Transverse force on a vortex and vortex mass: effects of free bulk and vortex-core bound quasiparticles

TL;DR

This paper revisits the longstanding controversy over the transverse force and vortex mass in superfluid and Fermi liquids, clarifying the roles of quasiparticles, spectral flow, and backflow effects with new insights.

Contribution

It demonstrates that the transverse force is due to the Aharonov--Bohm effect and is unrelated to spectral flow, and clarifies the backflow's role in vortex mass renormalization.

Findings

Transverse force originates from the Aharonov--Bohm effect.

No steady spectral flow occurs in vortex cores of superfluid Fermi liquids.

Backflow compensates core bound state currents, renormalizing vortex mass.

Abstract

The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquid, originates from the Aharonov--Bohm effect. However, in the Fermi liquid one should take into account peculiarities of the Aharonov--Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the SNS junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.