TRANSVERSE FORCE ON A QUANTIZED VORTEX IN A SUPERCONDUCTOR

The total transverse force acting on a quantized vortex in a type-II s uperconductor determines the Hall response in the mixed state, yet a c onsensus as to its correct form is still lacking. In this paper we pre sent an essentially exact expression for this force, valid in the supe rclean limit, which was obtained by generalizing the recent work by Th ouless, Ao, and Niu [D. J. Thouless, P. Ao, and Q. Niu, Phys. Rev. Let t. 76, 3758 (1996)] on the Magnus force in a neutral superfluid. We fi nd the transverse force per unit length to be f = rho K X 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 vort ex velocity.