N-$p$ orbitals.
In particular, except in the vicinity of the Fermi level, from $-0.2$ to
$-1.2$ eV, the N-$p$ orbitals’s contribution to the valence band is even
greater than that of other orbitals, including Mo-$d$ orbitals.

##  IV Zigzag edge nanoribbon

The scenario for zigzag MoSi2N4 NRs is totally different to the armchair NRs.
The band structure calculations in Fig. 4(a) shows metallic behavior for
zigzag NRs with sufficient states at the Fermi surface to satisfy the Stoner
criterion, thus the zigzag NRs exhibit magnetization. Total magnetizations for
zigzag NRs with widths 1, 2, 3, and 4 are 1.8, 1.7, 2.15, and 2.44 $\mu_{B}$,
respectively. The zigzag NRs with odd and even widths experience different
magnetic symmetries so that we should compare odd and even widths, separately.
For both groups, we can observe the total magnetization increases with the
width, where the spin density occurs at the edges of the zigzag NRs (see Fig.
4b-c). With increasing width of the zigzag NRs, the region of spin
polarization penetrates inside the zigzag NRs which results in higher
magnetization. The anisotropy observed in the different MoSi2N4 NRs, that is,
the spin-polarized magnetic zigzag NRs versus the non-magnetic semiconductor
armchair NRs, is attractive for spintronic applications. Difference from
armchair NRs, the band structures of the zigzag NRs show a metallic character
for both spin configurations as depicted in Fig. 4(a). The band structures of
zigzag NRs are asymmetric for all investigated ribbon-widths and spin
configurations. There are some energy levels (two or three) in each spin
configuration cross the Fermi level and eliminate the band gap of zigzag NRs.
Also, metallic characteristic of zigzag NRs is found in all investigated width
$W$ of nanoribbon $(W=1,2,3,4)$.

Figure 4: (a) Electronic band structure of zigzag MoSi2N4 NR for different
widths. (b) Contour plot of the electron localization function (ELF) of zigzag
NR for w=2. Red (blue) color indicates high (low) electron density. (c)
Difference spin density of zigzag NR for w=2. The green and yellow regions
represent the $\uparrow$ and $\downarrow$ spin states, respectively. The zero
of energy is set to Fermi-level. Figure 5: (a) Optimized structures of zigzag
MoSi2N4 NR with respect to (a) I, (b) II and (c) III configurations.
Electronic band structure with corresponding each NRs is shown in bottom
panel. The zero of energy is set to Fermi-level.

Investigating more, we specify two configuration, Figs. 5(a-c), near the
zigzag MoSi2N4 NRs with $W=2$, Fig. 4(b). As can be seen, in configuration I,
the total magnetization decreases to 0.95 $\mu_{B}$, while in configuration
III, the total magnetization vanishes and a tilted Dirac cone appears which is
promising for valley filtering in p-n junctions[41] and the generation of a
photocurrents[42]. The synthesis of this kind of Dirac point is challenging
[43] as they require materials whose constituent atoms are arranged in
lattices with intricate electron hopping[44]. In the configurations I and II,
some subbands across the Fermi level and close the energy gap leading to both
configurations preserving the metallic behavior as shown in Figs. 5(a,b).
Interestingly, the Dirac coin is found in the configuration III as illustrated
in Fig. 5(c). However, unlike for pristine graphene, the Dirac coin for
MoSi2N4 NR as presented in Fig. 5(c) is anisotropic because the linear
dispersions along $\Gamma$–K and its perpendicular direction are different.
This may lead to the anisotropy in the Fermi velocities in the configuration I
of MoSi2N4 NR which is due to the nature of one-dimensional nanoribbon
structure. Half-metallic behavior with anisotropic Dirac point was also found
in zigzag graphene NRs on graphene [45]. This finding could be useful in
applications for electronic devices.

##  V Conclusion

In conclusion, we investigated the electronic properties of MoSi2N4
nanoribbons using first-principles calculations. The electronic properties
showed spin-polarization in zigzag-edges MoSi2N4 NRs and semiconducting
character in armchair-edges MoSi2N4 NRs. In armchair edges of MoSi2N4
nanoribbons, we identify an indirect to direct band gap shift compared to the
MoSi2N4 monolayer, where the bandgap increase with increasing width. The
appearance of the Dirac-semimetal in one type of MoSi2N4 NRs with zigzag-edges
is a wonderful feature, which can give rise to many interesting physical
properties, such as quantum electronic transport.

##  VI Declaration of competing interest

The authors declare that they have no known competing financial interests or
personal relationships that could have appeared to influence the work reported
in this paper.

