Frequency dependent conductivity of vortex cores in type II superconductors

The recent optical transmission experiment of Karräi et al. has probed the localized quasiparticle excitations of vortices in the superconductor YBa2Cu3O7. In this paper we develop a microscopic description of single vortex dynamics, based on the Bogoliubov-deGennes equations and self-consistency through the gap equation, to determine the response of vortices to a transverse time dependent electric field. It is applicable to the low temperature, clean, extreme type II limit. In the limit of large planar mass anisotropy it simplifies. Thus it may be especially relevent to materials such as NbSe2 and high temperature superconductors. Of particular interest is the response of the vortex at frequencies near the minigap, ∆/EF , where ∆ is the bulk energy gap and EF is the fermi energy. A dissipative equation of motion for vortex cores valid at non-zero frequencies is derived. We give a clear microscopic meaning to the vortex drag parameter. The expected dipole transition between quasi-particle states localized at the core is hidden because of the self-consistent nature of the vortex potential. Instead the vortex itself moves and has a resonance at the frequency of the transition. We calculate the conductivity of vortices as a function of frequency. A analogy is made to the Mattis-Bardeen result for the electrodynamic response of bulk superconductors that, unless translation invariance is broken, single particle