Quantum Hall Research Articles

Coulomb oscillations of a quantum antidot formed by an airbridged pillar gate in the integer and fractional quantum Hall regime

Abstract Quantum antidots (QAD) are attractive for manipulating quasiparticles in quantum Hall (QH) systems. Here, we form a QAD in the integer and fractional QH regimes at nominal Landau-level filling factor ν = 2, 1, and 2/3 using a submicron pillar gate with an airbridge connection. After confirming the required conditions for a fully depleted QAD, we analyze the observed Coulomb oscillations in terms of the area of the QAD and the effective charge for the oscillation period in an identical gate voltage range. The area at ν= 2/3 is significantly smaller than that at ν = 2 and 1, in qualitative agreement with the previous report. By assuming a constant gate capacitance, the effective charge at ν= 2/3 is about 2/3 of that at ν = 2 and 1. The QAD device can be used to capture and emit charges in the unit of 2e/3.

Spin-Hall conductivity and optical characteristics of noncentrosymmetric quantum spin Hall insulators: the case of PbBiI

Quantum spin Hall insulators have attracted significant attention in recent years. Understanding the optical properties and spin Hall effect in these materials is crucial for technological advancements. In this study, we present theoretical analyses to explore the optical properties, Berry curvature and spin Hall conductivity of pristine and perturbed PbBiI using the linear combination of atomic orbitals and the Kubo formula. The system is not centrosymmetric and it is hosting at the same time Rashba spin-splitting and quantized spin Hall conductivity. Our calculations reveal that the electronic structure can be modified using staggered exchange fields and electric fields, leading to changes in the optical properties. Additionally, the spin Berry curvature and spin Hall conductivity are investigated as a function of the energy and temperature. The results indicate that due to the small dynamical spin Hall conductivity, generating an ac spin current in the PbBiI requires the use of external magnetic fields or magnetic materials.

Andreev Reflection in the Quantum Hall Regime at an Al/InAs Junction on a Cleaved Edge.

We have fabricated a superconductor/semiconductor junction composed of Al and InAs using cleaved edge overgrowth. By exploiting the unique geometry with a thin Al/Pt/Al trilayer formed on the side surface of an in situ cleaved InAs quantum well heterostructure wafer, we achieve a superconducting critical field of ∼5 T, allowing superconductivity and quantum Hall (QH) effects to coexist down to filling factor ν = 3. Andreev reflection at zero magnetic field shows a conductance enhancement limited solely by the Fermi velocity mismatch, demonstrating a virtually barrier-free junction. Bias spectroscopy in the QH regime reveals the opening of a superconducting gap, with the reduced downstream resistance indicating electron-hole Andreev conversion. Our results, obtained in a new experimental regime characterized by a clean edge-contacted junction with a superconducting electrode narrower than the coherence length, open new avenues for both theoretical and experimental studies of the interplay between superconductivity and QH effects.

Novel Bulk Quantum Hall Effect in Nanostructured TaP Macroscopic Crystals.

Bulk quantum Hall effect (QHE), the natural extension of the two-dimensional (2D) QHE, is one of the representative phenomena of coherent electron transport. However, bulk QHE has rarely been reported in real materials with macroscopic sizes. Here, we report a novel bulk QHE in macroscopic millimeter-sized and nanostructured TaP crystals consisting of nanometer-scale lamellae. Specifically, the simultaneous quantum plateaus were observed in both transverse resistivity ρxy and vertical resistivity ρzz. The bulk QHE is attributable to synergetic action between Landau cyclotron movement under magnetic field B and periodically modulated potential due to the nanometer-scaled lamellae. This mechanism would form the fixed number of edge states along B-perpendicular and B-parallel directions respectively, equivalent to stacked 2D-QHE layers, leading to quantized ρxy and ρzz. Our work verifies that microstructure engineering could result in the coherent transport of electrons and generate new quantum phenomena in bulk materials.