## ACKNOWLEDGMENTS

This work was supported by the National Research Foundation of Korea (NRF)
grant funded by the Korea government (MSIT) (NRF-2015M2B2A4033123).

## DATA AVAILABILITY

The data that support the findings of this study are available from the
corresponding author upon request.

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An extension of the low-rank Lyapunov ADI to non-zero initial values and its applications

$\dagger\ast$]Jonas Schulze 0000-0002-2086-7686
$\dagger$]Jens Saak 0000-0001-5567-9637
[$\dagger$]Max Planck Institute for Dynamics of Complex Technical Systems,
Sandtorstr. 1, 39106 Magdeburg, Germany.
[$\ast$]Corresponding author<EMAIL_ADDRESS>
J. Schulze, J. Saak

15A24, 65F10, 65F45, 65F55

We introduce the notion of fully commuting splitting schemes to solve arbitrary linear systems,
and derive the ADI method in that context.
This allows us to extend the low-rank  ADI to non-zero initial values.
Furthermore, we generalize the permutation invariance of ADI iterates
to a more general class of algorithms,
as well as the existence of a real-valued ADI double-step for complex-conjugated shifts
to arbitrary linear systems.


# Smart Contracts, Smarter Payments: Innovating Cross Border Payments and
Reporting Transactions

Maruf Ahmed Mridul  Department of Computer Science
Rensselaer Polytechnic Institute
Troy, NY, USA
<EMAIL_ADDRESS>Kaiyang Chang  Aparna Gupta  Department of Computer Science
Rensselaer Polytechnic Institute
Troy, NY, USA
<EMAIL_ADDRESS>Lally School of Management
Rensselaer Polytechnic Institute
Troy, NY
<EMAIL_ADDRESS>Oshani Seneviratne  Department of Computer Science
Rensselaer Polytechnic Institute
Troy, NY, USA
<EMAIL_ADDRESS>
###### Abstract

The global financial landscape is experiencing significant transformation
driven by technological advancements and evolving market dynamics. Moreover,
blockchain technology has become a pivotal platform with widespread
applications, especially in finance. Cross-border payments have emerged as a
key area of interest, with blockchain offering inherent benefits such as
enhanced security, transparency, and efficiency compared to traditional
banking systems. This paper presents a novel framework leveraging blockchain
technology and smart contracts to emulate cross-border payments, ensuring
interoperability and compliance with international standards such as ISO20022.
Key contributions of this paper include a novel prototype framework for
implementing smart contracts and web clients for streamlined transactions and
a mechanism to translate ISO20022 standard messages. Our framework can provide
a practical solution for secure, efficient, and transparent cross-border
transactions, contributing to the ongoing evolution of global finance and the
emerging landscape of decentralized finance.

###### Index Terms:

Blockchain, Smart Contracts, Cross-Border Payments, ISO20022, FinTech,
Interoperability, Decentralized Finance.

##  I Introduction

Cross-border payments face several significant challenges affecting
efficiency, cost, and accessibility. Traditional international transactions
are often slow, taking days to complete due to the involvement of multiple
intermediaries such as correspondent banks [1]. Each intermediary adds time
and increases transaction fees, making cross-border payments expensive.
Moreover, the lack of transparency in the process can lead to uncertainties
regarding transaction status and final settlement times. Regulatory compliance
is another hurdle, as transactions must adhere to the varying financial
regulations of each country involved, which includes fulfilling anti-money
laundering (AML) and combating the financing of terrorism (CFT) requirements.
Additionally, currency conversion in these transactions introduces further
complexity and cost, with fluctuating exchange rates potentially affecting the
final amounts received by beneficiaries. These issues create a cumbersome,
opaque, and costly process that impacts consumers, businesses, and financial
institutions engaged in global trade and remittances.

The quest for a solution to this problem has been ongoing throughout
international commerce, where the need to facilitate payments across borders
has always been critical. In response to these enduring challenges, emerging
fintech solutions, particularly those involving Decentralized Finance (DeFi)
using blockchain technology, could provide promising avenues that could
potentially revolutionize cross-border payments within the next decade [2].
Blockchain’s inherent attributes—decentralization, immutability, and
transparency—offer a new paradigm for addressing the inefficiencies and
complexities of traditional payment systems.

Recognizing the transformative potential of blockchain technology, we
contribute to advancing cross-border payment systems by developing a framework
that leverages blockchain technology and smart contracts to enable seamless,
secure, and efficient international transactions. Our contributions include:

  * •

Proposing a novel framework for cross-border payments leveraging blockchain
technology in an interoperable ecosystem.

  * •

Implementation of the proposed framework, integrating smart contracts and web
clients to streamline transactions and ensure transparency, efficiency, and
security.

