Characterization of three-dimensional topological insulators by two-dimensional invariants

The prediction of nontrivial topological phases in Bloch insulators in three dimensions has recently been experimentally verified. Here, I provide a picture for obtaining the Z(2) invariants for a three-dimensional (3D) topological insulator by deforming suitable 2D planes in momentum space and by using a formula for the 2D Z(2) invariant based on the Chern number. The physical interpretation of this formula is also clarified through the connection between this formulation of the Z(2) invariant and the quantization of spin Hall conductance in two dimensions.