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Keywords = Quantum Hall Effect

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10 pages, 2219 KB  
Article
Electronic and Magnetic Properties of Fluorinated Transition Metal Dichalcogenide 1T-MX2F2 (X = S, Se, Te) Monolayers
by Lixia Zheng, Chenzhi Liu, Yunfei Gao, Aolin Li, Haiming Duan and Fangping Ouyang
Nanomaterials 2026, 16(4), 256; https://doi.org/10.3390/nano16040256 - 15 Feb 2026
Viewed by 473
Abstract
Two-dimensional transition metal dichalcogenides (TMDCs) have attracted worldwide attention due to their rich physical and chemical properties. How to regulate their electronic structures to meet different application requirements is a crucial issue. In this work, based on first-principle calculations, we demonstrate that surface [...] Read more.
Two-dimensional transition metal dichalcogenides (TMDCs) have attracted worldwide attention due to their rich physical and chemical properties. How to regulate their electronic structures to meet different application requirements is a crucial issue. In this work, based on first-principle calculations, we demonstrate that surface fluorination can be a powerful method for tailoring the electronic and magnetic properties of TMDC monolayers. The fluorinated T-MX2F2 (X = S, Se, Te) monolayers cover semiconductors, half-metals, semimetals, and half-semimetals. In particular, monolayer T-CrS2F2 is a half-semimetal, and the spin–orbit coupling effect changes it to a quantum anomalous Hall insulator. Monolayer T-HfS2F2 is a non-magnetic semimetal, and monolayer T-CoS2F2 is a half-metal. These findings not only suggest that fluorination can dramatically alter the electronic properties of two-dimensional TMDCs but also provide a new research platform for developing nanoelectronic devices. Full article
(This article belongs to the Special Issue Theoretical Calculations and Simulations of Low-Dimensional Materials)
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15 pages, 4564 KB  
Article
Experimental Evidence of a Dirac Gap Opening in Carbon-Doped Topological Insulator Bi2Se3
by Qiya Liu, Xinsheng Yang and Min Zhang
Nanomaterials 2026, 16(3), 205; https://doi.org/10.3390/nano16030205 - 5 Feb 2026
Cited by 1 | Viewed by 514
Abstract
Magnetic topological insulators (TIs) are promising candidates for realizing the quantum anomalous Hall effect (QAHE) and advancing the development of next-generation low-energy transistors and electronic devices. Doping Bi2Se3 with nano-carbon can introduce magnetic order and open the Dirac gap without [...] Read more.
Magnetic topological insulators (TIs) are promising candidates for realizing the quantum anomalous Hall effect (QAHE) and advancing the development of next-generation low-energy transistors and electronic devices. Doping Bi2Se3 with nano-carbon can introduce magnetic order and open the Dirac gap without introducing extrinsic magnetic impurities. In this work, the C0.06Bi2Se3 single crystal was prepared using the Bridgman method, and their electrical and magnetotransport properties were systematically investigated. Temperature-dependent resistivity and magnetoresistance measurements revealed a magnetic-field-induced metal–insulator-like transition near 152 K. Angle-resolved photoemission spectroscopy (ARPES) detected an energy gap of about 43 meV at the Dirac point, confirming that carbon doping modulates the surface state and opens the gap. Pronounced Shubnikov–de Haas oscillations indicate high carrier mobility in C0.06Bi2Se3. Furthermore, the temperature-dependent Kerr spectra shows that the spin relaxation behavior of C0.06Bi2Se3 differs significantly from that of pure Bi2Se3; the relaxation process of spin electrons from the surface state (τs) dominates the spin dynamics and exhibits distinct trends around 30 K and 150 K due to the interplay of the Dirac gap and impurity-induced states. These results demonstrate the potential of magnetic topological insulator C0.06Bi2Se3 for novel electronic and spintronic applications. Full article
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10 pages, 652 KB  
Article
Magnetotransport and Magneto-Thermoelectric Properties of the Nodel-Line Semimetal SnTaS2
by Long Ma, Hao Tian, Xiaojian Wu and Dong Chen
Materials 2026, 19(3), 556; https://doi.org/10.3390/ma19030556 - 30 Jan 2026
Viewed by 415
Abstract
Topological semimetals with nontrivial band structures host a variety of unconventional transport phenomena and have attracted significant attention in condensed matter physics. SnTaS2, a recently proposed topological nodal-line superconductor with a centrosymmetric layered structure, provides an ideal platform to explore the [...] Read more.
