Transverse forces on vortices in superfluids in a periodic potential

Abstract

The paper analyzes the transverse forces (the Magnus and the Lorentz forces) on vortices in superfluids put into periodic potentials at $T=0$. The case of weak potential and the tight-binding limit described by the Bose-Hubbard model were addressed. The analysis was based on the balance of true momentum and quasimomentum. A special attention was paid to the superfluid close to the superfluid-insulator transition. In this area of the phase diagram the theory predicts the particle-hole symmetry line where the Magnus force changes sign with respect to that expected from the sign of velocity circulation. Our analysis has shown that the magnitude of the Magnus force is a continuous function at crossing the particle-hole symmetry line. This challenges the theory connecting the magnitude of the Magnus force with topological Chern numbers and predicting a jump at crossing this line. Disagreement is explained by the role of intrinsic pinning and guided vortex motion ignored in the topological approach. It is one more evidence that in general topological arguments are not sufficient for derivation of equations of vortex motion.