Quantum Hall Research Articles

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.

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.

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.

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.

Interface Dependent Coexistence of Two‐Dimensional Electron and Hole Gases in Mn‐doped InAs/GaSb

AbstractThe interface of common III‐V semiconductors InAs and GaSb can be utilized to realize a two‐dimensional (2D) topological insulator state. The 2D electronic gas at this interface can yield Hall quantization from coexisting electrons and holes. This anomaly is a determining factor in the fundamental origin of the topological state in InAs/GaSb. Here, the coexistence of electrons and holes in InAs/GaSb is tied to the chemical sharpness of the interface. Magnetotransport, in samples of Mn‐doped InAs/GaSb cleaved from wafers grown at a spatially inhomogeneous substrate temperature, is studied. It is reported that the observation of quantum oscillations and a quantized Hall effect whose behavior, exhibiting coexisting electrons and holes, is tuned by this spatial nonuniformity. Through transmission electron microscopy measurements, it is additionally found that samples that host this co‐existence exhibit a chemical intermixing between group III and group V atoms that extends over a larger thickness about the interface. The issue of intermixing at the interface is systematically overlooked in electronic transport studies of topological InAs/GaSb. These findings address this gap in knowledge and shed important light on the origin of the anomalous behavior of quantum oscillations seen in this 2D topological insulator.

Intrinsic anomalous, spin and valley Hall effects in ’ex-so-tic’ van-der-Waals structures

We consider the anomalous, spin, valley, and valley spin Hall effects in a pristine graphene-based van-der-Waals (vdW) heterostructure consisting of a bilayer graphene (BLG) sandwiched between a semiconducting van-der-Waals material with strong spin-orbit coupling (e.g., WS2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {WS}_2$$\\end{document}) and a ferromagnetic insulating vdW material (e.g. Cr2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Cr}_2$$\\end{document}Ge2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Ge}_2$$\\end{document}Te6\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\hbox {Te}_6$$\\end{document}). Due to the exchange proximity effect from one side and spin-orbit proximity effect from the other side of graphene, such a structure is referred to as graphene based ’ex-so-tic’ structure. First, we derive an effective Hamiltonian describing the low-energy states of the structure. Then, using the Green’s function formalism, we obtain analytical results for the Hall conductivities as a function of the Fermi energy and gate voltage. For specific values of these parameters, we find a quantized valley Hall conductivity.

Planar Thermal Hall Effect from Phonons in Cuprates

A surprising “planar” thermal Hall effect, whereby the field is parallel to the current, has recently been observed in a few magnetic insulators; this effect has been attributed to exotic excitations such as Majorana fermions or chiral magnons. Here, we investigate the possibility of a planar thermal Hall effect in three different cuprate materials, in which the conventional thermal Hall conductivity κxy (with an out-of-plane field perpendicular to the current) is dominated by either electrons or phonons. Our measurements show that the planar κxy from electrons in cuprates is zero, as expected from the absence of a Lorentz force in the planar configuration. By contrast, we observe a sizable planar κxy in those samples where the thermal Hall response is due to phonons, even though it should, in principle, be forbidden by the high crystal symmetry. Our findings call for a careful reexamination of the mechanisms responsible for the phonon thermal Hall effect in insulators. Published by the American Physical Society 2024

Three-component fractional quantum Hall effect in topological flat bands

Three-component fractional quantum Hall effect in topological flat bands

Microscopic Theory of Nonlinear Hall Effect in Three-dimensional Magnetic Systems

Abstract The nonlinear Hall effect (NLHE) has been detected in various of condensed matter systems. Unlike linear Hall effect, NLHE may exist in physical systems with broken inversion symmetry in the crystal. On the other hand, real space spin texture may also break inversion symmetry and result in NLHE. In this letter, we employ the Feynman diagrammatic technique to calculate nonlinear Hall conductivity (NLHC) in three-dimensional magnetic systems. The results connect NLHE with the physical quantity of emergent electrodynamics which originates from the magnetic texture. The leading order contribution of NLHC $\chi_{abb}$ is proportional to the emergent toroidal moment $\mathcal{T}_{a}^{e}$ which reflects how the spin textures wind in three dimension.

Topological protection revealed by real-time longitudinal and transverse transport measurements

Topology is essential for achieving unchanged (or protected) quantum properties in the presence of perturbations. A challenge facing the application is the variable protection levels displayed in real systems associated with the reconstructive behaviors of the dissipationless modes. Despite various insights on potential causes of backscattering, the edge-state-based approach is incomplete because the bulk states also contribute indispensably. This study investigates sample-scale reconstruction where dissipationless modes are global objects instead of being restricted to the sample edge. An integer quantum Hall effect hosted in a Corbino geometry is adopted and brought to the verge of a breakdown. Two independent and simultaneous detections are performed to capture transport responses in both longitudinal and transverse directions. The real-time correspondence between orthogonal results confirms two facts. 1. Dissipationless modes undergo frequent reconstruction in response to electrochemical potential changes, causing dissipationless current paths to expand transversely into the bulk while preserving chirality. A breakdown only occurs when a backscattering emerges between reconstructed dissipationless current paths bridging opposite edge contacts. 2. Topological protection is subject to an interplay of disorder, electron-electron interaction, and topology. The proposed reconstruction mechanism qualitatively explains the robustness variations, beneficial for protection optimization.

Universality of quantum phase transitions in the integer and fractional quantum Hall regimes

Fractional quantum Hall (FQH) phases emerge due to strong electronic interactions and are characterized by anyonic quasiparticles, each distinguished by unique topological parameters, fractional charge, and statistics. In contrast, the integer quantum Hall (IQH) effects can be understood from the band topology of non-interacting electrons. We report a surprising super-universality of the critical behavior across all FQH and IQH transitions. Contrary to the anticipated state-dependent critical exponents, our findings reveal the same critical scaling exponent κ = 0.41 ± 0.02 and localization length exponent γ = 2.4 ± 0.2 for fractional and integer quantum Hall transitions. From these, we extract the value of the dynamical exponent z ≈ 1. We have achieved this in ultra-high mobility trilayer graphene devices with a metallic screening layer close to the conduction channels. The observation of these global critical exponents across various quantum Hall phase transitions was masked in previous studies by significant sample-to-sample variation in the measured values of κ in conventional semiconductor heterostructures, where long-range correlated disorder dominates. We show that the robust scaling exponents are valid in the limit of short-range disorder correlations.

Orbital Hall Effect Accompanying Quantum Hall Effect: Landau Levels Cause Orbital Polarized Edge Currents.

The quantum Hall effect emerges when two-dimensional samples are subjected to strong magnetic fields at low temperatures: Topologically protected edge states cause a quantized Hall conductivity in multiples of e^{2}/h. Here we show that the quantum Hall effect is accompanied by an orbital Hall effect. Our quantum mechanical calculations fit well the semiclassical interpretation in terms of "skipping orbits." The chiral edge states of a quantum Hall system are orbital polarized akin to a hypothetical orbital version of the quantum anomalous Hall effect in magnetic systems. The orbital Hall resistivity scales quadratically with the magnetic field, making it the dominant effect at high fields.