Weak localization and universal conductance fluctuations in multi-layer graphene

We have performed magneto transport measurements on a multi-layer graphene device fabricated by conventional mechanical exfoliation. Suppression of weak localization (WL) as evidenced by the negative magnetoresistance (NMR) centered at zero field, and reproducible universal conductance fluctuations (UCFs) are observed. Interestingly, it is found that the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are longer than those determined from fitting the amplitudes of the UCFs to theory in the low temperature regime (T ≤ 8 K). In the high temperature regime (T > 8 K), the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory. Our new results therefore indicate a difference in the electron phase-breaking process between the two models of WL and UCFs in graphene. We speculate that the presence of the capping and bottom graphene layers, which leads the enhancement of disorder in-between, improves the localization condition for WL effect during carrier transportation in the low temperature regime. With increasing temperature, the localization condition for WL in multi-layer graphene becomes much weaker due to strong thermal damping. Therefore, the phase coherence lengths calculated by fitting the observed NMR to conventional WL theory are shorter than those determined from fitting the amplitudes of the UCFs to theory at high temperatures.     

Edge state propagation direction in the fractional quantum Hall regime: multi-terminal magnetocapacitance experiment

The propagation direction of fractional quantum Hall effect (FQHE) edge states has been investigated experimentally via the symmetry properties of the multi-terminal capacitances of a two-dimensional electron gas. Although strong asymmetries with respect to zero magnetic field appear, no asymmetries with respect to even denominator Landau level filling factor ν are seen. This indicates that current-carrying FQHE edge states propagate in the same direction as integer QHE edge states. In addition, anomalous capacitance features, indicative of enhanced bulk conduction, are observed at and .     

Current breakdown of the integer and fractional quantum Hall effects detected by torque magnetometry

We have developed a novel technique that enables measurements of the breakdown of both the integer and fractional quantum Hall effects in a two-dimensional electron system without the need to contact the sample. The critical Hall electric fields that we measure are significantly higher than those reported by other workers, and support the quasi-elastic inter-Landau-level tunnelling model of breakdown. Comparison of the fractional quantum Hall effect results with those obtained on the integer quantum Hall effect allows the fractional quantum Hall effect energy gap to be determined and provides a test of the composite-fermion theory. The temperature dependence of the critical current gives an insight into the mechanism by which momentum may be conserved during the breakdown process.     

Quantum phase fluctuations responsible for pseudogap

The effect of ordering field phase fluctuations on the normal and superconducting properties of a simple 2D model with a local four-fermion attraction is studied. Neglecting the coupling between the spin and charge degrees of freedom an analytical expression has been obtained for the fermion spectral function as a single integral over a simple function. From this we show that, as the temperature increases through the 2D critical temperature and a nontrivial damping for a phase correlator develops, quantum fluctuations fill the gap in the quasiparticle spectrum. Simultaneously the quasiparticle peaks broaden significantly above the critical temperature, resembling the observed pseudogap behavior in high-T_c superconductors.     

Towards a field theory of the plateau transitions in the integer quantum Hall effect

We suggest a procedure for calculating correlation functions of the local densities of states (DOS) at the plateau transitions in the integer quantum Hall effect (IQHE). We argue that their correlation functions are appropriately described in terms of the SL( )/SU(2) WZNW model (at the usual Ka –Moody point and with the level 6≤k≤8 ). In this model we have identified the operators corresponding to the local DOS, and derived the partial differential equation determining their correlation functions. The OPEs for powers of the local DOS obtained from this equation are in agreement with available results.     

Length-independent voltage fluctuations in small conductors

The mean-squared voltage fluctuation of a disordered conductor of lengthL smaller than the phase coherence lengthL _ϕ, is independent of the distance between the probes. We obtain this result using the voltage additivity and the known results for the conductance fluctuation. Our results complement the recent theoretical and experimental findings.     

Toward realistic effective models of quantum-Hall edges

We have investigated the dynamical properties of edge excitations in the (fractional) quantum-Hall regime for a sharp confining potential, emphasizing the effects resulting from the presence of long-range interaction. Our study uses chiral-Luttinger-liquid models that are motivated by the close analogy between the physics of edge excitations and that of plasmons in quasi-one-dimensional electron systems. We find that incorporating realistic long-range interaction is especially important for multi-branch edges. Results are presented for the tunneling-IV-curve power-law exponent and the two-terminal conductance.     

Fixed-phase diffusion Monte Carlo study of the quantum-Hall effect on the Haldane sphere

A generalized diffusion Monte Carlo method for solving the many-body Schrödinger equation on curved manifolds is introduced and used to perform a ‘fixed-phase’ simulation of the integer and fractional quantum-Hall effect on the Haldane sphere. The effect of Landau level mixing on the and energy gaps and the relative stability of spin-polarized and spin-reversed quasielectron excitations are studied using the new method.     

Rashba自旋轨道耦合下square-octagon晶格的拓扑相变

本文研究了各向同性square-octagon晶格在内禀自旋轨道耦合、Rashba自旋轨道耦合和交换场作用下的拓扑相变,同时引入陈数和自旋陈数对系统进行拓扑分类.系统在自旋轨道耦合和交换场的影响下会出现许多拓扑非平庸态,包括时间反演对称破缺的量子自旋霍尔态和量子反常霍尔态.特别的是,在时间反演对称破缺的量子自旋霍尔效应中,无能隙螺旋边缘态依然能够完好存在.调节交换场或者填充因子的大小会导致系统发生从时间反演对称破缺的量子自旋霍尔态到自旋过滤的量子反常霍尔态的拓扑相变.边缘态能谱和自旋谱的性质与陈数和自旋陈数的拓扑刻画完全一致.这些研究成果为自旋量子操控提供了一个有趣的途径.     