  * •

Development of mechanisms for translating ISO20022 standard messages using a
web client, facilitating seamless communication and interoperability across
disparate systems.

##  II Background

###  II-A Blockchain Technologies

Over the past decade, technological advancements have reshaped the landscape
of these transactions, with blockchain technology emerging as a disruptive
force. One of the notable shifts has been the growing prominence of blockchain
technology in facilitating cross-border payments [3]. Blockchain, originally
introduced as the underlying technology behind cryptocurrencies like Bitcoin
[4], has evolved into a versatile platform with applications across various
sectors, including finance. The decentralized and immutable nature of
blockchain offers inherent advantages for cross-border payments, promising
enhanced security, transparency, and efficiency compared to traditional
banking systems. As a result, academia and industry have turned their
attention to exploring blockchain’s potential to revolutionize international
financial transactions.

Originally defined by Nick Szabo [5] and popularized by Vitalik Buterin on the
Ethereum ecosystem [6], smart contracts are self-executing code that is
deployed across a distributed, decentralized blockchain network, which results
in transactions that are trackable and irreversible. Since smart contracts
automate and enforce the terms of agreements without intermediaries, they
offer potential cost savings and efficiency gains in international
transactions [7]. Meanwhile, DeFi protocols leverage blockchain technology to
create decentralized financial ecosystems that offer open, interoperable, and
transparent financial services [8]. However, there is a critical
interoperability issue among different blockchain platforms, with several
blockchain interoperability platforms developed to address the challenges and
risks associated with adopting a single blockchain implementation [9]. In our
CBPR+ implementation, we assumed EVM-compatible interoperable blockchains
would interact seamlessly to ensure compliance with international standards
such as ISO20022.

###  II-B Cross-Border Payments and Reporting Plus (CBPR+)

CBPR+ is an industry-led initiative that aims to standardize global payment
transactions and harmonize standards. It focuses on improving the efficiency
of cross-border payments. It utilizes the ISO20022 [10] messaging format to
ensure a consistent customer experience across geographical boundaries.
ISO20022 offers a richer and more flexible standard compared to its
predecessors, facilitating innovation and efficiency in cross-border payment
systems. Adopting international standards, such as ISO20022, is essential in
standardizing communication protocols and data formats in financial
transactions [11]. The adoption and impact of ISO20022 in facilitating
effective communication and standardization in financial transactions are
critically examined by Bouille and Haase [11] and further elaborated by McGill
[10]. Their discussions emphasize the importance of this standard in ensuring
interoperability and efficiency, which is crucial for the framework our
research seeks to develop.

The CBPR+ process involves a series of ISO20022 message exchanges facilitating
seamless fund transfers across borders. Key messages include but are not
limited to the following:

  * •

pacs.008: Customer Credit Transfer Initiation message

  * •

pacs.002: Payment Status Report message

  * •

pacs.004: Payment Return message

The term pacs.008 is a specific identifier within the ISO 20022 standard for
financial messaging, defining various messages for financial transactions. The
abbreviation pacs stands for “Payments Clearing and Settlement,” and the .008
identifies the specific message type for customer credit transfers. These
messages form the foundation of transaction management within CBPR+, covering
initiation, status reporting, and error handling.

###  II-C Blockchain for Cross Border Payments

Emerging technologies like smart contracts and DeFi present new opportunities
for streamlining cross-border payments. However, despite the promise of
blockchain and related technologies, challenges persist in achieving
widespread adoption and scalability in cross-border payments. Many issues,
such as transaction finality, regulatory compliance, and user experience,
remain areas of active research and development [12, 1]. In exploring
blockchain technology for cross-border payments, blockchain interoperability
emerges as a crucial element, profoundly discussed by Mohanty et al. [13] and
Belchior et al. [14]. These studies underscore the necessity of seamless
integration across different blockchain systems to enable more robust and
sustainable financial infrastructures, which directly informs the objectives
of our project.

