Nonlinear Hall effect in a quasi-two-dimensional electron system

The nonlinear electron transport in GaAs double quantum wells with two occupied size-quantization levels has been studied at a temperature of 4.2 K in the magnetic fields B < 1 T. It has been found that a sinusoidal electric current I _ac induces the generation of higher harmonics of both longitudinal V _xx (B) and Hall V _xy (B) voltages in the quasi-two-dimensional electron system under consideration. The Hall voltage oscillating in the magnetic field has been shown to appear in the electron system with two occupied size-quantization levels in the presence of microwave radiation and dc electric current I _dc. The experimental data indicate the independent contributions of the diagonal and off-diagonal components of the conductivity tensor to the nonlinear magnetotransport at high filling factors.     

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。     

Quantum Hall effect in a two-dimensional electron gas with spin-orbit coupling in the field of a surface superlattice

The Hall conductance of a two-dimensional electronic system with Rashba spin-orbit coupling in the presence of an external periodic potential of a superlattice and a perpendicular magnetic field has been calculated. The calculations were performed for an electron gas with parameters typical both of a system with weak spin-orbit coupling (AlGaAs/GaAs) and a system with relatively strong Rashba coupling (InGaAs/InAs).     

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 spin Hall effect

The quantum Hall liquid is a novel state of matter with profound emergent properties such as fractional charge and statistics. The existence of the quantum Hall effect requires breaking of the time reversal symmetry caused by an external magnetic field. In this work, we predict a quantized spin Hall effect in the absence of any magnetic field, where the intrinsic spin Hall conductance is quantized in units of 2(e/4pi). The degenerate quantum Landau levels are created by the spin-orbit coupling in conventional semiconductors in the presence of a strain gradient. This new state of matter has many profound correlated properties described by a topological field theory.     

Quantum Hall effect in a quasi-three-dimensional HgTe film

Magnetotransport of a quasi-three-dimensional (100-nm) HgTe film in quantized magnetic fields has been experimentally investigated. It has been found that the film exhibits pronounced quantization of the Hall resistance accompanied by deep minima of the dissipative resistance. A transition from the three-dimensional behavior of Shubnikov-de Haas oscillations in semiclassical magnetic fields (ω_cτ _q ≤ 1) to a two-dimensional one in the quantum-Hall-effect regime has been discovered. The conduction electron cyclotron effective mass in mercury telluride has been determined from the temperature dependence of the Shubnikov-de Hass oscillations in such magnetic fields.     

Fractional quantum Hall effect at high fillings in a two-subband electron system

Magnetotransport measurements in a clean two-dimensional electron system confined to a wide GaAs quantum well reveal that, when the electrons occupy two electric subbands, the sequences of fractional quantum Hall states observed at high fillings (ν>2) are distinctly different from those of a single-subband system. Notably, when the Fermi energy lies in the ground state Landau level of either of the subbands, no quantum Hall states are seen at the even-denominator ν=5/2 and 7/2 fillings; instead, the observed states are at ν=[i+p/(2p±1)], where i=2, 3, 4 and p=1, 2, 3, and include several new states at ν=13/5, 17/5, 18/5, 25/7, and 14/3.     

Quantum Hall effect in restricted geometries

The confinement of electrons in narrow quasi-two-dimensional conducting channels, modelled with a parabolic well, leads to asymmetric Hall plateaus about complete Landau-level fillings and to saw-toothed oscillations of the dc resistivity _xx as a function of the magnetic field B. The peaks in _xx are displaced to lower B and drastically reduced from their wide-channel values. The peak values of _xx increase with increasing channel width. The corrections to σ_yx for finite channel widths and the response to oscillating electric fields are evaluated.     

Quantum spin Hall effect in graphene

We study the effects of spin orbit interactions on the low energy electronic structure of a single plane of graphene. We find that in an experimentally accessible low temperature regime the symmetry allowed spin orbit potential converts graphene from an ideal two-dimensional semimetallic state to a quantum spin Hall insulator. This novel electronic state of matter is gapped in the bulk and supports the transport of spin and charge in gapless edge states that propagate at the sample boundaries. The edge states are nonchiral, but they are insensitive to disorder because their directionality is correlated with spin. The spin and charge conductances in these edge states are calculated and the effects of temperature, chemical potential, Rashba coupling, disorder, and symmetry breaking fields are discussed.     

Quantum Hall effect in higher dimensions

Following recent work on the quantum Hall effect on S⁴, we solve the Landau problem on the complex projective spaces $\text{C}\text{P}{}^{\mathrm{k}}$ and discuss quantum Hall states for such spaces. Unlike the case of S⁴, a finite spatial density can be obtained with a finite number of internal states for each particle. We treat the case of $\text{C}\text{P}{}^2$ in some detail considering both Abelian and nonAbelian background fields. The wavefunctions are obtained and incompressibility of the Hall states is shown. The case of $\text{C}\text{P}{}^3$ is related to the case of S⁴.     

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.