Magnus and Other Forces on Vortices in Superfluids and Superconductors

The motion of vortices is the only significant source of dissipation in a superconductor, making it a topic of some technological importance. Much of the modern work on vortex dynamics relates to many-vortex interaction effects so it is rather surprising to find that there is still considerable debate about the forces acting on an individual vortex. This debate was sparked by the claim in papers by Ao, Thouless and Niu that there exists a universal, exact expression for the transverse Magnus force on a vortex. Arising from topological effects, the magnitude of this Magnus force should not be affected by impurities or quasiparticles except in that they change the value of the superfluid density. The Ao-Thouless-Niu papers stimulated a number of authors to re-examine the problem with conclusions ranging between support for their viewpoint, through the suggestion that spectral flow, yet another topological effect, partly cancels the Magnus force, to claims that there are no topological effects at all. It has also led to an ingeneous experiment aimed at a direct measurement of the force. Given the interests of the audience at this conference, I will focus on only one aspect of this problem — the effect, if any, electromagnetic interactions have on the topological Magnus force. In the next section I will review the connection between the topological phase and the Magnus force for neutral superfluids, and then show how the phase accounting is modified by Aharonov-Casher phases due to the motion of the magnetic flux which is tied to the vortices. In the third section I will show how the various phase cancellations reflect a purely classical re-routing of the momentum flux from the charged superfluid to the background lattice. A final discussion section will, for completeness, briefly review how spectral flow induces relaxation effects that need to be incuded to complete the picture.