Deng [3] analyzes the application modes and advantages of blockchain
technology in cross-border payments, highlighting its potential to address the
shortcomings of traditional cross-border trade. Deng’s insights provide
valuable context for understanding the challenges and opportunities of
leveraging blockchain for international transactions. Similarly, Isaksen [15]
investigates how blockchain technology may benefit banks’ positions in the
cross-border payment segment. By exploring the potential benefits and
challenges of utilizing blockchain in financial institutions, Isaksen offers
insights into the practical implications and adoption barriers of blockchain
technology in real-world financial systems. This understanding is crucial for
designing solutions that align with the needs and constraints of existing
financial infrastructures. He [1] analyzes the broader context of digitization
in cross-border payments, noting significant global efforts to enhance
transactional efficiency. This perspective is valuable for understanding the
environmental and systemic changes influencing our research direction.
Meanwhile, Le Quoc et al. [16] offer a specific example of blockchain
application in the letter-of-credit system for international trade, presenting
a case study that mirrors the potential applications of our research. Zilnieks
and Erins [12] explore cross-chain bridges to standardize distributed ledger
technologies, a discussion particularly relevant to our project’s aim to
enable smooth interoperable transactions across different blockchain
platforms. Another related work by Schär [8] discusses DeFi, providing
insights into the infrastructure and potential of blockchain-based financial
markets to offer more open, interoperable, and transparent services. Together,
these contributions provide a comprehensive backdrop against which our
research is situated. They illuminate the current state of blockchain
technology in financial applications and highlight the diverse approaches and
potential enhancements that our project could integrate. By leveraging these
insights, our framework aims to contribute effectively to the evolving
landscape of global financial transactions, offering solutions that are not
only technologically advanced but also aligned with global financial practices
and standards.

Our proposed solution aims to enable seamless, secure, and efficient
international transactions leveraging blockchain technologies and existing
standards to provide interoperability with existing systems and regulatory
compliance. At the heart of our transaction system lies the smart contracts,
robust and autonomous entities deployed on Ethereum Virtual Machine (EVM)
compatible blockchains to demonstrate the system’s interoperability for
smarter payments in cross-border scenarios. Our smart contract-based
implementation embodies the principles of transparency, efficiency, and
security within the decentralized network and is also interoperable through
standards.

##  III Methodology

Our methodology includes a blockchain-based framework to replicate and enhance
the CBPR+ process. It uses smart contracts and web clients to streamline and
secure cross-border transactions within a decentralized environment. Within
our framework, the smart contract serves as an autonomous agent managing the
logic and state of each transaction, while the web client acts as the
interface between traditional banking systems and a blockchain. Together, they
emulate the CBPR+ process in a distributed ledger environment.

###  III-A Detailed System Architecture

To illustrate our framework’s functionality, let’s consider a simulated CBPR+
transaction scenario involving multiple banks across different blockchains.
Refer to Figure 1 for a depiction of the following discussion. The workflow
initiates with the debtor, who provides transaction instructions. The debtor’s
agent bank (Bank A) communicates these instructions to its corresponding smart
contract, which debits the debtor’s account and emits a confirmation message.
Subsequently, the web client generates an ISO20022 pacs.008 message for the
next agent and triggers the respective smart contract. This process iterates
sequentially through intermediary banks until reaching the creditor agent,
concluding the transaction.

Figure 1: Workflow of the Framework for an Example Transaction involving a
Debtor and Creditor for a Cross Border Payment.

####  III-A1 Smart Contracts

Engineered to emulate and enhance the CBPR+ methodology, the smart contracts
encapsulate the essential functions and rules governing cross-border payment
transactions, from initialization and access control to transactional
validation and event-driven communication.

  * •

Initialization and Access Control: This smart contract establishes an access
control hierarchy upon deployment, designating the deploying address as the
owner with administrative privileges. Role-based access control mechanisms
ensure that only authorized entities can execute critical functions that alter
the contract’s state or configuration. By enforcing access restrictions, the
contract safeguards against unauthorized manipulation or misuse, preserving
the integrity and reliability of the transaction system.

  * •

Account Management: This smart contract manages two distinct account types:
_Nostro Accounts_ and _General Accounts_. Nostro Accounts facilitate holding
funds in foreign currencies, essential for cross-border transactions, while
General Accounts cater to everyday transactional needs. Account creation
within the contract involves specifying a unique account number and
distinguishing between account types. The specific account management actions
include mapping and tracking account addresses, verifying account existence
and uniqueness, and maintaining a state variable for tracking available funds
in each account.

  * •

Transaction Details: _Solidity structs_ define structured data entities to
capture and process transaction details. These structs encapsulate essential
transactional information, including currency and amounts (Amount), debtor
instructions (DbtrInstruction), and comprehensive transaction metadata
(MsgInfo). Mirroring the ISO20022 message structures, these defined structs
enable the seamless integration of cross-border payment transactions within
the blockchain framework. For example, the following code snippet shows the
DbtrInstruction struct in the smart contract.

struct DbtrInstruction { Amount IntrBkSttlmAmt; address DbtrAgt; string
DbtrAcct; string DbtrAgtIsoMsg; address NxtAgt; }

For this specific data structure, the web client extracts the required
information from the XML-formatted pacs.008 message using the following Python
function, where the specific attributes correspond directly to the ISO20022
data schema to facilitate ease of integration and maintain consistency. This
implementation enhances interoperability and compatibility with external
systems and messaging standards by standardizing transactional data formats.

