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

摘要

The wave functions of quasiparticles in a vortex line, moving with velocity <(upsilon)over right arrow>(L) relative to the lattice when a transport current with drift velocity <(upsilon)over right arrow>(T) is applied, are calculated by solving the time-dependent Bogoliubov-de Gennes equations for a high-kappa superconductor in contact with a reservoir of chemical potential mu. Far away from the vortex core the pair potential has the constant modulus Delta(proportional to). 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 > Delta(proportional to), and the penetration lengths of states with energy E < Delta(proportional to) by a term +/- epsilon(upsilon)cos Theta. Here Theta is the azimuthal angle of cylinder coordinates with the z direction parallel to the vortex axis, and epsilon(upsilon) = hk(rho)upsilon; upsilon = <(upsilon)over right arrow>(T) - <(upsilon)over right arrow>(L) and k rho = root(2m/h(2))mu - k(z)(2), with kz being the wave number of propagation in the z direction. If one neglects terms of the order of epsilon(upsilon)(2) tn the spectrum of bond 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 upsilon-modified wave functions. It transfers half of the Magnus force from the moving condensate to the unpaired quasiparticles in the vortex core. [References: 27]