Bound values for Hall conductivity and percolation under quantum Hall effect conditions

The percolation under Quantum Hall Effect conditions in inhomogeneous medium has been studied. The lower and upper bound possible values for effective Hall conductivity values have been established. It has been shown that these bound values for Hall conductivity differ from bound values for metal conductivity. It comes from unusual character of current percolation under Quantum Hall Effect conditions. The physical sense of obtained results has been discussed.     

Ballistic transport under quantum Hall effect conditions

The paper addresses details of the single-particle electron spectrum ?_l(p)${?}_l(p)$ in narrow Coulomb channels (l is the transverse spectrum part discrete index and p   is the continuous longitudinal electron momentum). The channel is said to be narrow if differences between transverse spectrum branches ?_l(p)${?}_l(p)$ are larger than temperature. Considered are two extreme cases with respect to magnetic field. For the first case where ?_F≥?ω_c${?}_F\ge \mathit{?}{\omega }_c$, the spectrum ?_l(p)${?}_l(p)$ first calculated by Stern et al. numerically is obtained with approximate analytical analysis (here ?_F${?}_F$ is the Fermi energy of the 2D electron system ?ω_c$\mathit{?}{\omega }_c$ is the cyclotron frequency). In the second case the proposed formalism is extended to high magnetic fields satisfying the inequality ?_F≤?ω_c${?}_F\le \mathit{?}{\omega }_c$. Calculated results are compared with available experimental data.     

量子霍尔效应

从经典的霍尔效应开始,比较系统地、深入浅出地介绍了量子霍尔效应及其所涉及的一些新概念和实际应用。     

Jain hierarchy for the fractional quantum Hall effect

We propose the effective hierarchical partition function which is able to describe both the Jain states and the Jain-type hierarchical states. Using this partition function (effective Lagrangian) we calculate the charge of the quasiparticle excitations. We show that the Jain-type hierarchical states are equivalent to the system of anyons in the external magnetic field.     

从分数量子霍尔效应到拓扑量子计算*

分数量子霍尔效应系统是奇异的量子液体,其中的准粒子激发可以带分数电荷,甚至具有非阿贝尔的统计性质。理论研究表明,这些准粒子可以用来实现在硬件上可容错的量子计算,即拓扑量子计算。文章在介绍分数量子霍尔效应及其在拓扑量子计算中的潜在应用基础上,重点回顾了近五年来对填充因子为5/2的分数量子霍尔态中非阿贝尔准粒子的实验探测和部分相关理论诠释。     

从分数量子霍尔效应到拓扑量子计算

分数量子霍尔效应系统是奇异的量子液体,其中的准粒子激发可以带分数电荷,甚至具有非阿贝尔的统计性质。理论研究表明,这些准粒子可以用来实现在硬件上可容错的量子计算,即拓扑量子计算。文章在介绍分数量子霍尔效应及其在拓扑量子计算中的潜在应用基础上,重点回顾了近五年来对填充因子为5/2的分数量子霍尔态中非阿贝尔准粒子的实验探测和部分相关理论诠释。     

铁磁石墨烯体系的CT不变量子自旋霍尔效应

文章作者在垂直磁场作用下的铁磁石墨烯体系里预言了一种新类型的量子自旋霍尔效应.这量子自旋霍尔效应与自旋轨道耦合无关,体系也不具有时间反演不变性;但是有CT不变（C为电子-空穴变换、T为时间反演变换）.由于量子自旋霍尔效应,体系的纵向电阻和自旋霍尔阻出现量子化平台.特别是,自旋霍尔阻的量子化平台有很强的抗杂质干扰能力.     

An analogue of the quantum Hall conductivity for a magnetic quadrupole moment

The quantum dynamics of a moving particle with a magnetic quadrupole moment that interacts with electric and magnetic fields is introduced. Then, it is discussed which conditions the external fields must satisfy so that an analogue of the Landau quantization can be obtained. Finally, by dealing with the lowest Landau level associated with the magnetic quadrupole system, an analogue of the quantum Hall conductivity is obtained.

     

The robustness of the quantum spin Hall effect to the thickness fluctuation in HgTe quantum wells

The quantum spin Hall effect(QSHE) was first realized in HgTe quantum wells(QWs),which remain the only known two-dimensional topological insulator so far.In this paper,we have systematically studied the effect of the thickness fluctuation of HgTe QWs on the QSHE.We start with the case of constant mass with random distributions,and reveal that the disordered system can be well described by a virtual uniform QW with an effective mass when the number of components is small.When the number is infinite and corresponds to the real fluctuation,we find that the QSHE is not only robust,but also can be generated by relatively strong fluctuation.Our results imply that the thickness fluctuation does not cause backscattering,and the QSHE is robust to it.     

