2 9 Ja n 20 01 Electron localization in the insulating state : Application to crystalline semiconductors

The insulating state of matter is characterized by the excitation spectrum, but also by qualitative features of the electronic ground state. The insulating ground wavefunction in fact: (i) sustains macroscopic polarization, and (ii) is localized. We describe both properties using essentially the same formalism, based on Berry phases and related quantities, and specializing to the case of a crystalline system of independent electrons. We measure localization in different materials by means of a “localization tensor”: we analyze its properties, and we actually compute it from first principles for several tetrahedrally coordinated semiconductors. We discuss the trends in our calculated quantity, and we relate our findings to related recent work. We also address orbitals (“hermaphrodite orbitals”) which are optimally localized (Wannier–like) in a given direction, and delocalized (Bloch–like) in the two orthogonal directions: we prove numerically that their localization is exponential. Typeset using REVTEX 1