Topological linear response of hyperbolic Chern insulators

We establish a connection between the electromagnetic Hall response and band topological invariants in hyperbolic Chern insulators by deriving a hyperbolic analog of the Thouless-Kohmoto-Nightingale-den Nijs (TKNN) formula. By generalizing the Kubo formula to hyperbolic lattices, we show that the Hall conductivity is quantized to -e^2C_{ij}/h−e2Cij/h, where C_{ij}Cij is the first Chern number. Through a flux-threading argument, we provide an interpretation of the Chern number as a topological invariant in hyperbolic band theory. We demonstrate that, although it receives contributions from both Abelian and non-Abelian Bloch states, the Chern number can be calculated solely from Abelian states, resulting in a tremendous simplification of the topological band theory. Finally, we verify our results numerically by computing various Chern numbers in the hyperbolic Haldane model.

Pseudo-Quantum Electrodynamics: 30 Years of Reduced QED

Charged quasiparticles, which are constrained to move on a plane, interact by means of electromagnetic (EM) fields which are not subject to this constraint, living, thus, in three-dimensional space. We have, consequently, a hybrid situation where the particles of a given system and the EM fields (through which they interact) live in different dimensions. Pseudo-Quantum Electrodynamics (PQED) is a U(1) gauge field theory that, despite being strictly formulated in two-dimensional space, precisely describes the real EM interaction of charged particles confined to a plane. PQED is completely different from QED(2 + 1), namely, Quantum Electrodynamics of a planar gauge field. It produces, for instance, the correct 1/r Coulomb potential between static charges, whereas QED(2 + 1) produces lnr potential. In spite of possessing a nonlocal Lagrangian, it has been shown that PQED preserves both causality and unitarity, as well as the Huygens principle. PQED has been applied successfully to describe the EM interaction of numerous systems containing charged particles constrained to move on a plane. Among these are p-electrons in graphene, silicene, and transition-metal dichalcogenides; systems exhibiting the Valley Quantum Hall Effect; systems inside cavities; and bosonization in (2 + 1)D. Here, we present a review article on PQED (also known as Reduced Quantum Electrodynamics).

Preparation Methods and Quantum Hall Effect of Graphene

Graphene is a two-dimensional ultra-thin functional material. It has the characteristics of light weight, and it exhibits stable chemical properties. In recent years, it has become an excellent candidate material for the modification of various functional devices due to its excellent electrical performance. The performance of graphene is significantly influenced by the preparation method. Therefore, it is necessary to summarize the preparation methods of graphene. In addition, these functional devices typically operate in complex external environments, including magnetic fields, temperature fields, and electric fields. Therefore, studying the quantum Hall effect of graphene is of great significance for the use of graphene based devices. This article is written in order to provide a quicker understanding of this field. The preparation methods of graphene are briefly described. Among these methods, several industrialized methods of graphene production are also highlighted. Then, the progresses of quantum Hall effect in graphene are also presented. This work is of great significance for promoting the application of graphene based devices in complex external field environments.

Accelerating spin Hall conductivity predictions via machine learning

AbstractAccurately predicting the spin Hall conductivity (SHC) is crucial for designing novel spintronic devices that leverage the spin Hall effect. First‐principles calculations of SHCs are computationally intensive and unsuitable for quick high‐throughput screening. Here, we have developed a residual crystal graph convolutional neural network (Res‐CGCNN) deep learning model to classify and predict SHCs solely based on the structural and compositional information. This is enabled by having access to 9249 instances of SHCs data and incorporating extra residual networks into the standard CGCNN framework. We found that Res‐CGCNN surpasses CGCNN, achieving a mean absolute error of 115.4 (ℏ/e) (S/cm) for regression and an area under the receiver operating characteristic curve of 0.86 for classification. Additionally, we utilized Res‐CGCNN to conduct high‐throughput screenings of materials in the Materials Project database that were absent in the training set. This led to the prediction of several previously unreported materials displaying large SHCs exceeding 1000 (ℏ/e) (S/cm), which were validated through first‐principles calculations. This study represents the inaugural endeavor to construct a machine learning model capable of effectively capturing the intricate nonlinear relationship between SHCs and crystal structure and composition, serving as a useful tool for the efficient screening and design of materials exhibiting high SHCs.