Topological semimetals with nontrivial band structures host a variety of unconventional transport phenomena and have attracted significant attention in condensed matter physics. SnTaS2, a recently proposed topological nodal-line superconductor with a centrosymmetric layered structure, provides an ideal platform to explore the interplay between topology and electronic transport. Here, we report a comprehensive study of the normal-state magnetotransport and magneto-thermoelectric properties of SnTaS2 single crystals. We observed large magnetoresistance and nonlinear Hall resistivity at low temperatures, which can be well described by a two-band model, indicating the coexistence of electron and hole carriers. The Seebeck and Nernst coefficients were found to exhibit pronounced and nonmonotonic magnetic field dependences at low temperatures, consistent with multiband transport behavior. Moreover, clear quantum oscillations with a single frequency are detected in both electrical and thermoelectric measurements. Analysis of the oscillations reveals a small effective mass and a nontrivial Berry phase, suggesting that the corresponding Fermi surface arises from a topologically nontrivial band. These findings shed light on the normal-state electronic structure of SnTaS2 and highlight the important role of topological bands in shaping its transport properties. Full article
(This article belongs to the Section Quantum Materials)
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11 pages, 1282 KB  
Article
Photo–Hall Effect Characteristics of InAs/GaAs Quantum Dot Photoconductors with Sub-Bandgap Photoexcitation
by Osamu Wada, Takahiro Kitada, Yasuo Minami, Yukihiro Harada, Toshiyuki Kaizu and Takashi Kita
Photonics 2026, 13(1), 59; https://doi.org/10.3390/photonics13010059 - 8 Jan 2026
Viewed by 425
Abstract
The photoconductive properties of an InAs/GaAs quantum dot (QD) superlattice have been characterized using photo–Hall measurements under sub-bandgap illumination. The multi-stacked InAs/GaAs QD structure was grown using molecular beam epitaxy and photo–Hall effect measurements were performed under illumination using light-emitting diodes with three [...] Read more.
The photoconductive properties of an InAs/GaAs quantum dot (QD) superlattice have been characterized using photo–Hall measurements under sub-bandgap illumination. The multi-stacked InAs/GaAs QD structure was grown using molecular beam epitaxy and photo–Hall effect measurements were performed under illumination using light-emitting diodes with three different emission wavelengths: 940 nm, 1300 nm, and 1550 nm. The results have shown that the sign reversal occurs in the Hall coefficient (RH) as the illumination wavelength changes: RH is negative at 940 nm and 1300 nm, and positive at 1550 nm. The photocurrent at 940 nm illumination is ascribed to the electron hole pair generation in QDs, whereas the photocurrent at 1550 nm is dominated by the hole current generated through the midgap states in the structure. A simplified rate equation model involving two-step photoexcitation through the midgap states has revealed that the dominant photocarriers and the Hall coefficient can change depending on the photoexcitation power. The steady-state photocurrent behavior including the observed sign reversal in the Hall coefficient has been interpreted by the proposed model. Full article
(This article belongs to the Section Optoelectronics and Optical Materials)
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22 pages, 5454 KB  
Article
Extreme Strengthening of Nickel by Ultralow Additions of SiC Nanoparticles: Synergy of Microstructure Control and Interfacial Reactions During Spark Plasma Sintering
by Leonid Agureev, Svetlana Savushkina and Artem Ashmarin
Inventions 2026, 11(1), 1; https://doi.org/10.3390/inventions11010001 - 29 Dec 2025
Viewed by 506
Abstract
Ni–ySiC system (where y = 0.001, 0.005, and 0.015 wt.%) composite materials with enhanced mechanical properties have been fabricated and comprehensively investigated. The composites were synthesized using a combined technology involving preliminary mechanical activation of powder components in a planetary mill followed by [...] Read more.
