INTRODUCTION TO BASICS OF NEW TOPOLOGICAL MATERIAL RESEARCH Ⅱ: VARIOUS TOPOLOGICAL MATERIALS

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 second part. Based on the quantum Hall effects (integer, fractional, anomalous, spin) reviewed in the first paper of this topic, we give a brief introduction in this paper to several new topological materials: graphene, topological insulators and topological semimetals. As the examples of the two-band model describing the quantum anomalous Hall effects, we discuss the tight-binding model in graphene and square lattices, with emphasis placed on the relationship between energy bands and topological invariants, as well as the resulting bulk-boundary correspondence. The reader is suggested to strengthen the capability of theoretical calculation by paying attention to spin-orbit coupling, Fourier transform of Hamiltonian, solving energy bands, and the calculation of topological invariants and edge states. Finally a brief introduction to the energy bands and the corresponding surface states are also presented for different types of semimetals.