Electron localization in the insulating state: Application to crystalline semiconductors - art. no. 115202

We measure electron localization in different materials by means of a "loca lization tensor", based on Berry phases and related quantities. We analyze its properties, and we actually compute such tensor from first principles f or several tetrahedrally coordinated semiconductors. We discuss the trends in our calculated quantity, and we relate our findings to recent work by ot her authors, We also address the "hermaphrodite orbitals", which are locali zed (Wannier-like) in a given direction, and delocalized (Bloch-like) in th e two orthogonal directions: our tensor is related to the optimal localizat ion of these orbitals. We also prove numerically that the decay of the opti mally localized hermaphrodite orbitals is exponential.