def get_debtor_instructions(xml_data): dict_data = convert_to_dict(xml_data)
dbtr_instruction = { "IntrBkSttlmAmt": dict_data[’Document’]
[’FIToFICstmrCdtTrf’][’CdtTrfTxInf’] [’IntrBkSttlmAmt’], "DbtrAgt":
dict_data[’Document’] [’FIToFICstmrCdtTrf’][’CdtTrfTxInf’]
[’DbtrAgt’][’FinInstnId’][’BICFI’], "DbtrAcct": dict_data[’Document’]
[’FIToFICstmrCdtTrf’][’CdtTrfTxInf’] [’DbtrAcct’][’Id’][’Othr’][’Id’],
"DbtrAgtIsoMsg": xml_data, "NxtAgt": dict_data[’Document’]
[’FIToFICstmrCdtTrf’][’GrpHdr’] [’InstdAgt’][’FinInstnId’][’BICFI’] } return
dbtr_instruction

  * •

Transactional Methods: The key to the smart contract’s functionality is
transactional methods, which are responsible for initiating, validating, and
processing cross-border payment transactions. The functions in the smart
contract, alongside making the transactions, serve as gatekeepers, ensuring
the security, integrity, and validity of fund transfers. They validate account
existence, balances, and transaction parameters before initiating fund
transfers. They also incorporate comprehensive checks such as control sum
verification and nostro account balance validation.

  * •

Event-Driven Confirmation Mechanism: The smart contract employs an event-
driven confirmation mechanism to facilitate real-time communication and
transactional synchronization. At crucial transactional milestones, the
contract emits events such as MakeTransfer and PassISOMessageAlong, signaling
transaction state changes and facilitating communication with external
systems, including web clients that correspond to different organizations
within our simulated system. These events serve as immutable audit trails,
providing a transparent history of transaction actions and enabling
stakeholders to verify transactional integrity and compliance with regulatory
standards. By leveraging event-driven mechanisms, the contract enhances
transparency, accountability, and trust within the cross-border payment
ecosystem.

####  III-A2 Web Client

The web client plays an important role within our framework, bridging
traditional banking systems and the decentralized blockchain network. Its
primary function is to orchestrate the flow of cross-border payment
transactions, ensuring seamless communication, data integrity, and
transactional transparency. The web client’s major roles are as follows:

  * •

Message Parsing and Construction: This component ensures the accurate
interpretation and transmission of ISO20022 messages within our framework. The
web client dissects incoming pacs.008 messages, extracting essential
transaction details such as the debtor’s instructions, payment amounts, and
beneficiary information.

Upon parsing the incoming message, the web client structures all the
transaction requests in a format compatible with the smart contract’s defined
data structures. This process involves mapping parsed data to corresponding
fields within the DbtrInstruction struct, ensuring integration with the
contract’s transactional methods.

Moreover, the web client continuously monitors contract events to facilitate
the modification of ISO messages. When triggered by events such as
MakeTransfer or PassISOMessageAlong emitted by the smart contract, the web
client takes in the updated ISO message as an instruction set for the next
agent in the process.

  * •

Transaction Initiation and Propagation: Facilitating transaction initiation
and propagation is a core function of the web client, serving as the
intermediary between user instructions and smart contract execution. Upon
receiving debtor instructions, the web client initiates transactions by
interfacing with the initiate_transfer function of the smart contract.

In this process, the web client extracts pertinent details from the debtor’s
instructions, such as payment amounts, beneficiary information, and
transaction metadata. It then passes this structured data to the smart
contract, initiating the transaction. Concurrently, the web client monitors
transaction progress through emitted contract events, updating transactional
states and facilitating subsequent actions. As transaction events unfold, the
web client dynamically propagates transaction updates to relevant parties
within the blockchain network.

  * •

Event Handling: The web client’s event-handling capabilities are important in
maintaining transactional integrity and facilitating real-time communication
between the blockchain framework and external systems. Designed to respond to
contract events triggered during transaction execution, the web client employs
event-driven mechanisms to synchronize transactional states and propagate
updates.

Upon receiving event notifications from the smart contract, the web client
dynamically triggers corresponding actions based on predefined event handlers.
For instance, when notified of a MakeTransfer event indicating the need to
craft an outgoing ISO message, the web client invokes message construction
routines, incorporating transactional details and metadata.

Similarly, PassISOMessageAlong events signal the requirement to transmit
updated ISO messages to subsequent transactional participants, prompting the
web client to initiate message transmission protocols.

  * •

Interaction with Smart Contract: The web client and smart contract form our
framework’s backbone of transactional operations. Through seamless
communication channels, the web client orchestrates transaction execution and
state management, leveraging the capabilities of the underlying smart contract
infrastructure.

