Berry’s phase and the Magnus force for a vortex line in a superconductor

Abstract
We show that the existence of the Magnus force is a general property of a vortex line in a superconductor by calculating the Berry phase for an adiabatic motion around a closed loop at zero temperature. We find that there is no influence of the disorder and the electromagnetic field on the existence of the Magnus force in the superconducting state, and its magnitude is proportional to the superfluid electron density.