Widths of the Hall Conductance Plateaus

We study the charge transport of the noninteracting electron gas in a two-dimensional quantum Hall system with Anderson-type impurities at zero temperature. We prove that there exist localized states of the bulk order in the disordered-broadened Landau bands whose energies are smaller than a certain value determined by the strength of the uniform magnetic field. We also prove that, when the Fermi level lies in the localization regime, the Hall conductance is quantized to the desired integer and shows the plateau of the bulk order for varying the filling factor of the electrons rather than the Fermi level.     

Insensitivity of Quantized Hall Conductance to Disorder and Interactions

A two-dimensional quantum Hall system is studied for a wide class of potentials including single-body random potentials and repulsive electron–electron interactions. We assume that there exists a nonzero excitation gap above the ground state(s), and then the conductance is derived from the linear perturbation theory with a sufficiently weak electric field. Under these two assumptions, we prove that the Hall conductance _xy and the diagonal conductance _yy satisfy | _xy+e ² /h|const·L ^–1/2 and | _yy|const·L ^–1/12. Here e ²/h is the universal conductance with the charge –e of the electron and the Planck constant h; is the filling factor of the Landau level; and L is the linear dimension of the system. In the thermodynamic limit, our results show _xy=–e ² /h and _yy=0. The former implies that integral and fractional filling factors with a gap lead to, respectively, integral and fractional quantizations of the Hall conductance.     

The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect

Recently, a generalization of Laughlin‘s wave function expressed in Haldane‘s spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we usenon-Abelian Berry phase to analyze the statistics of this membrane wave function. Our results show that the membranewave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensional spacethan 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.     

Quantum spin Hall and quantum valley Hall effects in trilayer graphene and their topological structures

The present study pertains to the trilayer graphene in the presence of spin orbit coupling to probe the quantum spin/valley Hall effect. The spin Chern-number C_s for energy-bands of trilayer graphene having the essence of intrinsic spin–orbit coupling is analytically calculated. We find that for each valley and spin, C_s is three times larger in trilayer graphene as compared to single layer graphene. Since the spin Chern-number corresponds to the number of edge states,consequently the trilayer graphene has edge states, three times more in comparison to single layer graphene. We also study the trilayer graphene in the presence of both electric-field and intrinsic spin–orbit coupling and investigate that the trilayer graphene goes through a phase transition from a quantum spin Hall state to a quantum valley Hall state when the strength of the electric field exceeds the intrinsic spin coupling strength. The robustness of the associated topological bulk-state of the trilayer graphene is evaluated by adding various perturbations such as Rashba spin–orbit(RSO) interaction αR, and exchange-magnetization M. In addition, we consider a theoretical model, where only one of the outer layers in trilayer graphene has the essence of intrinsic spin–orbit coupling, while the other two layers have zero intrinsic spin–orbit coupling.Although the first Chern number is non-zero for individual valleys of trilayer graphene in this model, however, we find that the system cannot be regarded as a topological insulator because the system as a whole is not gaped.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall （QH） effect on a noncommutative phase space （NCPS）. By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and θ^-, respectively. In our calculation, we assume that these parameters vary from laver to laver.     

The Fractional Statistics of Generalized Haldane Wave Function in 4D Quantum Hall Effect

Recently, a generalization of Laughlin‘s wave function expressed in Haldane‘s spherical geometry is con-structed in 4D quantum Hall effect. In fact, it is a membrane wave function in CP3 space. In this article, we use non-Abelian Berry phase to anaJyze the statistics of this membrane wave function. Our results show that the membrane wave function obeys fractional statistics. It is the rare example to realize fractional statistics in higher-dimensiona space than 2D. And, it will help to make clear the unresolved problems in 4D quantum Hall effect.     

Noncommutative Quantum Hall Effect of Bilayer Systems

In this paper we study the bilayer quantum Hall (QH) effect on a noncommutative phase space (NCPS). By using perturbation theory, we calculate the energy spectrum, eigenfunction, Hall current, and Hall conductivity of the bilayer QH system, and express them in terms of noncommutative parameters θ and \bar{θ}, respectively. In our calculation, we assume that these parameters vary from layer to layer.     

