Effects of electric and magnetic fields on electronic states and transport of a Hall bar

We study the edge-state band and transport property for a HgTe/CdTe quantum well Hall bar under the combined coupling of a transverse electric field and a perpendicular magnetic field. It is demonstrated that a weak magnetic field can protect one of the two edge states, open or enlarge a gap of the other edge state in the Hall bar. However, an appropriate electric field can remove the gap, restoring the quantum spin Hall effect. Using the scattering matrix method, we study the electronic transport of the system. We find that the electric field can not only make the switch from pure spin-up to spin-down current, but also open or close the edge-state channels in a narrow Hall bar under a weak magnetic field, which provides us with a new way to construct a topological insulator-based spin switch and charge switch.     

Optical properties of quasi-zero-dimensional magneto-excitons

We discuss the evolution of optical properties of semiconductor quantum wells, as the quasi-two-dimensional electronic states are further confined into quasi-zero dimensions by a perpendicular magnetic field. We show that confinement in all three directions strongly modifies both linear and nonlinear optical response. In particular, quasi-zero-dimensionality makes an ensemble of magneto-excitons a unique many-body system, distinct from higher-dimensional excitons and the one-component Coulomb system in the fractional quantum Hall regime or Wigner crystal.     

Direct measurement of the coherence length of edge states in the integer quantum Hall regime

We have determined the finite temperature coherence length of edge states in the integer quantum Hall effect regime. This was realized by measuring the visibility of electronic Mach-Zehnder interferometers of different sizes, at filling factor 2. The visibility shows an exponential decay with the temperature. The characteristic temperature scale is found inversely proportional to the length of the interferometer arm, allowing one to define a coherence length l_(phi). The variations of l_(phi) with magnetic field are the same for all samples, with a maximum located at the upper end of the quantum Hall plateau. Our results provide the first accurate determination of l_(phi) in the quantum Hall regime.     

三角形石墨烯纳米片电子和磁学性质的尺寸效应

基于密度泛函理论, 本文研究了氢钝化锯齿形边缘三角形石墨烯纳米片的电子结构和磁学性质, 这种石墨烯纳米结构的基态表现出强烈的磁性边缘态和量子尺寸效应。 我们应用多种交换关联泛函, 对体系的自旋密度和电子结构进行了第一性原理计算和理论分析, 结果表明三角形石墨烯纳米片的总磁矩和自旋随尺寸线性变化,平均磁矩随着尺寸变大而增加, 并逐渐趋于一个定值。 与此同时, 体系的能隙随着尺寸增加而减小, 其中自旋不变能隙的调控对光学响应和光子激发有着重要意义。 计算得到的单电子能谱表明, 费米能级的简并度与体系尺寸成正比。 应用多种交换关联泛函的计算结果表明, 三角形石墨烯纳米片具有可调控的自旋和能隙, 为其在纳米级光电器件和磁性半导体的应用方面提供了理论依据.     

Topological aspects of graphene

Topological aspects of the electronic properties of graphene, including edge effects, with the tight-binding model on a honeycomb lattice and its extensions to show the following: (i) Presence of the pair of massless Dirac dispersions, which is the origin of anomalous properties including a peculiar quantum Hall effect (QHE), is not accidental to honeycomb, but is generic for a class of two-dimensional lattices that interpolate between square and π-flux lattices. Topological stability guarantees persistence of the peculiar QHE. (ii) While we have the massless Dirac dispersion only around E=0, the anomalous QHE associated with the Dirac cone unexpectedly persists for a wide range of the chemical potential. The range is bounded by van Hove singularities, at which we predict a transition to the ordinary fermion behaviour accompanied by huge jumps in the QHE with a sign change. (iii) We establish a coincidence between the quantum Hall effect in the bulk and the quantum Hall effect for the edge states, which is another topological effect. We have also explicitly shown that the E=0 edge states in honeycomb in zero magnetic field persist in magnetic field. (iv) We have also identified a topological origin of the fermion doubling in terms of the chiral symmetry.     

Realizing universal edge properties in graphene fractional quantum Hall liquids

Universal chiral Luttinger liquid behavior has been predicted for fractional quantum Hall edge states, but so far has not been observed experimentally in semiconductor-based two-dimensional electron gases. One likely cause of this absence of universality is the generic occurrence of edge reconstruction in such systems, which is the result of a competition between confinement potential and Coulomb repulsion. We show that due to a completely different mechanism of confinement, edge reconstruction can be avoided in graphene, which allows for the observation of the predicted universality.     

