Microscopic theory of vortex dynamics in homogeneous superconductors

Vortex dynamics in a type-II superconductor is systematically investigated by the influence functional method. The irrelevant fermionic degrees of freedom are integrated out and their effects on the dynamics are treated in terms of the vortex coordinate. When an isolated vortex is moving against its background, forces proportional to the first order of vortex velocity on the vortex are calculated within the present formulation. The total transverse force on the moving vortex is explicitly shown to be proportional to the superfluid number density and insensitive to impurities. Its equivalent expressions in terms of the Berry phase and the various summations of transitions between quasiparticle (hole) stares are discussed. At finite temperatures, due to the finite population of quasiparticle (hole) excitations above (below) the energy gap, there is a friction against vortex motion which diverges logarithmically in the low-frequency limit. Nonmagnetic impurities give rise to an additional friction from the core states which saturates to a value independent of the normal-state resistivity in the dirty limit. In this limit, the coupling to the electromagnetic field does not change the conclusions if charge neutrality in the superconductor is maintained. Macroscopic constraints on vortex dynamics by the second law of thermodynamics and by the fluctuation-dissipation theorems are also discussed. [S0163-1829(99)10129-2].