When triggered by user instructions or contract events, the web client
interfaces with the smart contract through structured function calls, passing
relevant transactional data and metadata. These function calls invoke
predefined contract methods responsible for transaction initiation,
validation, and propagation, ensuring the seamless execution of cross-border
payment transactions.

Furthermore, the web client monitors contract events, dynamically responding
to state changes and transactional progress. Upon receiving event
notifications from the smart contract, the web client initiates corresponding
actions, updating transactional states and propagating transactional updates
to relevant stakeholders.

The symbiotic relationship between the web client and the smart contract
facilitates the seamless execution and management of cross-border payment
transactions within the blockchain framework, ensuring transactional
integrity, transparency, and efficiency.

###  III-B Security Protocols

Our framework incorporates comprehensive security measures at various levels
of the transactional lifecycle to safeguard transactional integrity and
protect sensitive financial data.

  * •

Access Control: Our smart contract implements stringent access control
mechanisms, restricting critical functions to authorized entities such as
account holders or institutional owners. By validating user identities and
permissions, the contract ensures that only authorized parties can execute
sensitive operations, mitigating the risk of unauthorized access or
manipulation.

  * •

Transaction Integrity: Leveraging structured data and Solidity’s type system,
our smart contract enforces transaction validation protocols, verifying
transactional parameters and data integrity before processing. By encoding
transactions within predefined data structures and enforcing type validation,
the contract mitigates the risk of fraudulent or malicious transactions,
safeguarding transactional integrity and consistency.

  * •

Audit Trails: Our framework maintains comprehensive audit trails through
event-driven mechanisms, providing transparent and verifiable transaction
histories. Contract events such as MakeTransfer and  PassISOMessageAlong are
recorded in immutable audit logs, capturing key transactional actions and
state changes. These audit trails enable stakeholders to trace transactional
activities, verify compliance with regulatory standards, and detect anomalous
behavior.

##  IV Evaluation

In this section, we evaluate the performance and cost-effectiveness of our
blockchain-based framework for CBPR+. We present gas consumption metrics
obtained from a local development environment using the Ganache Command Line
Interface111Ganache (https://archive.trufflesuite.com/ganache) is a command-
line tool designed for Ethereum developers to create and manage personal
Ethereum blockchains for testing and development purposes. and the live
testnet deployment on the Sepolia test Ethereum network222Sepolia
(https://sepolia.etherscan.io) is one of the several test networks used by the
Ethereum blockchain for development and testing purposes. Unlike the Ethereum
mainnet, where real transactions occur with actual economic value, Sepolia
provides a controlled environment where developers can test new applications,
smart contracts, and upgrades without financial risk. . Additionally, we
discuss the implications of gas consumption on transaction fees and contract
deployment costs.

###  IV-A Gas Consumption Metrics

Gas consumption metrics provide insights into the computational efficiency and
resource utilization of smart contract operations within the blockchain
network. Table I summarizes the gas consumption statistics obtained from our
gas report analysis during testing.

TABLE I: Gas Consumption Metrics (Gas Units) Function Name | min | avg | median | max | # calls
---|---|---|---|---|---
create_account | 26660 | 43201 | 46560 | 69676 | 17
deposit | 30351 | 38939 | 38939 | 47527 | 12
get_balance | 921 | 921 | 921 | 921 | 14
initiate_transfer | 121580 | 121580 | 126279 | 131428 | 12
make_transfer | 135213 | 135213 | 140352 | 146192 | 12

The gas report provides detailed information on gas consumption for each smart
contract function, including minimum, average, median, and maximum gas costs
per function call. These metrics offer insights into the computational
complexity and resource requirements of individual operations within the smart
contract.

###  IV-B Transaction Fees and Contract Deployment Costs

Transaction fees and contract deployment costs are critical considerations for
assessing the economic viability of blockchain-based solutions. The following
metrics indicate the cost of executing transactions and deploying smart
contracts on the Sepolia Testnet. The deployed contract address on Sepolia is
0x7bD82fFA76A4a45ddF468c7106536354c9cc6909.

  * •

Transaction Fees: 0.003543387976528597 ETH

  * •

Gas Fees: 3.095497367 Gwei

Transaction fees are calculated based on the gas consumed by each transaction,
while gas fees represent the price per unit of gas specified in Gwei333GWei,
which is a commonly used unit of measurement in Ethereum. Wei is the smallest
denomination of Ether, the native cryptocurrency of Ethereum. One GWei is
equivalent to one billion wei..

##  V Discussion

Our implementation of the blockchain-based framework for cross-border
payments, leveraging smart contracts and web clients, represents a significant
step towards enhancing the efficiency and security of global financial
transactions. By replicating and streamlining the CBPR+ process within a
decentralized environment, our framework offers a promising solution to the
challenges associated with traditional cross-border payment systems.