Assorted optical solitons of the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrödinger equations using modified extended tanh-function technique

In this research article, the (1+1)- and (2+1)-dimensional Chiral nonlinear Schrödinger equations (CNLSEs) are studied, which play an important role in the development of quantum mechanics, particularly in the field of quantum Hall effect. Our primary goal is to obtain the analytical solutions utilizing novel methodology, particularly the modified extended tanh-function technique. We concentrate on the search to solitary wave solutions inside the (1+1)- and (2+1)-dimensional CNLSEs, which are relevant in domains such as optics, electro-magnetic wave propagation, plasma physics, optics and quantum mechanics. Our objective is to increase knowledge of this equation and give insight into the behavior of solitary waves by employing a novel mathematical technique. This will be accomplished by displaying our findings in 2D and 3D graphics. We believe that our results would pave a way for future research generating optical memories based on the nonlinear solitons.

Nonlinear edge transport in a quantum Hall system.

Nonlinear transport phenomena in condensed matter reflect the geometric nature, quantum coherence, and many-body correlation of electronic states. Electric currents in solids are classified into (i) ohmic current, (ii) supercurrent, and (iii) geometric or topological current. While the nonlinear current-voltage (I-V) characteristics of the former two categories have been extensive research topics recently, those of the last category remains unexplored. Among them, the quantum Hall current is a representative example. Realized in two-dimensional electronic systems under a strong magnetic field, the topological protection quantizes the Hall conductance in the unit of e2/h (e, elementary charge; and h, Planck constant), of which the edge transport picture gives a good account. Here, we theoretically study the nonlinear I-VH characteristic of the edge transport up to third order in VH. We find that nonlinearity arises in the Hall response from electron-electron interaction between the counterpropagating edge channels with the nonlinear energy dispersions. We also discuss possible experimental observations.

What Controls the Dawn‐Dusk Asymmetry of Dayside Alfvénic Power: Interplanetary Magnetic Field or Ionospheric Conductance?

AbstractAlfvén waves are important carriers of solar wind energy into the Earth's magnetosphere and upper atmosphere. The observed distribution of Alfvénic power at low altitude exhibits significant dawn‐dusk asymmetry with different causes and impacts on the dayside and nighside. The nightside asymmetry has been shown to be controlled by the meridional gradient in the ionospheric Hall conductance. It is not clear what controls the dayside asymmetry. Both the ionospheric conductance gradient and orientation of the y‐component of the interplanetary magnetic field (IMF) are possible factors. We examined both possibilities using global magnetohydrodynamic (MHD) simulations. Our results show: (a) The dayside distribution of Alfvénic power is very sensitive to the orientation of IMF By, with enhanced power in the dawn (dusk) sector of the northern hemisphere for positive (negative) By (and opposite in the southern hemisphere); and (b) gradients in ionospheric conductance exert a weaker influence on the dayside asymmetry.

Atomic disorder and intrinsic anomalous Hall effect in a half-metallic ferromagnet Co2VAl

Half-metallic ferromagnets, conducting for one spin channel while insulating for the other, are highly desirable for spintronic applications due to 100 % spin polarization around the Fermi level. Cobalt-based half-metallic Heusler compounds have attracted enormous attention due to their large spin polarization and a high magnetic transition temperature. In the present study, we report the experimental and theoretical investigation of crystal structure and anomalous Hall effect (AHE) in half-metallic ferromagnet Co2VAl. The structural investigation of high-resolution synchrotron x-ray diffraction data reveals 10 % antisite disorder between V and Al atoms within the L21 ordered crystal structure. The scaling analysis of anomalous Hall data shows that the AHE in our system is mainly driven by the Berry curvature in the momentum space. The magnitude of experimental intrinsic anomalous Hall conductivity (AHC) due to the momentum space Berry curvature is about 44.67 ± 0.02 S/cm at 5 K, which is less than the theoretically calculated AHC for the ordered structure. Our theoretical calculations suggest that the lower AHC obtained for the present system is due to the reduced Berry curvature in the disordered case with negligible impact on half-metallicity of the system.

