Transverse force on a quantized vortex in a superconductor

TL;DR

This paper derives an exact expression for the transverse force on a vortex in a superconductor, clarifying the Hall response in the mixed state by generalizing superfluid vortex force theory.

Contribution

It provides an essentially exact formula for the transverse force on a vortex in a superconductor, valid in the superclean limit, extending previous superfluid vortex force work.

Findings

The transverse force per unit length is $f = ho K imes V$.

The force depends on total mass density $ ho$, circulation $K$, and vortex velocity $V$.

The expression is valid in the superclean limit.

Abstract

The total transverse force acting on a quantized vortex in a type-II superconductor determines the Hall response in the mixed state, yet a consensus as to its correct form is still lacking. In this paper we present an essentially exact expression for this force, valid in the superclean limit, which was obtained by generalizing the recent work by Thouless, Ao, and Niu [D. J. Thouless, P. Ao, and Q. Niu, Phys. Rev. Lett. 76, 3758 (1996)] on the Magnus force in a neutral superfluid. We find the transverse force per unit length to be $f = \rho K \times V$, where $\rho = \rho_{n} + \rho_{s}$ is the sum of the mass densities of the normal and superconducting components, $K$ is a vector parallel to the line vortex with a magnitude equal to the quantized circulation, and $V$ is the vortex velocity.