###  V-A Flexibility and Customizability

One key advantage of our framework is its flexibility and customizability,
which allows it to accommodate diverse transactional requirements and be
robust against any changes to regulatory frameworks governing smart contract
applications. Financial institutions deploying our framework have the
flexibility to customize the smart contract logic and message parsing rules
according to their specific needs and compliance requirements. As long as the
financial institutions can determine which portions of the ISO20022 messages
are necessary to process their existing transactions, they can easily modify
the extracted message fields and implement the smart contract logic within our
framework to achieve their specific use cases. Additionally, financial
institutions can ensure compliance with various regulatory requirements by
embedding specific rules and standards directly into the smart contracts. This
customization flexibility ensures the framework remains agile and responsive
to evolving market demands and regulatory changes. It is important to note
that legacy systems must be made blockchain-compatible to integrate with our
framework. To facilitate smooth integration with existing legacy systems in
financial institutions, a future version of our framework could include
Web3-enabled adapters or middleware solutions that bridge the gap between the
legacy infrastructure and our smart contract-based framework, ensuring
seamless data flow and operational continuity.

###  V-B Smart Contract Logic

The smart contract is the backbone of our transaction system, encapsulating
the core functions and rules governing cross-border payments. However, the
logic embedded within the smart contract is scenario-dependent and may vary
based on the type of transaction and regulatory framework. Our implementation
provides a starting point for financial institutions to build upon, allowing
them to update and modify the smart contract logic to align with their unique
business processes, use cases, and regulatory obligations. However, we must
consider certain factors when implementing smart contracts across various
blockchain platforms concerning their termination mechanisms [17], especially
in light of regulatory changes such as the EU Data Act. We may also need to
handle unexpected situations that may arise during normal business operations
relating to cross-border payment activities, such as account recovery in case
of a catastrophic failure in one of the entities engaged in the trade [18]. In
such cases, we could leverage supplementary techniques to strengthen the smart
contract logic, such as computational social choice mechanisms [19] and
ontology-aided mechanisms [20]. This flexibility empowers financial
institutions to adapt the framework to their specific use cases while
maintaining compliance with relevant regulations.

###  V-C Message Parsing and Information Extraction

Similarly, the web client’s predefined instructions for message parsing and
information extraction represent a starting point for processing ISO20022
messages within the blockchain framework. However, the specific information
required for transaction processing may vary depending on the transaction type
and regulatory requirements. Financial institutions deploying our framework
must assess their specific information needs and customize the message parsing
rules accordingly. Providing an easily configurable and extensible framework
empowers financial institutions to tailor the system to their unique
operational requirements while ensuring interoperability and compliance with
industry standards.

Drawing parallels from our prior work, the BlockIoT project introduced a
robust mechanism for integrating data from various sources in an interoperable
manner that allows seamless incorporation of diverse data types, ensuring
comprehensive data availability for subsequent processing in healthcare
scenarios [21]. Similarly, in our financial framework, integrating various
data sources—such as customer information, transaction history, and regulatory
guidelines—can enhance the completeness and accuracy of cross-border payment
transactions. Additionally, these information extraction processes can be made
more streamlined using an off-chain read-execute-transact-erase-loop [22],
which will ensure that only the necessary data is processed and stored on-
chain, optimizing resource utilization and maintaining privacy, while being
up-to-date and providing higher throughput.

##  VI Related Work

Emerging technologies and innovative approaches also significantly enhance the
security and efficiency of cross-border payments. For instance, Vinayak et al.
[7] propose a solution for the automation and transparency of smart contracts
on distributed ledgers, similar to our work. However, our research offers a
more comprehensive and globally applicable solution compared to their narrower
focus on collateral management within financial institutions. Furthermore,
Narendra and Aghila [23] focus on a quantum-resistant smart contract model,
suggesting a frontier for future-proof financial transactions prioritizing
security. However, their model does not address interoperability, a key aspect
of our framework designed to ensure seamless global transactions. Flynn et al.
[24] presents a data- and language-agnostic system designed to integrate and
analyze data from various sources in DeFi with interoperability and
scalability in mind, where they showcase how different programming languages
can interact with a unified backend system. However, unlike their work, we
have focused on international standards such as ISO20022 in achieving
interoperability. Li et al. emphasize using standardized ontological concepts
to ensure interoperability and trustworthy data sharing across institutions
and mining transaction logs to detect anomalies and misuse [25]. In our
framework for cross-border payments, we aim to achieve similar
interoperability and compliance by leveraging international standards such as
ISO20022 and blockchain-based transactions.