Ni–ySiC system (where y = 0.001, 0.005, and 0.015 wt.%) composite materials with enhanced mechanical properties have been fabricated and comprehensively investigated. The composites were synthesized using a combined technology involving preliminary mechanical activation of powder components in a planetary mill followed by consolidation via spark plasma sintering (SPS) at 850 °C. The microstructure and phase composition were studied by scanning electron microscopy (SEM), transmission electron microscopy (TEM), and X-ray diffraction (XRD). The physico-mechanical properties were evaluated by density measurements (hydrostatic weighing), three-point bending tests (25 °C and 400 °C), and Young’s modulus measurement using an ultrasonic method (25–750 °C). It was found that the introduction of ultralow amounts of SiC nanoparticles (0.001 wt.%) leads to an extreme increase in flexural strength: by 115% at 20 °C (up to 1130 MPa) and by 86% at 400 °C (up to 976 MPa) compared to pure nickel. Microstructural analysis revealed the formation of an ultrafine-grained structure (0.15–0.4 µm) with the presence of pyrolytic carbon and probable nickel silicide interlayers at the grain boundaries. Thermodynamic and kinetic modeling, including the calculation of chemical potentials and diffusion coefficients, confirmed the possibility of reactions at the Ni/SiC interface with the formation of nickel silicides (Ni2Si, NiSi) and free carbon. The scientific novelty of the work lies in establishing a synergistic strengthening mechanism combining the Hall–Petch, Orowan (dispersion), and solid solution strengthening effects, and in demonstrating the property extremum at an ultralow content of the dispersed phase (0.001 wt.%), explained from the standpoint of quantum-chemical analysis of phase stability. The obtained results are of practical importance for the development of high-strength and thermally stable nickel composites, promising for application in aerospace engineering. Full article
(This article belongs to the Section Inventions and Innovation in Applied Chemistry and Physics)
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31 pages, 5710 KB  
Review
Recent Progress in the Theory of Flat Bands and Their Realization
by Izumi Hase
Condens. Matter 2025, 10(4), 64; https://doi.org/10.3390/condmat10040064 - 5 Dec 2025
Viewed by 2578
Abstract
Flat electronic bands, characterized by a nearly dispersionless energy spectrum, have emerged as fertile ground for exploring strong correlation effects, unconventional magnetism, and topological phases. This review paper provides an overview of the theoretical basis, material realization, and emergent phenomena associated with flat [...] Read more.
Flat electronic bands, characterized by a nearly dispersionless energy spectrum, have emerged as fertile ground for exploring strong correlation effects, unconventional magnetism, and topological phases. This review paper provides an overview of the theoretical basis, material realization, and emergent phenomena associated with flat bands. We begin by discussing the geometric and topological origins of flat bands in lattice systems, emphasizing mechanisms such as destructive interference and compact localized states. We will also explain the relationship between quantum metrics and flat bands, which are recent theoretical findings. We then survey various classes of materials—ranging from engineered lattices and Moiré structures to transition metal compounds—where flat bands have been theoretically predicted or experimentally observed. The interplay between flat-band physics and strong correlations is explored through recent developments in ferromagnetism, superconductivity, and various Hall effects. Finally, we outline open questions and potential directions for future research, including the quest for ideal flat-band systems, the role of spin–orbit coupling, and the impact of disorder. This review aims to bridge fundamental concepts with cutting-edge advances, highlighting the rich physics and material prospects of flat bands. Full article
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10 pages, 875 KB  
Article
Hidden Momentum and the Absence of the Gravitational Spin Hall Effect in a Uniform Field
by Andrzej Czarnecki and Ting Gao
Universe 2025, 11(11), 365; https://doi.org/10.3390/universe11110365 - 6 Nov 2025
Cited by 1 | Viewed by 496
Abstract
We re-examine the recent claim that a Dirac particle freely falling in a uniform gravitational field exhibits a spin-dependent transverse deflection (gravitational spin Hall effect). Using a circulating mass model, we show that hidden momentum arises in uniform fields when an object carries [...] Read more.