From magnetically doped topological insulator to the quantum anomalous Hall effect

Quantum Hall effect （QHE）, as a class of quantum phenomena that occur in macroscopic scale, is one of the most important topics in condensed matter physics. It has long been expected that QHE may occur without Landau levels so that neither external magnetic field nor high sample mobility is required for its study and application, Such a QHE free of Landau levels, can appear in topological insulators （TIs） with ferromagnetism as the quantized version of the anomalous Hall effect, i.e., quantum anomalous Hall （QAH） effect. Here we review our recent work on experimental realization of the QAH effect in magnetically doped TIs. With molecular beam epitaxy, we prepare thin films of Cr-doped （Bi,Sb）2Te3 TIs with well- controlled chemical potential and long-range ferromagnetic order that can survive the insulating phase. In such thin films, we eventually observed the quantization of the Hall resistance at h/e2 at zero field, accompanied by a considerable drop in the longitudinal resistance. Under a strong magnetic field, the longitudinal resistance vanishes, whereas the Hall resistance remains at the quantized value. The realization of the QAH effect provides a foundation for many other novel quantum phenomena predicted in TIs, and opens a route to practical applications of quantum Hall physics in low-power-consumption electronics.     

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.     

Localization length at the conductivity minima of the quantum Hall effect

The quantum localization is known to be responsible for the deep conductivity minima of the quantum Hall effect. In this paper we calculate the localization length as a function of magnetic field at such minima for several models of disorder (“white-noise”, short-range, and long-range random potentials). We find that with the exponent between one and , depending on the model. In particular, for the “white-noise” random potential roughly coincides with the classical cyclotron radius. Our results are in agreement with available experimental data.     

Quark confinement and the fractional quantum Hall effect

Working in the physics of Wilson factor and Aharonov-Bohm effect, we find in the fluxtube-quark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect (FQHE) in condensed matter. This similarity yields the result that the constituent quarks of baryon have the ``filling factor' 1/3, thus the previous conjecture that quark confinement is a correlation effect is confirmed. Moreover, by deriving a Hamiltonian of the system analogous to that of FQHE, we predict an energy gap for the ground state of a heavy three-quark system.     

Quark confinement and the fractional quantum Hall effect

Working in the physics of Wilson factor and Aharonov-Bohm effect,we find in the fluxtubequark system the topology of a baryon consisting of three heavy flavor quarks resembles that of the fractional quantum Hall effect(FQHE)in condensed matter.This similarity yields the result that the constituent quarks of baryon have the"filling factor"1/3.thus the previous conjecture that quark confinement is a correlation effect is confirmed.Moreover,by deriving a Hamiltonian of the system analogous to that of FQHE,we predict an energy gap for the ground state of a heavy three-quark system.     

原子霍尔效应中复合粒子和场描述

研究了原子霍尔效应中复合粒子描述方法，并进一步给出Chern－Simon－Gross－Pitaevskii(CSGP)有效场描述。研究结果表明从平均场和复合粒子的角度来看原子霍尔效应和电子霍尔效应是一致的。     

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.     

Prediction of quantum anomalous Hall effect in CrI3/ScCl2 bilayer heterostructure

Based on first-principles calculations, a two-dimensional (2D) van der Waals (vdW) bilayer heterostructure consisting of two topologically trivial ferromagnetic (FM) monolayers CrI₃ and ScCl₂ is proposed to realize the quantum anomalous Hall effect (QAHE) with a sizable topologically nontrivial band gap of 4.5 meV. Its topological nature is attributed to an interlayer band inversion between the monolayers and critically depends on the symmetry of the stacking configuration. We further demonstrate that the topologically nontrivial band gap can be increased nearly linearly by the application of a perpendicular external pressure and reaches 8.1 meV at 2.7 GPa, and the application of an external out-of-plane electric field can also modulate the band gap and convert the system back to topologically trivial via eliminating the band inversion. An effective model is developed to describe the topological phase evolution in this bilayer heterostructure. This work provides a new candidate system based on 2D vdW materials for realization of potential high-temperature QAHE with considerable controllability.     

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.     

Anomalous quantum Hall effect induced by nearby quantum dots

Transport measurements in high magnetic fields have been performed on two-dimensional electron system (2DES) separated by a thin barrier layer from a layer of InAs self-assembled quantum dots (QDs). Clear feature of quantum Hall effect was observed in spite of presence of QDs nearby 2DES. However, both magnetoresistance, ρ_xx, and Hall resistance, ρ_xy, are suppressed significantly only in the magnetic field range of filling factor in 2DES ν<1 and voltage applied on a front gate . The results indicate that the electron state in QDs induces spin-flip process in 2DES.