量子霍尔效应曲线的分形特征

继冯·克利青 (vonKlitzing) 1980年发现整数量子霍尔效应之后 ,美籍华裔科学家崔琦于 1982年发现了分数量子霍尔效应———受限于平面的二维电子气 ,在强外场B垂直于平面的条件下 ,其霍尔电压VH 作为B的函数表现出一连串的平台 ;与每一平台相对应的霍尔电阻VH/I(I是沿平面的纵向电流 )恰好等于物理常数h/e2 除以一个分数ν(ν =2 / 3,3/ 5 ,2 / 5 ,1/ 3… ) .当外场B较低时 ,发生整数量子霍尔效应 ,此时 ,与上述ν相对应的是克里青整数i(i =1,2 ,3… ) ,i的物理意义是每一根量子磁通所分摊到的电子数 .在外场的作用下 ,每一个电子绕其…     

量子霍尔效应的发展历程

量子霍尔效应的发现是新兴的低维凝聚态物理发展中的一件大事,分数量子霍尔效应的发现更是开创了一个研究多体现象的新时代,并将影响到物理学的很多分支,这个领域两次被授予诺贝尔物理奖,引起了人们很大的兴趣,文章介绍了量子霍尔效应发展的历程,主要内容包括１８９７年霍尔发现霍尔效应、１９８０年Ｋｌａｕｓ ｖｏｎ Ｋｌｉｔｚｉｎｇ发现整数量子霍尔效应、１９８２年崔琦和Ｈｏｒｓｔ Ｌ．Ｓｔｏｒｍｅｒ发现分数量子霍     

自旋霍尔效应电信号的直接探测

一块长方形的金属板置于磁场中，磁场的方向（z方向）垂直于板面，在板的纵向（x方向）通入电流，则在板的横向（y方向）可检测到霍尔电压。1879年，Edwin Hall发现了上述正负电荷非平衡聚积的现象，后来被命名为霍尔效应。100年后，1980年和1982年，von Klitzing和崔琦等利用二维电子气作为样品，在高场下分别发现了整数量子霍尔效应和分数量子霍尔效应，并先后获得诺贝尔物理学奖。最近，来自哈佛大学物理系的Tinkham等在Nature剧刊撰文，报告了他们用电学方法在探测自旋霍尔效应的实验中所取得的进展。     

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。     

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     

Graphene的物理性质与器件应用

Graphene因其新奇的物理性质和广泛的应用前景已迅速成为国际新材料领域的研究前沿和热点.文章详细介绍了Graphene奇特的物理性质(多体相互作用、量子霍尔效应、双极场效应、弱局域化效应等),并对其在微纳米器件、分子电子学、自旋电子学等领域的应用进展给出了综述.     

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。     

整数量子霍尔效应的问题与解答

本文的目的是让学生运用学过的大学物理中的量子力学知识来解释整数量子霍尔效应．在探究问题的过程中需要掌握薛定谔方程及其对线性谐振子的解，用对易算符建立相应的本征值，熟悉周期性边界条件，以及用哈密顿量中的磁场的矢势来描述磁场与电子的相互作用。     

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.     

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.     

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.     

Bound values for Hall conductivity of heterogeneous medium under quantum Hall effect conditions

Bound values for Hall conductivity under quantum Hall effect (QHE) conditions in inhomogeneous medium has been studied. It is shown that bound values for Hall conductivity differ from bound values for metallic conductivity. This is due to the unusual character of current percolation under quantum Hall effect conditions.      

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.     

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.     

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 .     

The quantum Hall＇s effect： A quantum electrodynamic phenomenon

<正>We have applied Maxwell’s equations to study the physics of quantum Hall’s effect.The electromagnetic properties of this system are obtained.The Hall’s voltage,V_H = 2πh²n_s/em,where n_s is the electron number density,for a 2- dimensional system,and h = 2πh is the Planck’s constant,is found to coincide with the voltage drop across the quantum capacitor.Consideration of the cyclotronic motion of electrons is found to give rise to Hall’s resistance. Ohmic resistances in the horizontal and vertical directions have been found to exist before equilibrium state is reached. At a fundamental level,the Hall’s effect is found to be equivalent to a resonant LCR circuit with L_H = 2πm/e²n_s and C_H = me²/2πh²n_s satisfying the resonance condition with resonant frequency equal to the inverse of the scattering （relaxation） time,τ_s.The Hall’s resistance is found to be R_H =（（L_H）/C_H）^1/2.The Hall’s resistance may be connected with the impedance that the electron wave experiences when it propagates in the 2-dimensional gas.