We re-examine the recent claim that a Dirac particle freely falling in a uniform gravitational field exhibits a spin-dependent transverse deflection (gravitational spin Hall effect). Using a circulating mass model, we show that hidden momentum arises in uniform fields when an object carries angular momentum. On the quantum side, we analyze the Dirac Hamiltonian in a uniform potential, construct its Foldy–Wouthuysen form, and evaluate the Heisenberg evolution of spin-polarized Gaussian packets. The state used previously, with p=0, is not at rest: because canonical and kinetic momenta differ, the packet carries a spin-dependent hidden momentum from t=0. Imposing x(0)=v(0)=0 requires a compensating spin-dependent p(0); with this preparation x(t)=0 to leading order in the gravitational acceleration g. Generalizing, an exact Foldy–Wouthuysen transformation (linear in g but to all orders in 1/c) shows that spin-dependent transverse motion begins no earlier than at O(g2) for a broad class of wave packets. We conclude that a uniform field does not produce a gravitational spin Hall effect at linear order; the previously reported drift stems from inconsistent initial states and misinterpreting canonical momentum. Full article
(This article belongs to the Special Issue Geometric Theories of Gravity)
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16 pages, 3174 KB  
Review
Quantum Transport Behavior in Quasi-One-Dimensional Topological Matter Bi4X4 (X = Br, I)
by Zixin Gong, Jingyuan Zhong, Qiyi Li, Huayi Shen, Jincheng Zhuang and Yi Du
Physchem 2025, 5(4), 47; https://doi.org/10.3390/physchem5040047 - 4 Nov 2025
Viewed by 1351
Abstract
Quasi-one-dimensional (quasi-1D) topological matter Bi4X4 (X = Br, I) possesses versatile topological phases determined by its molar ratio of halide and the stacking mode. Establishing the intrinsic relationship between these topological orders and the quantum transport properties is extremely [...] Read more.
Quasi-one-dimensional (quasi-1D) topological matter Bi4X4 (X = Br, I) possesses versatile topological phases determined by its molar ratio of halide and the stacking mode. Establishing the intrinsic relationship between these topological orders and the quantum transport properties is extremely crucial for both of fundamental research and device applications. Here we review the recent work on the characteristic quantum transport behavior of the Bi4X4 system originating from various electronic states, including three-dimensional (3D) bulk states, two-dimensional (2D) surface states, and one-dimensional (1D) topological hinge states. Specifically, variable range hopping effect, Lifshitz transition, metal–insulator transition, and Shubnikov de Haas oscillations are evoked by the gapped bulk states with significant doping carriers. In 2D limits, the (100) surface states exhibit Dirac-type dispersion to produce weak antilocalization, which is a strong 1D nature due to quasi-1D crystal and electronic structure and evidenced by anomalous planar Hall effect. Last but not the least, coherent transport with Aharonov–Bohm oscillations is observed in thin-layer devices, implying the existence of 1D topological hinge states separated by the (100) surface. These unconventional quantum transport features verify the topological nature of Bi4X4 in different dimensions, signifying an ideal platform to design and utilize multiple topological orders in this quasi-one-dimensional material system. Full article
(This article belongs to the Section Surface Science)
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14 pages, 19249 KB  
Article
Topological Phase Transition in Two-Dimensional Magnetic Material CrI3 Bilayer Intercalated with Mo
by Chen-En Yin, Angus Huang and Horng-Tay Jeng
Materials 2025, 18(20), 4751; https://doi.org/10.3390/ma18204751 - 16 Oct 2025
Viewed by 1037
Abstract
Motivated by the seminal discoveries in graphene, the exploration of novel physical phenomena in alternative two-dimensional (2D) materials has attracted tremendous attention. In this work, through theoretical investigation using first-principles calculations, we reveal that Mo-intercalated CrI3 bilayer exhibits ferromagnetic semiconductor behavior with [...] Read more.