Lattice electrons on a cylinder surface in the presence of rational magnetic flux and disorder

We consider a disordered two-dimensional system of independent lattice electrons in a perpendicular magnetic field with rigid confinement in one direction and generalized periodic boundary conditions (GPBC) in the other direction. The objects investigated numerically are the orbits in the plane spanned by the energy eigenvalues and the corresponding center of mass coordinate in the confined direction, parameterized by the phase characterizing the GPBC. The Kubo Hall conductivity is expressed in terms of the winding numbers of these orbits. For vanishing disorder the spectrum of the system consists of Harper bands with energy levels corresponding to the edge states within the band gaps. Disorder leads to broadening of the bands. For sufficiently large systems localized states occur in the band tails. We find that within the mobility gaps of bulk states the Diophantine equation determines the value of the Hall conductivity as known for systems with torus geometry (PBCs in both directions). Within the spectral bands of extended states the Hall conductivity fluctuates strongly. For sufficiently large systems the generic behavior of localization-delocalization transitions characteristic for the quantum Hall effect are recovered.     

Quenching of non-local electron transport in tilted magnetic fields

A variety of transport phenomena observed at laterally confined two- dimensional electron systems (2DES) prove the occurrence of non-local contributions to the electronic conductance in these systems. However, this non-local regime accompanied by a non-equilibrium population of the edge states with respect to the 2D bulk state is quenched at rather low values of current-driving electric fields.We analyse the non-Ohmic behaviour of SdH oscillations at GaAs/GaAlAs Quantum Hall conductors on the basis of a model including edge and bulk conduction and deduce the non-equilibrium population of edge and bulk states quantitatively.The spatial separation between edge and bulk states was changed by tilting the samples with respect to the magnetic field. The resulting angular dependences of equilibration parameters could be quantitatively explained by the change of the ratio of spin splitting to cyclotron energy being present in 2DES in tilted magnetic fields.PACS index numbers: 73.20.Dx; 73.40.Hm     

Edge physics of graphene in the quantum Hall regime

We study the electronic edge states of graphene in the quantum Hall regime. For non-interacting electrons, graphene supports both electron-like and hole-like edge states. We find there are half as many edge states of each type in the lowest Landau level compared to higher Landau levels, leading to a quantization of the Hall conductance that is shifted relative to standard two dimensional electron gases. We also consider the effect of quantum Hall ferromagnetism on this edge structure, and find an unusual Luttinger liquid at the edge in undoped graphene. This arises due to a domain wall that forms near the edge between partially spin-polarized and valley-polarized regions. The domain wall has a U(1) degree of freedom which generates both collective and charged gapless excitations, whose consequences for tunneling experiments are discussed.     

Measurement of safety factor using Hall probes on CASTOR tokamak

Hall sensors offer an attractive true non-inductive method of magnetic field measurements for fusion devices. However, there is only limited experience in using of these sensors in such demanding environment (high heat loads, radiation, and electromagnetic noise). Recently, a combined magnetic probe was developed for CASTOR tokamak, which contains 3 Hall sensors and 3 coils arranged to measure all three components of magnetic field approximately in a single point of space. The probe is compatible with in-vessel use well in confinement region of CASTOR. It is fully controlled by multi-functional electronic system that drives the Hall probes, amplifies their output signals, performs the A/D conversion and stores the measured data on PC. The bandwidth of the system is up to 200 kHz. Design of the system and its implementation on CASTOR is reviewed. Results obtained using this diagnostic on CASTOR tokamak is presented. Radial profile of the poloidal magnetic field is used to deduce radial profile of safety factor.     

Broken symmetries in the reconstruction of ν=1 quantum Hall edges

Spin-polarized reconstruction of the ν=1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon–Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern–Simons Ginzburg–Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region.     

Novel optical probe for quantum Hall system

Surface photovoltage (SPV) spectroscopy has been used for the first time to explore Landau levels of a two-dimensional electron gas (2DEG) in modulation doped InP/InGaAs/InP QW in the quantum Hall regime. The technique gives spectroscopically distinct signals from the bulk Landau levels and the edge states. Evolution of the bulk Landau levels and the edge electronic states is investigated at 2.0 K for magnetic field up to 8 T using SPV spectroscopy.     

Intrinsic spin and orbital angular momentum Hall effect

A generalized definition of intrinsic and extrinsic transport coefficients is introduced. We show that transport coefficients from the intrinsic origin are solely determined by local electronic structure, and thus the intrinsic spin Hall effect is not a transport phenomenon. The intrinsic spin Hall current is always accompanied by an equal but opposite intrinsic orbital angular momentum Hall current. We prove that the intrinsic spin Hall effect does not induce a spin accumulation at the edge of the sample or near the interface.     

