Nonlocal approach to energy bands in periodic lattices and emergence of electron mass enhancement

In this study, we analyze energy bands in periodic lattices based on the nonlocal-in-time kinetic energy approach introduced recently by Suykens. We consider the electron dynamics in the periodic potential and construct a nonlocal approach to the weak binding case in three dimensions. A number of features are revealed. In particular, we demonstrate an effective mass enhancement for electrons of around m∗≈167α−2Gev/c2 for typical solids, where α is a real free parameter.