拓扑新材料研究前沿的理论基础导引Ⅰ:量子霍尔效应

INTRODUCTION TO BASICS OF NEW TOPOLOGICAL MATERIAL RESEARCHⅠ:QUANTUM HALL EFFECTS

本专题旨在为感兴趣且学有余力的本科生和低年级研究生提供一条从大学物理到当前二维、三维拓扑新材料研究前沿的学习路径。专题包含两篇,本文是第一篇。本科生在大学阶段中已修习过电动力学、量子力学、固体物理等课程,但各类教材往往停留在介绍该课程的传统内容,而缺乏向前多走一步、和领域前沿研究相衔接的努力。我们希望能稍微填补这一空当。第一篇从本科生学过的经典霍尔(Hall)效应讲起,首先介绍量子力学是如何被引入二维或(2+1)维霍尔系统研究中的,然后引导到各种量子霍尔效应(包括整数、分数、反常、自旋)及其中的拓扑不变量。

We aim to provide a way for interested undergraduate and postgraduate students to launch from college physics to access the cutting edge of the current international research on two-dimensional and three-dimensional new topological materials.This topic contains two parts,this paper is the first part.Undergraduates have learned electrodynamics,quantum mechanics,solid state physics,and other courses in the university stage.However,many textbooks often stay in the introduction of the traditional content of the course,fail to extend the scope to the latest progress of modern quantum physics.This paper serves as an attempt to fill this gap.Starting from the classical Hall effect in college physics,we first introduce the technique how to apply quantum mechanics to the study of a Hall system in 2-dimension or(2+1)dimensions.Then various quantum Hall effects(integral,fractional,spin and anomalous)and topological invariants existence in them are introduced.