Enhanced spin Hall ratio in two-dimensional semiconductors

The conversion efficiency from charge current to spin current via the spin Hall effect is evaluated by the spin Hall ratio (SHR). Through state-of-the-art ab initio calculations involving both charge conductivity and spin Hall conductivity, we report the SHRs of the III-V monolayer family, revealing an ultrahigh ratio of 0.58 in the hole-doped GaAs monolayer. In order to find more promising 2D materials, a descriptor for high SHR is proposed and applied to a high-throughput database, which provides the fully relativistic band structures and Wannier Hamiltonians of 216 exfoliable monolayer semiconductors and has been released to the community. Among potential candidates for high SHR, the MXene monolayer Sc2CCl2 is identified with the proposed descriptor and confirmed by computation, demonstrating the descriptor validity for high SHR materials discovery.

Tutorial: From Topology to Hall Effects—Implications of Berry Phase Physics

AbstractThe Berry phase is a fundamental concept in quantum mechanics with profound implications for understanding topological properties of quantum systems. This tutorial provides a comprehensive introduction to the Berry phase, beginning with the essential mathematical framework required to grasp its significance. We explore the intrinsic link between the emergence of a non-trivial Berry phase and the presence of topological characteristics in quantum systems, showing the connection between the Berry phase and the band structure as well as the phase’s gauge-invariant nature during cyclic evolutions. The tutorial delves into various topological effects arising from the Berry phase, such as the quantum, anomalous, and spin Hall effects, which exemplify how these quantum phases manifest in observable phenomena. We then extend our discussion to cover the transport properties of topological insulators, elucidating their unique behaviour rooted in the Berry phase physics. This tutorial aims at equipping its readers with a robust understanding of the basic theory underlying the Berry phase and of its pivotal role in the realm of topological quantum phenomena.

Floquet Flux Attachment in Cold Atomic Systems.

Flux attachment provides a powerful conceptual framework for understanding certain forms of topological order, including most notably the fractional quantum Hall effect. Despite its ubiquitous use as a theoretical tool, directly realizing flux attachment in a microscopic setting remains an open challenge. Here, we propose a simple approach to realizing flux attachment in a periodically driven (Floquet) system of either spins or hard-core bosons. We demonstrate that such a system naturally realizes correlated hopping interactions and provides a sharp connection between such interactions and flux attachment. Starting with a simple, nearest-neighbor, free boson model, we find evidence-from both a coupled-wire analysis and large-scale density matrix renormalization group simulations-that Floquet flux attachment stabilizes the bosonic integer quantum Hall state at 1/4 filling (on a square lattice), and the Halperin-221 fractional quantum Hall state at 1/6 filling (on a honeycomb lattice). At 1/2 filling on the square lattice, time-reversal symmetry is instead spontaneously broken and bosonic integer quantum Hall states with opposite Hall conductances are degenerate. Finally, we propose an optical-lattice-based implementation of our model on a square lattice and discuss prospects for adiabatic preparation as well as effects of Floquet heating.

Selective Control of Electric Charge of Weyl Fermions in Pyrochlore Iridates.

Weyl fermions can exhibit exotic phenomena due to their magnetic charge in momentum space, while Weyl nodes are usually located away from Fermi energy, which forms electron or hole pockets as the electric charges. Previous studies have mostly focused on the magnetic charge, however, the electric charges are rarely explored. Here, the intriguing Hall responses arising from the interplay between magnetic and electric charges of Weyl fermions in pyrochlore iridates are reported. Explicitly, unexpected linear scaling is observed between the anomalous Hall conductivity and Hall carrier density in strained Nd2Ir2O7 thin films, and its slope shows a sign change approaching the Néel temperature of Nd. Theoretical calculations unveil that the cluster magnetic multipoles induce local energy inversion of Weyl nodes, which alters the electric charge of Weyl fermions and accounts for the observed nontrivial Hall responses. Moreover, the correlation between the magnetic and electric charges is further probed by voltage-controlled hydrogenation, which leads to the suppression of the anomalous Hall effect through electron filling. This work not only reveals the essential role of the both magnetic and electric charges of Weyl fermions, but also demonstrates the hydrogenation as an effective tuning knob in exploring correlated topological properties.