Additionally, there are several efforts to automatically generate smart
contracts, which simplifies the implementation process. For example, Choudhury
et al. [26], Tateishi et al. [27], and Frantz and Nowostawski [28] have all
contributed to this field, each focusing on distinct applications and methods.
Yet, all share the common objective of translating business logic into
executable code. Another such work is the methodology to automate construction
payments by formalizing them into smart contracts proposed by Luo, Han, et al.
[29]. However, while these automation approaches facilitate smart contract
creation, they lack the precision needed for sensitive tasks like cross-border
payments. Given the complexity and critical importance of financial standards
like ISO20022 in enabling cross-border interoperable financial transactions,
our framework’s tailored approach to ISO20022 translations ensures a higher
level of expressivity and compliance with regulatory bodies. Furthermore, Kang
et al. [30] investigate the potential of Large Language Models (LLMs) to
automate health insurance processes by generating smart contracts from textual
policies. Van Woensel et al. [31] explore translating high-level decision
logic from clinical practice guidelines into executable smart contracts on
blockchain platforms like Ethereum and Hyperledger Fabric. Both these works
emphasize transforming domain-specific rules and guidelines from healthcare
into smart contracts, similar to our goal of implementing cross-border
payments and reporting transactions in the finance domain.

##  VII Conclusion

Our proposed blockchain-based framework offers an innovative solution for
enhancing the efficiency and security of cross-chain transactions. By
integrating smart contracts and web clients, we align closely with the CBPR+
initiative and employ the ISO20022 messaging format to guarantee a uniform
user experience globally. Our framework facilitates a seamless, secure, and
efficient mechanism for managing cross-chain transactions, which are crucial
in today’s globalized blockchain economy.

The detailed system architecture and security protocols we have developed
ensure that our framework replicates and augments the current CBPR+ process.
Through the strategic use of smart contracts on an EVM-compatible blockchain,
we enforce stringent access controls and transaction integrity while enabling
real-time transactional updates via an advanced event-driven architecture.
This process results in a robust system that reduces risks and enhances
transparency throughout the transaction lifecycle. Additionally, the
flexibility embedded within our smart contract design allows for custom
adaptations to meet diverse regulatory and institutional needs, making our
system highly adaptable to future changes in the global financial landscape.

Our research contributes to the evolving financial technology landscape by
providing a scalable, secure, and efficient framework for cross-chain
transactions. The adoption of this framework by financial institutions and
regulatory bodies can lead to significant improvements in cross-border payment
processes, reducing transaction times and costs while enhancing compliance and
security. Furthermore, by demonstrating the feasibility and benefits of a
blockchain-based approach, we pave the way for future innovations that can
build on our foundational work.

Future research could explore the integration of advanced machine-learning
techniques for real-time fraud detection and anomaly monitoring within the
transaction process. Additionally, expanding the framework to support multiple
non-EVM blockchain platforms could further enhance interoperability and user
adoption. Collaborations with regulatory bodies to refine and standardize
smart contract protocols will be essential to ensure the widespread acceptance
and reliability of this technology.

In summary, our blockchain-based framework offers a flexible, customizable,
and secure solution for cross-border payments, addressing the inefficiencies
and complexities of traditional financial (TradFi) systems. By integrating
smart contracts, web clients, and advanced data processing techniques, our
framework sets a new standard for global financial transactions, promoting
transparency, compliance, and efficiency. This innovation bridges the gap
between TradFi and DeFi, leveraging the strengths of blockchain technology to
enhance financial operations in both domains. By providing a robust,
adaptable, and secure solution, we contribute to the broader goal of creating
a more transparent and efficient global financial system, which will
ultimately benefit consumers, financial institutions, and regulatory
authorities alike. By adopting our framework, financial institutions can
benefit from the robustness and transparency of DeFi while maintaining the
regulatory compliance and operational stability essential to TradFi,
ultimately resulting in a more integrated and efficient global financial
ecosystem.

## Resources

The source code of our implementation is available at
https://github.com/blockchain-interoperability/bi-in-finance, along with a
video demonstration of an example transaction using our implemented framework.

## Acknowledgments

The authors acknowledge the support from NSF IUCRC CRAFT Center research grant
(CRAFT Grant #22008) for this research. The opinions expressed in this
publication do not necessarily represent the views of NSF IUCRC CRAFT. We are
also grateful for the advice from our CRAFT Industry Advisory Board members in
shaping this work, especially the input from Jack Pouderoyen and Giri
Krishnapillai from SWIFT.

## References

  * [1] D. He, “Digitalization of cross-border payments,” _China Economic Journal_ , vol. 14, no. 1, pp. 26–38, 2021.
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