Inter-layer edge tunneling and transport properties in separately contacted double-layer quantum-Hall systems

A theory of transport in the quantum-Hall regime is developed for separately contacted double-layer electron systems. Inter-layer tunneling provides a channel for equilibration of the distribution functions in the two layers at the edge states. Resistances and transresistances for various configurations of the electrodes are calculated as functions of the inter-layer tunneling amplitude. Induced current in one of the layer by a current in the other is also calculated. It is shown that reflection at the leads causes change in the results for some electrode configurations. The results obtained in this work is consistent with recent experiments.     

Experimental evidence for a metal–insulator transition and geometric effect in a half-filled Landau level

We have measured the low-temperature transport properties of a high-mobility front-gated GaAs/Al Ga As heterostructure. By changing the applied gate voltage, we can vary the amount of disorder within the system. At a Landau level filling factor , where the system can be described by the composite fermion picture, we observe a crossover from metallic to insulating behaviour as the disorder is increased, in agreement with theory. We also report experimental evidence of geometric effect for composite fermions induced by an effective magnetic field.     

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。     

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 fluctuations of the antiferro-antiferromagnetic double-layer

This paper stuides the magnetization and quantum fluctuations of an antiferro-antiferromagnetic (AF-AF) double-layer at zero temperature. It is found that the exchanges and anisotropy constants affect the quantum fluctuations of spins. If the anisotropy exists, there will be no acoustic energy branch in the system. The anisotropy constant, antiferromagnetic intralayer and interlayer coupling have important roles in a balance of the quantum competition.     

Current distribution in the integer quantum Hall effect: The role of bulk states

The role of bulk and edge currents in a two-dimensional electron gas under the conditions of the integer quantum Hall effect (IQHE) was studied by means of an inductive coupling to Hall bar geometry. From this study we conclude that the extended states at the bulk of the sample below the Fermi energy are capable of carrying a substantial amount of Hall current. For Hall bar geometry sample with a back gate we demonstrated that injected current can be pushed from one edge to another by reversing the direction of the external magnetic field.     

Collapse of quantized Hall resistance and breakdown of dissipationless state in the integer quantum Hall effect: filling factor dependence

Magnetic field dependence of critical current for collapse of quantized Hall resistance I_cr(collapse) and critical current for breakdown of dissipationless state I_cr(breakdown) have been measured near the filling factor ν=4 of Landau levels in a GaAs/AlGaAs heterostructure Hall bar. The difference I_cr(breakdown)−I_cr(collapse) decreases against the increase and the decrease in ν from 4 and the critical behavior disappears outside of the region 3.85<ν<4.15.     

Shape and phase transitions in quantum-Hall skyrmions

The shape deformability of quantum-Hall skyrmions leads to a rich phase diagram in the –g space. We study the long-wavelength physics of a collection of interacting skyrmions using a nonlinear sigma model. At zero temperature the ground state is crystalline with generalized Nèel order. As a function of the filling factor , the skyrmion crystal undergoes a sequence of structural transitions driven by a change of shape of the individual skyrmions. Quantum effects lead to melting and orientational disordering transitions at high and low skyrmion densities, respectively. We show that moment of inertia of skyrmions also arises from the shape deformability of the skyrmions.     

Control of topological phase transitions in Dirac semimetal films by exchange fields

The exchange field effects on topological Dirac semimetal(DSM) films are discussed in this article. A topological phase transition can be controlled by tuning the exchange field together with the quantum confinement effects. What is more interesting is that the system can transit into the quantum anomalous Hall(QAH) state from the topologically trivial state(Z_2 = 0) or from the topologically nontrivial state(Z_2 = 1), depending on the thickness of the DSM films. This provides a useful mechanism to realize the QAH state from the DSM.     

Vacuum lightcone fluctuations in a dielectric

A model for observable effects of time modulated electromagnetic vacuum fluctuations is presented. The model involves a probe pulse which traverses a slab of nonlinear optical material with a nonzero second order polarizability. We argue that the pulse interacts with the ambient vacuum fluctuations of other modes of the quantized electric field, and these vacuum fluctuations cause variations in the flight time of the pulse through the material. The geometry of the slab of material defines a sampling function for the quantized electric field, which in turn determines that vacuum modes whose wavelengths are of the order of the thickness of the slab give the dominant contribution. Some numerical estimates are made, which indicate that fractional fluctuations in flight time of the order of 10⁻⁸$10^{-8}$ are possible in realistic situations. The model presented here is both an illustration of a physical effect of vacuum fluctuations occurring in a finite interval of time, and an analog model for the lightcone fluctuations predicted by quantum gravity.     

Theory of the integer quantum Hall effect in graphene

A Hall resistivity formula for the 2DES in graphene is derived from the zero-mass Dirac field model adopting the electron reservoir hypothesis. The formula reproduces perfectly the experimental resistivity data [K.S. Novoselov, et al., Nature 438 (2005) 201]. This perfect agreement cannot be achieved by any other existing models. The electron reservoir is shown to be the 2DES itself.