The Transport Properties Of Weyl Semimetals

Weyl semimetals are three-dimensional topological states of matter, whose valence and conduction bands contact with each other at some points of the momentum space, the so-called Weyl points. In the vicinity of the Weyl points, the quasiparticle excitations have linear dispersion, following the Weyl equations of massless relativistic particles. When the Fermi surface near the Weyl nodes is closed, we call those semimetals the type-I semimetals. If the Fermi surface is open, we call those type-II Weyl semimetals. It has been established from both theory and experiment that the type-I Weyl semimetals show a number of novel transport properties under electric-magnetic fields. The main purpose of the present Thesis is to study the transport properties of the type-II Weyl semimetals under magnetic fields.This Thesis consists of four chapters. In Chapter One we introduce the topological aspects and the classcification of the Weyl semimetals. In Chapter Two we review the recent experimental advances on the type-I and type-II Weyl semimetals. In Chapter Three we first review the previous transport theory of the type-I Weyl semimetals. We then discuss how to extend such theory to the type-II Weyl semimetals. Here we mainly focus on the formation of the Landau level under various magnetic fields and conductance based on the self-consistent Born approximation. In Chapter Four we present a brief summary. The main results of our study are the following:1.We use the geometric method to calculate the density of states of type-â…¡ Weyl semimetals.2. We present the detailed analytical solution of the Landau levels of the Weyl semimetals which have no kinetic energy term under various magnetic fields.3. We calculate the Fermi-velocity-dependent conductivity of the type-II Weyl semimetals.These results provide a theoretical prediction for the magneto-conductivity or magneto-resistance of the type-II Weyl semimetals.