Motivated by the seminal discoveries in graphene, the exploration of novel physical phenomena in alternative two-dimensional (2D) materials has attracted tremendous attention. In this work, through theoretical investigation using first-principles calculations, we reveal that Mo-intercalated CrI3 bilayer exhibits ferromagnetic semiconductor behavior with a small easy-plane magnetocrystalline anisotropy energy (MAE) of 0.618 meV/Cr(Mo) between (100) and (001) magnetizations. The spin–orbit coupling (SOC) opens a narrow band gap at the Fermi level for both magnetization orientations with nonzero Chern number for realizing the quantum anomalous Hall effect (QAHE) in the former and with trivial topology in the latter. The small MAE implies the efficient experimental manipulation of magnetization between distinct topologies through an external magnetic field. Our findings provide compelling evidence that the QAHE in this system originates from the quantum spin Hall effect (QSHE), driven by intrinsic magnetism under broken time-reversal symmetry. These unique properties position Mo-intercalated CrI3 as a promising candidate for tunable spintronic applications. Full article
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33 pages, 3240 KB  
Review
Recent Advances in Magnetic Two-Dimensional van der Waals Heterostructures: Synthesis, Properties, and Spintronic Applications: A Review
by Meri Algarni
Nanomaterials 2025, 15(20), 1569; https://doi.org/10.3390/nano15201569 - 15 Oct 2025
Cited by 3 | Viewed by 3567
Abstract
Two-dimensional (2D) van der Waals (vdW) magnetic materials have emerged as a frontier in condensed matter physics and materials science, offering unprecedented opportunities for next-generation spintronic technologies. This review examines the synthesis, properties, and transport phenomena of 2D magnetic materials, with particular emphasis [...] Read more.
Two-dimensional (2D) van der Waals (vdW) magnetic materials have emerged as a frontier in condensed matter physics and materials science, offering unprecedented opportunities for next-generation spintronic technologies. This review examines the synthesis, properties, and transport phenomena of 2D magnetic materials, with particular emphasis on their integration into spintronic devices. A comprehensive historical overview of magnetic materials is provided, tracing the evolution of intrinsic ferromagnetism in the 2D limit, highlighting key materials such as Cr2Ge2Te6, Fe3GeTe2, and CrI3. Special attention is devoted to the fundamental magnetic properties—including magnetic anisotropy, Curie temperature, and spin polarization—that underpin their functional performance. Major synthesis strategies are evaluated, including chemical vapor deposition, micromechanical exfoliation, and molecular beam epitaxy, focusing on scalability, interface control, and material purity. Furthermore, hallmark transport phenomena are discussed, such as giant magnetoresistance, the quantum anomalous Hall effect, spin–orbit torque, and the role of exchange bias and skyrmions in vdW heterostructures. Throughout the review, current limitations, unresolved questions, and emerging research directions are identified that will accelerate the deployment of 2D magnetic materials in flexible, reconfigurable, and quantum spintronic systems. This work aims to guide ongoing experimental and theoretical efforts and articulate a vision for advancing the field toward device-level implementation. Full article
(This article belongs to the Section Synthesis, Interfaces and Nanostructures)
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15 pages, 2035 KB  
Article
Real-Time Technique for Semiconductor Material Parameter Measurement Under Continuous Neutron Irradiation with High Integral Fluence
by Ivan S. Vasil’evskii, Aleksey N. Klochkov, Pavel V. Nekrasov, Aleksander N. Vinichenko, Nikolay I. Kargin, Almas Yskakov, Maksim V. Bulavin, Aleksey V. Galushko, Askhat Bekbayev, Bagdaulet Mukhametuly, Elmira Myrzabekova, Nurdaulet Shegebayev, Dana Kulikbayeva, Rassim Nurulin, Aru Nurkasova and Ruslan Baitugulov
Electronics 2025, 14(19), 3802; https://doi.org/10.3390/electronics14193802 - 25 Sep 2025
Viewed by 943
Abstract
The degradation of the electronic properties of semiconductor materials and electronic devices under neutron irradiation is a critical issue for the development of electronic systems intended for use in nuclear and thermonuclear energy facilities. This study presents a methodology for real-time measurement of [...] Read more.
