Frequency dependent conductivity of vortex cores in type II superconductors

Abstract

Recent experiments by Karraï et al. probed vortices in YBa 2Cu 3O 7 at frequencies near the “minigap” between discrete core states, Δ 2/ E F. E F is the Fermi energy and Δ is the bulk energy gap. Here we calculate the conductivity, σ(ω), of vortices using a novel, microscopic description of single vortex dynamics based on the Bogoliubov-deGennes equations and self-consistency through the gap equation. It is applicable to the low temperature, clean, type II limit. An equation of motion for vortex cores valid at non-zero frequencies, including Magnus, drag, and pinning forces, is derived. The cyclotron resonance as well as structure at the minigap appear in σ(ω). The expected dipole transition between localized states is hidden because the vortex is a self-consistent potential. Unless translation invariance is broken, single particle properties are invisible to a long wavelength probe. Upon adding drag and pinning, dissipation near h ̵ hω≈Δ 2/ E F appears.