Berry phase for a potential well transported in a homogeneous magnetic field

Abstract

We consider a two-dimensional particle of charge $e$ interacting with a homogeneous magnetic field perpendicular to the plane and a potential well which is transported along a closed loop in the plane. We show that a bound state corresponding to a simple isolated eigenvalue acquires at that Berry's phase equal to $2π{\rm sgn} e$ times the number of flux quanta through the oriented area encircled by the loop. We also argue that this is a purely quantum effect since the corresponding Hannay angle is zero.