三维量子Hall效应电阻平台与能隙

The Resistance Platform and Energy Gap of 3D Quantum Hall Effect

量子Hall效应最先在强磁场中的二维电子气体中产生,是一种内部绝缘、边缘单向导电、电阻为零的拓扑绝缘态,电阻平台的出现及纵向电阻的消失是量子Hall效应产生的标志。对于三维电子气体,z方向的自由度会破坏体系内部绝缘,阻碍量子Hall效应产生。解决问题的方法是让z方向磁场引诱体系在费米能级处产生能隙,从而保障内部绝缘。三维量子Hall效应是研究量子相变很好的平台,z方向磁场引发两种相变:在xy平面引发拓扑相变,在z方向引发体系由金属态向绝缘态的朗道相变。三维量子Hall效应最近在ZrTe5、HfTe5材料中观察到,与二维整数量子Hall效应的电阻平台出现在整数处不同,三维量子Hall效应的电阻平台出现在h/e^(2)λ_(F,z)/2处,其中λF,z为电子在磁场z方向的费米波长。本文讨论量子Hall效应电阻平台出现以及纵向电阻消失的原因:朗道能级填满阻止左右边缘态电子的相互散射,保障了体系边缘的单向导电性和零电阻;用规范不变性理论推导三维量子Hall效应电阻平台的理论值,理论值与实验结果符合得很好;从自旋与轨道耦合理论出发,推导磁场在费米能级处产生能隙,从而引发三维量子Hall效应。

The quantum Hall effect is first generated in the two-dimensional electron gas in the strengthened magnetic field,it is a topological insulator with internal insulation,edge Unidirectional conduction and zero resistance.The emergence of resistance plateau and the disappearance of longitudinal resistance are the hallmarks of the generation of quantum Hall effect.For threedimensional electron gas,the degree of freedom in the z direction destroys the internal insulating state.The solution to the problem is let the z-direction magnetic field inducing the system to produce an energy gap at the Fermi level,which remains internal insulation.Three-dimensional quantum Hall effect is a good platform for studying quantum phase transition,one parameter(magnetic field in Z direction)causes two kinds of phase transitions:topological phase transition in XY plane and Landau phase transition from metal to insulator in Z direction.Recently,it has been realized experimentally in bulk ZrTe_(5) and HfTe_(5) crystals.Unlike the integer resistance platform of two-dimensional integer quantum Hall effect,the resistance plateau of three-dimensional quantum Hall effect appearsh/e^(2)(λ_(F,z)/2),where A_(F,Z) is the Fermi wavelength along the field direction(z axis).In this paper,the reason why the quantum Hall effect resistance plateau appears and the longitudinal resistance disappears is analyzed:Landau level is filled to prevent the scattering between left and right edge state electrons,so as to ensure the unidirectional conductivity and zero resistance of bulk edge,the resistance plateau value of three-dimensional quantum Hall effect is derived by using gauge invariance theory,the theoretical values are in good agreement with the experimental results.Based on the spin orbit coupling theory,it is deduced that the magnetic field produces an energy gap at the Fermi level,which leads to the generation of three-dimensional quantum Hall effect.