The degradation of the electronic properties of semiconductor materials and electronic devices under neutron irradiation is a critical issue for the development of electronic systems intended for use in nuclear and thermonuclear energy facilities. This study presents a methodology for real-time measurement of the electrical parameters of semiconductor structures during neutron irradiation in a high-flux reactor environment. A specially designed irradiation fixture with an electrical measurement system was developed and implemented at the WWR-K research reactor. The system enables simultaneous measurement of electrical conductivity and the Hall effect, with automatic temperature control and remote data acquisition. The sealed fixture, equipped with radiation-resistant wiring and a temperature control, allows for continuous measurement of remote material properties at neutron fluences exceeding 1018 cm−2, eliminating the limitations associated with post-irradiation handling of radioactive samples. The technique was successfully applied to the two different InGaAs-based heterostructures, revealing distinct mechanisms of radiation-induced modification: degradation of mobility and carrier concentration in the InGaAs quantum well structure on GaAs substrate, and transmutation-induced doping effects in the heterostructure on InP substrate. The developed methodology provides a reliable platform for evaluating radiation resistance and optimizing materials for magnetic sensors and electronic components designed for high-radiation environments. Full article
(This article belongs to the Special Issue Radiation Effects on Advanced Electronic Devices and Circuits)
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18 pages, 3329 KB  
Article
Landau Levels and Electronic States for Pseudospin-1 Lattices with a Bandgap: Application to a Lieb Lattice
by Liubov Zhemchuzhna, Lovely Joseph, Andrii Iurov, Godfrey Gumbs and Danhong Huang
Magnetism 2025, 5(3), 22; https://doi.org/10.3390/magnetism5030022 - 16 Sep 2025
Viewed by 1490
Abstract
We have carried out detailed theoretical and numerical calculations and developed a physics-based model for quantitatively describing the Landau levels of several pseudospin-1 structures with a flat band and a finite bandgap in their electronic-energy spectrum under a strong and uniform magnetic field. [...] Read more.
We have carried out detailed theoretical and numerical calculations and developed a physics-based model for quantitatively describing the Landau levels of several pseudospin-1 structures with a flat band and a finite bandgap in their electronic-energy spectrum under a strong and uniform magnetic field. We have investigated the Landau-level-based dynamics, as well as the corresponding eigenstates, for gapped graphene, a dice lattice with both a zero and finite bandgap and, eventually, for the Lieb lattice, which represents a separate type of square lattice with a very special non-symmetric (elevated) location of the flat band which intersects the conduction band at its lowest point. Exact analytical consideration of Landau-level states has been performed and explained when dealing with all types of considered lattices. Our model could be further generalized for treating cases with an arbitrary position for the flat band between the valence and conduction bands. Our current results have direct implications for a deep-level investigation of the quantum Hall effect, as well as other magnetic and topological properties of these novel materials. Full article
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10 pages, 5326 KB  
Article
Probing Chirality of the Quantum Hall Effect via the Landauer–Büttiker Formalism with Two Current Sources
by Kyung Ho Kim
Mathematics 2025, 13(18), 2981; https://doi.org/10.3390/math13182981 - 15 Sep 2025
Viewed by 1284
Abstract
The quantum Hall effect is a paradigmatic example of topological order, characterized by precisely quantized Hall resistance and dissipationless edge transport. These edge states are chiral, propagating unidirectionally along the boundary, and their directionality is determined by the external magnetic field. While chirality [...] Read more.