The renormalization group and quantum edge states

The role of edge states in phenomena like the quantum Hall effect is well known, and the basic physics has a wide field-theoretic interest. In this paper we introduce a new model exhibiting quantum Hall-like features. We show how the choice of boundary conditions for a one-particle Schrödinger equation can give rise to states localized at the edge of the system. We consider both the example of a free particle and the more involved example of a particle in a magnetic field. In each case, edge states arise from a non-trivial scaling limit involving the boundary condition, and chirality of the boundary condition plays an essential role. Second quantization of these quantum mechanical systems leads to a multi-particle ground state carrying a persistent current at the edge. We show that the theory quantized with this vacuum displays an “anomaly” at the edge which is the mark of a quantized Hall conductivity in the presence of an external magnetic field. These models therefore possess characteristics which make them indistinguishable from the quantum Hall effect at macroscopic distances. We also offer interpretations for the physics of such boundary conditions which may have a bearing on the nature of the excitations in these models.     

Reconstruction of the quantum Hall edge

The sharp quantum Hall edge present for hard confinement is shown to have two modes that go soft as the confining potential softens. This signals a second order transition to a reconstructed edge that is either a depolarized spin-texture edge or a polarized charge density wave edge.     

Electronic transport and quantum hall effect in bipolar graphene p-n-p junctions

We have developed a device fabrication process to pattern graphene into nanostructures of arbitrary shape and control their electronic properties using local electrostatic gates. Electronic transport measurements have been used to characterize locally gated bipolar graphene p-n-p junctions. We observe a series of fractional quantum Hall conductance plateaus at high magnetic fields as the local charge density is varied in the p and n regions. These fractional plateaus, originating from chiral edge states equilibration at the p-n interfaces, exhibit sensitivity to interedge backscattering which is found to be strong for some of the plateaus and much weaker for other plateaus. We use this effect to explore the role of backscattering and estimate disorder strength in our graphene devices.     

Nonlinear quantum shock waves in fractional quantum Hall edge states

Using the Calogero model as an example, we show that the transport in interacting nondissipative electronic systems is essentially nonlinear and unstable. Nonlinear effects are due to the curvature of the electronic spectrum near the Fermi energy. As is typical for nonlinear systems, a propagating semiclassical wave packet develops a shock wave at a finite time. A wave packet collapses into oscillatory features which further evolve into regularly structured localized pulses carrying a fractionally quantized charge. The Calogero model can be used to describe fractional quantum Hall edge states. We discuss perspectives of observation of quantum shock waves and a direct measurement of the fractional charge in fractional quantum Hall edge states.     

Mn3Sn的高压物性研究

非共线三角晶格的反铁磁体Mn_(3)Sn,由于其动量空间中非零的贝里曲率而表现出反常霍尔效应.利用金刚石对顶砧研究压力对Mn_(3)Sn低温电输运性质和反常霍尔效应的影响.结果表明:Mn_(3)Sn在0~60GPa压力范围内保持金属导电行为;从非共线磁有序到螺旋磁有序的转变温度随压力增加先降低,在5.5GPa以上迅速升高,对应一个等结构电子拓扑转变;Mn_(3)Sn的反常霍尔效应在5.5GPa被完全抑制.     

Effective field theory and tunneling currents in the fractional quantum Hall effect

We review the construction of a low-energy effective field theory and its state space for “abelian” quantum Hall fluids. The scaling limit of the incompressible fluid is described by a Chern–Simons theory in 2+1 dimensions on a manifold with boundary. In such a field theory, gauge invariance implies the presence of anomalous chiral modes localized on the edge of the sample. We assume a simple boundary structure, i.e., the absence of a reconstructed edge. For the bulk, we consider a multiply connected planar geometry. We study tunneling processes between two boundary components of the fluid and calculate the tunneling current to lowest order in perturbation theory as a function of dc bias voltage. Particular attention is paid to the special cases when the edge modes propagate at the same speed, and when they exhibit two significantly distinct propagation speeds. We distinguish between two “geometries” of interference contours corresponding to the (electronic) Fabry–Perot and Mach–Zehnder interferometers, respectively. We find that the interference term in the current is absent when exactly one hole in the fluid corresponding to one of the two edge components involved in the tunneling processes lies inside the interference contour (i.e., in the case of a Mach–Zehnder interferometer). We analyze the dependence of the tunneling current on the state of the quantum Hall fluid and on the external magnetic flux through the sample.