Quantum spin Hall effect in three dimensional materials: Lattice computation of Z$_2$ topological invariants and its application to Bi and Sb

摘要

We derive an efficient formula for Z$_2$ topological invariantscharacterizing the quantum spin Hall effect. It is defined in a latticeBrillouin zone, which enables us to implement numerical calculations forrealistic models even in three dimensions. Based on this, we study the quantumspin Hall effect in Bi and Sb in quasi-two and three dimensions using atight-binding model.