Moving vortex line: Electronic structure, Andreev scattering, and Magnus force

Abstract

The wave functions of quasiparticles in a vortex line, moving with velocity vL relative to the lattice when a transport current with drift velocity vT is applied, are calculated by solving the time-dependent Bogoliubov–de Gennes equations for a high-κ superconductor in contact with a reservoir of chemical potential μ. Far away from the vortex core the pair potential has the constant modulus Δ∞. Comparison with the wave functions of a vortex at rest shows that vortex motion modifies the amplitudes, the radial wave numbers of the states with energy E>Δ∞, and the penetration lengths of states with energy E<Δ∞ by a term ±ɛvcosΘ. Here Θ is the azimuthal angle of cylinder coordinates with the z direction parallel to the vortex axis, and ɛv=ħkρv; v=|vT−vL| and kρ=(2m/ħ2)μ−kz2, with kz being the wave number of propagation in the z direction. If one neglects terms of the order of ɛv2 in the spectrum of the bound states, one obtains the same eigenvalues as for the vortex at rest. The supercurrent force on the corresponding quasiparticles, caused by Andreev scattering at the core boundary, is calculated with the v-modified wave functions. It transfers half of the Magnus force from the moving condensate to the unpaired quasiparticles in the vortex core.

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