The quantum Hall effect is a paradigmatic example of topological order, characterized by precisely quantized Hall resistance and dissipationless edge transport. These edge states are chiral, propagating unidirectionally along the boundary, and their directionality is determined by the external magnetic field. While chirality is a central feature of the quantum Hall effect, directly probing it remains experimentally nontrivial. In this study, we introduce a simple and effective method to probe the chirality of edge transport using two independently controlled current sources in a Hall bar geometry. The system under investigation is monolayer epitaxial graphene grown on a silicon carbide substrate, exhibiting robust quantum Hall states. By varying the configurations of the two current sources, we measure terminal voltages and analyze the transport characteristics. Our results demonstrate that the observed behavior can be understood as a linear superposition of chiral contributions to the edge transport. This superposition enables tunable combinations of longitudinal and Hall resistances and enables additive or canceling behavior of Hall voltages depending on current source configuration. The Landauer–Büttiker formalism provides a quantitative framework to describe these observations, capturing the interplay between edge state chirality and the measurement configuration. This research offers a simple yet effective experimental and analytical approach for probing chiral edge currents and highlights the linear superposition principle in the quantum Hall effect. Full article
(This article belongs to the Special Issue Mathematics Methods in Quantum Physics and Its Applications)
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10 pages, 1102 KB  
Article
Dirac Point in the Charge Compensated Single-Crystal Ru3Sn7
by Xiaoyu Ji, Xuebo Zhou, Shilin Zhu, Fengcai Ma, Gang Li and Wei Wu
Materials 2025, 18(17), 4044; https://doi.org/10.3390/ma18174044 - 29 Aug 2025
Cited by 1 | Viewed by 866
Abstract
Ru3Sn7 crystallizes in the cubic Ir3Ge7-type structure (space group Im3m), a class of intermetallic compounds. Previous studies focused primarily on its crystal structure, band calculations, and basic transport properties. Here, we report a systematic investigation [...] Read more.
Ru3Sn7 crystallizes in the cubic Ir3Ge7-type structure (space group Im3m), a class of intermetallic compounds. Previous studies focused primarily on its crystal structure, band calculations, and basic transport properties. Here, we report a systematic investigation of high-quality single crystals via electrical resistivity, Hall effect, specific heat, and thermal transport measurements. The T3X7 intermetallic family—with its diverse electronic ground states—provides an ideal platform for exploring such topology–property relationships. Ru3Sn7 exhibits metallic behavior, with consistent Hall effect and Seebeck coefficient data indicating a compensated electron-hole two-band system. Temperature-dependent modulation of electronic states near the Fermi surface alters charge carrier transport, which may imply the presence of a Lifshitz transition in Ru3Sn7. More importantly, magnetic quantum oscillations are observed for the first time, confirming the presence of two Dirac points in its band structure. Full article
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25 pages, 44682 KB  
Article
Data-Driven Solutions and Parameters Discovery of the Chiral Nonlinear Schrödinger Equation via Deep Learning
by Zekang Wu, Lijun Zhang, Xuwen Huo and Chaudry Masood Khalique
Mathematics 2025, 13(15), 2344; https://doi.org/10.3390/math13152344 - 23 Jul 2025
Viewed by 1020
Abstract
The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse [...] Read more.
The chiral nonlinear Schrödinger equation (CNLSE) serves as a simplified model for characterizing edge states in the fractional quantum Hall effect. In this paper, we leverage the generalization and parameter inversion capabilities of physics-informed neural networks (PINNs) to investigate both forward and inverse problems of 1D and 2D CNLSEs. Specifically, a hybrid optimization strategy incorporating exponential learning rate decay is proposed to reconstruct data-driven solutions, including bright soliton for the 1D case and bright, dark soliton as well as periodic solutions for the 2D case. Moreover, we conduct a comprehensive discussion on varying parameter configurations derived from the equations and their corresponding solutions to evaluate the adaptability of the PINNs framework. The effects of residual points, network architectures, and weight settings are additionally examined. For the inverse problems, the coefficients of 1D and 2D CNLSEs are successfully identified using soliton solution data, and several factors that can impact the robustness of the proposed model, such as noise interference, time range, and observation moment are explored as well. Numerical experiments highlight the remarkable efficacy of PINNs in solution reconstruction and coefficient identification while revealing that observational noise exerts a more pronounced influence on accuracy compared to boundary perturbations. Our research offers new insights into simulating dynamics and discovering parameters of nonlinear chiral systems with deep learning. Full article
(This article belongs to the Special Issue Applied Mathematics, Computing and Machine Learning)
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