Quantum Hall effect in intentionally disordered two‐dimensional electron systems

In this work intentionally disordered two‐dimensional electron systems in modulation doped GaAs/GaAlAs heterostructures are studied by magnetotransport experiments. The disorder is provided by a δ‐doped layer of negatively charged beryllium acceptors. In low magnetic fields a strong negative magnetoresistance is observed that can be ascribed to magnetic‐field‐induced delocalization. At increased magnetic fields the quantum Hall effect exhibits broad Hall plateaus whose centers are shifted to higher magnetic fields, i.e. lower filling factors. This shift can be explained by an asymmetric density of states. Consistently, the transition into the insulating state of quantum Hall droplets in high magnetic fields occurs at critical filling factors around ν_c=0.4, i.e. well below the value 1/2 that is expected for symmetric disorder potentials. The insulator transition is characterized by the divergence of both the longitudinal resistance as well as the Hall resistance. This is contrary to other experiments which observe a finite Hall resistance in the insulating regime and has not been observed previously. According to recent theoretical studies the divergence of the Hall resistance points to quantum coherent transport via tunneling between quantum Hall droplets. The magnetotransport experiments are supplemented by simulations of potential landscapes for random and correlated distributions of repulsive scatterers, which enable the determination of percolation thresholds, densities of states, and oscillator strengths for far‐infrared excitations. These simulations reveal that the strong shift of the Hall plateaus and the observed critical filling factor for the insulator transition in high magnetic fields require an asymmetric density of states that can only be generated by a strongly correlated beryllium distribution. Cyclotron resonance on the same samples also indicates the possibility of correlations between the beryllium acceptors.     

Quantum anomalous Hall effect and giant Rashba spin-orbit splitting in graphene system co-doped with boron and 5d transition-metal atoms

Quantum anomalous Hall effect (QAHE) is a fundamental quantum transport phenomenon in condensed matter physics. Until now, the QAHE has only been experimentally realized for Cr/V-doped (Bi, Sb)₂Te₃ but at an extremely low observational temperature, thereby limiting its potential application in dissipationless quantum electronics. By employing first-principles calculations, we study the electronic structures of graphene co-doped with 5d transition metal and boron atoms based on a compensated n–p co-doping scheme. Our findings are as follows: i) The electrostatic attraction between the n- and p-type dopants effectively enhances the adsorption of metal adatoms and suppresses their undesirable clustering. ii) Hf-B and Os-B co-doped graphene systems can establish long-range ferromagnetic order and open larger nontrivial band gaps because of the stronger spin-orbit coupling with the non-vanishing Berry curvatures to host the high-temperature QAHE. iii) The calculated Rashba splitting energies in Re–B and Pt–B co-doped graphene systems can reach up to 158 and 85 meV, respectively, which are several orders of magnitude higher than the reported intrinsic spin-orbit coupling strength.     

超构材料中的光学量子自旋霍尔效应

电子的量子自旋霍尔效应的发现推进了当今凝聚态物理学的发展,它是一种电子自旋依赖的具有量子行为的输运效应.近年来,大量的理论和实验研究表明,描述电磁波场运动规律的麦克斯韦方程组内禀了光的量子自旋霍尔效应,存在于界面的倏逝波表现出强烈的自旋与动量关联性.得益于新兴的光学材料:超构材料(metamaterials)的发展,不仅能够任意设定光学参数,同时也能引入很多复杂的自旋-轨道耦合机理,让我们能够更加清晰地了解和验证其中的物理机理.本文对超构材料中量子自旋霍尔效应做了简要的介绍,内容主要包括真空中光的量子自旋霍尔效应的物理本质、电单负和磁单负超构材料能带反转导致的不同拓扑相的界面态、拓扑电路系统中光量子自旋霍尔效应等.     

Hamiltonians for the Quantum Hall Effect on Spaces with Non-Constant Metrics

The problem of studying the quantum Hall effect on manifolds with non constant metric is addressed. The Hamiltonian on a space with hyperbolic metric is determined, and the spectrum and eigenfunctions are calculated in closed form. The hyperbolic disk is also considered and some other applications of this approach are discussed as well. PACS numbers: 73.43.-f, 02.30.Jr.     

Integer quantum Hall effect in Kekulé-patterned graphene

Y-shaped Kekulébond textures in a honeycomb lattice on a graphene-copper superlattice have recently been experimentally revealed.In this paper,the effects of such a bond modulation on the transport coefficients of Kekulé-patterned graphene are investigated in the presence of a perpendicular magnetic field.Analytical expressions are derived for the Hall and longitudinal conductivities using the Kubo formula.It is found that the Y-shaped Kekulébond texture lifts the valley degeneracy of all Landau levels except that of the zero mode,leading to additional plateaus in the Hall conductivity accompanied by a split of the corresponding peaks in the longitudinal conductivity.Consequently,the Hall conductivity is quantized as±ne²/h for n=2,4,6,8,10,...,excluding some plateaus that disappear due to the complete overlap of the Landau levels of different cones.These results also suggest that DC Hall conductivity measurements will allow us to determine the Kekulébond texture amplitude.     

