The Magnus force in superfluids and superconductors

TL;DR

This paper investigates the various transverse forces acting on vortices in superfluids and superconductors, revealing that external fields can cancel the superfluid Magnus force, affecting the Hall effect.

Contribution

It provides a comprehensive analysis of transverse forces, including quasiparticle and external field effects, and demonstrates the cancellation of the Magnus force in certain systems.

Findings

Transverse forces from quasiparticles are derived using the Born approximation.

External fields can violate translational invariance and influence vortex forces.

In 2D Josephson junction arrays, the total transverse force on vortices vanishes.

Abstract

The forces on the vortex, transverse to its velocity, are considered. In addition to the superfluid Magnus force from the condensate (superfluid component), there are transverse forces from thermal quasiparticles and external fields violating the translational invariance. The forces between quasiparticles and the vortex originate from interference of quasiparticles with trajectories on the left and on the right from the vortex like similar forces for electrons interacting with the thin magnetic-flux tube (the Aharonov-Bohm effect). These forces are derived in the Born approximation for phonons from the equations of superfluid hydrodynamics, and for BCS quasiparticles from the Bogolyubov-de Gennes equations. The effect of external fields violating translational invariance is analyzed for vortices in the two-dimensional Josephson junction array. The symmetry analysis of the classical equations for the array shows that the total transverse force on the vortex vanishes. Therefore the Hall effect which is linear in the transverse force is absent also. This means that the Magnus force from the superfluid component exactly cancels with the transverse force from the external fields. The results of other approaches are also brought together for discussion.