Topological characterization of delocalization in a spin-orbit coupling system

We show that wave functions in a two-dimensional (2D) electron system with spin-orbit coupling can be characterized by a topological quantity—the Chern integer due to the existence of the intrinsic Kramers degeneracy. The localization-delocalization transition in such a system is studied in terms of such a Chern number description, which reproduces the known metal-insulator transition point. The present work suggests a unified picture for various known 2D delocalization phenomena based on the same topological characterization.