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

Abstract

It is well-known that quantum states of light and matter are basically nonlocal which reflect the fundamental property of wave-particle duality. Nonlocality which is the most fascinating and hardly understood phenomenon of the quantum theory is in general manifested when measurements (in space or in time) on two or additional isolated quantum mechanical systems are achieved. As a result, physical effects can be correlated technically to some extent defying any local classical explanation and for that reason quantum mechanics is nonlocal. It was argued in that an association between Heisenberg's uncertainty principle (HUP) and non locality holds for merely all physical systems and moreover a link between the "Einstein's spooky action at a distance" concept and HUP exits. We analyze energy bands in periodic lattices based on the nonlocal-in-time kinetic energy approach. 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 for typical solids, where is a real free parameter.