Absence of dipole transitions in vortices of type-II superconductors

The response of a single vortex to a time-dependent field is examined microscopically and an equation of motion for vortex motion at nonzero frequencies is derived. Of interest are frequencies near ${\mathrm{\Delta }}^2$/${\mathit{E}}_{\mathit{F}}$, where Δ is the bulk energy gap and ${\mathit{E}}_{\mathit{F}}$ is the Fermi energy. The low-temperature, clean, extreme-type-II limit and maintanance of equilibrium with the lattice are assumed. A simplification occurs for large planar mass anisotropy. Thus the results may be pertinent to materials such as ${\mathrm{NbSe}}_2$ and high-temperature superconductors. The expected dipole transition between core states 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.