A simple technique for evaluating dipole moments of Bloch states in tetrahedral semiconductors

Permanent dipole moments of electronics states in non-centro-symmetric materials play pivotal role in many phenomena. Correctly evaluating them presents an arduous task and usually requires full knowledge of the band structure as well as understanding the intricate concepts of Berry curvature. Here we show that in a few cases (e.g. zinc blende and wurtzite) a rather facile first-principle analytical derivation of the permanent dipole moments using L Hopital rule can be performed, and the values and dispersion of these dipoles near high symmetry points can be found using just a couple of widely available material parameters. The results will hopefully contribute to better understanding of shift currents, optical rectification and other electro-optical phenomena.