INTRODUCTION TO BASICS OF NEW TOPOLOGICAL MATERIAL RESEARCH Ⅰ: QUANTUM HALL EFFECTS

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.