石墨烯量子霍尔平台与平台之间转变的标度律关系

在2到50 K温度范围内测量了单层石墨烯量子霍尔平台与平台之间转变的标度律关系. 发现石墨烯的标度律指数κ不是普适的,在低温段的κ大约是0.13,在高温段的κ大约是0.33. 这一结果进一步验证了石墨烯中长程散射的主导地位. 关键词： 石墨烯 量子霍尔效应 标度律     

量子霍尔电阻计量技术的应用与分析

目前国际公认精度最高的现代电阻计量技术是量子霍尔电阻计量技术,但是其量子化、非连续特性使它在实际计量应用中受到很多限制。本文围绕先进的电阻比较与计量技术进行分类对比与分析,同时为实现10E-8量级相对不确定度的电阻溯源给出可行的技术方案。最后,针对不同方案给出分析结论,为相关计量实验室根据自身条件建立高精度电阻计量标准提供重要参考。     

Quantum spin Hall effect in a square-lattice model under a uniform magnetic field

We study a toy square-lattice model under a uniform magnetic field. Using the Landauer-Bttiker formula, we calculate the transport properties of the system on a two-terminal, a four-terminal and a six-terminal device. We find that the quantum spin Hall (QSH) effect appears in energy ranges where the spin-up and spin-down subsystems have different filling factors. We also study the robustness of the resulting QSH effect and find that it is robust when the Fermi levels of both spin subsystems are far away from the energy plateaus but is fragile when the Fermi level of any spin subsystem is near the energy plateaus. These results provide an example of the QSH effect with a physical origin other than time-reversal (TR) preserving spin-orbit coupling (SOC).     

Identifying Particle Correlations in Quantum Hall Regime

We introduce a method that allows the disclosure of correlations between particle positions in an arbitrary many‐body system. The method is based on a well‐known simulated annealing algorithm and the proposed artificial distribution technique. Additionally, we investigate correlations in quantum Hall liquids (we consider many‐body wave functions that have been recently determined via the cyclotron subgroup model) and present three‐dimensional plots of configuration probability distributions that have been established from numerical simulations. We demonstrate that the preferred simultaneous positions of particles (configurations of positions, which correspond to large values of a system's probability distribution, ) tend to form complicated geometric structures, which are equivalent to classical Wigner crystals only for Laughlin states. Furthermore, we claim that quantum Hall liquids attributed to non‐Laughlin fillings are correlated on subdomains rather than on a whole particle domain (due to a quantizing magnetic field, which modifies the topology of a system's dynamics). Finally, we characterize Hall‐like internal orders in terms of statistical correlations (one‐dimensional unitary representations of cyclotron subgroups). Our conclusions concerning the stability of many‐body states agree with transport measurements and various numerical studies.     

Quantum anomalous Hall effect in real materials

Under a strong magnetic field,the quantum Hall(QH) effect can be observed in two-dimensional electronic gas systems.If the quantized Hall conductivity is acquired in a system without the need of an external magnetic field,then it will give rise to a new quantum state,the quantum anomalous Hall(QAH) state.The QAH state is a novel quantum state that is insulating in the bulk but exhibits unique conducting edge states topologically protected from backscattering and holds great potential for applications in low-power-consumption electronics.The realization of the QAH effect in real materials is of great significance.In this paper,we systematically review the theoretical proposals that have been brought forward to realize the QAH effect in various real material systems or structures,including magnetically doped topological insulators,graphene-based systems,silicene-based systems,two-dimensional organometallic frameworks,quantum wells,and functionalized Sb(111) monolayers,etc.Our paper can help our readers to quickly grasp the recent developments in this field.     

Quantum spin Hall effect in inverted InAs/GaSb quantum wells

We review the recent experimental progress towards observing quantum spin Hall effect in inverted InAs/GaSb quantum wells (QWs). Low temperature transport measurements in the hybridization gap show bulk conductivity of a non-trivial origin, while the length and width dependence of conductance in this regime show strong evidence for the existence of helical edge modes proposed by Liu et al. [Phys. Rev. Lett., 2008, 100: 236601]. Surprisingly, edge modes persist in spite of comparable bulk conduction and show only weak dependence on magnetic field. We elucidate that seeming independence of edge on bulk transport comes due to the disparity in Fermi-wave vectors between the bulk and the edge, leading to a total internal reflection of the edge modes.