Berry's Phase of Bloch Electrons in Electromagnetic Fields

Abstract

Berry recognized in quantum mechanics a topological phase factor arising from the adiabatic transport of a system around a closed loop, which is essentially the Aharonov-Bohm effect in parameter space. In this paper we consider noninteracting electrons in a periodic potential in the presence of electromagnetic fields. The electric field is represented by a time-dependent vector potential. Adiabatic processes move states along a non-contractible closed loop in the magnetic Brillouin zone which is a torus. The existence of Berry's phases in such processes is shown. A relation with the quantized Hall effect is discussed.