Classification of Topological Insulators with Time-Reversal and Inversion Symmetry

Abstract

In this paper, we find that topological insulators with time-reversal symmetry and inversion symmetry featuring two-dimensional quantum spin Hall (QSH) state can be divided into 16 classes, which are characterized by four Z2 topological variables ζk = 0, 1 at four points with high symmetry in the Brillouin zone. We obtain the corresponding edge states for each one of these sixteen classes of QSHs. In addition, it is predicted that massless fermionic excitations appear at the quantum phase transition between different QSH states. In the end, we also briefly discuss the three-dimensional case.