Bottom-up stripping of graphene with controlled oxidation behaviors towards supercapacitors energy storage

Due to its distinctive two-dimensional planar structure, room temperature quantum Hall effect, and high strength, graphene has garnered significant interest in the fields of energy storage and conversion. In order to achieve high efficiency in the production of graphene, electrochemical peeling has been extensively investigated. Nevertheless, the intermolecular forces between graphite layers are disrupted during ion intercalation in solution, leading to inconsistent bonding forces and low yields. In order to address the issues above, this study introduces a novel bottom-up electrochemical peeling method, wherein graphite expansion occurs above the electrolyte. By preventing contact between the peeled graphene and the electrolyte, the oxidation of graphene is significantly minimized, resulting in a substantial yield of 88 %. At the current density of 1.0 A g−1, the Go-QAS displayed 225.5 F g−1, and kept about 220.2 F g−1 after 500 cycles. The well-designed bottom-up peeling process leads to graphene nanosheets with reduced structural degradation, high purity, and excellent conductivity. This technique is expected to introduce innovative concepts for the field.

Procedure for Fabrication and Characterization of Van-der-Waals Heterostructures

In this work we provide a step-by-step description of the technique for manufacturing various van der Waals heterostructures. First, we discuss the procedure to obtain monolayer and few-layer flakes from layered materials, in particular from graphite and hexagonal boron nitride. Next, we consider different approaches to the assembly depending on the required final device. Further, we describe in detail the procedure for making ohmic contacts and give the parameters for plasma chemistry and metal deposition. We observe the field effect in transport measurements but a number of features – a strong shift of the charge neutral point from the zero-gate voltage, a large resistance away from the charge neutral point, and low mobility – indicate a problem with the quality of the resulting devices. Nevertheless, one of the fabricated devices demonstrates reasonable quality – the maximum mobility is estimated at 15000 cm2V–1s–1, the magnetic field dependences demonstrate the quantum Hall effect, which is standard for high-quality graphene. Unexpectedly, scanning electron microscope images of the resulting devices reveal a large amount of contamination on the surface of the flakes, which may explain the corresponding quality of our devices. Preliminary results of flakes cleaning with chemical compounds and thermal treatment are given.

The Migdal jump under the quantum Hall regime

In two-dimensional electron systems at large values of the Wigner-Seits parameter rs and in the quantum Hall effect mode, the distribution function of particles over Landau levels was calculated. It turned out that at small filling factors, the tail of the distribution function and the magnitude of the Migdal jump are qualitatively different from the case of a Fermi liquid in a zero magnetic field. Due to the presence of the cyclotron energy gap, the Fermi-liquid distortion of the distribution function is significantly suppressed.

Ab-initio prediction of gigantic anomalous Nernst effect in ferromagnetic monolayer transition metal trihalides

The anomalous Hall conductivity of all transition metal trihalides was explored using first-principles calculations. Employing the Fukui-Hatsugai-Suzuki method, we found that ferromagnetic monolayersXBr3(X= Pd, Pt) possessed the quantized anomalous Hall conductivity (QAHC) with and without carrier doping. Due to unique QAHC, their transverse thermoelectric properties ofXBr3(X= Pd, Pt) were investigated. Employing the semi-classical Boltzmann transport theory, the transverse thermoelectric coefficient of each monolayer was analyzed. Anomalous Nernst coefficients (ANCs) of theXBr3monolayers were prominent both at and near the Fermi level. Under an assumed relaxation time of 10 fs, the maximum ANCs for the PdBr3(PtBr3) monolayer reached -54.1 (-23.3)µV K-1atT=300 K upon doping with 1.21 × 1014(5.64 × 1013) holes cm-2. The large ANCs of theXBr3monolayers were attributed to the opening of a narrow bandgap generated by spin-orbit coupling both at and near the Fermi level, which led to a large Seebeck-induced charge current and large anomalous Nernst conductivity. These results suggest that ferromagneticXBr3monolayers have significant potential for application in thermoelectric devices.