Electromagnetic Response of a Vortex in Layered Superconductors

We calculate the response of a vortex core in a layered superconductor to {\em ac} electromagnetic fields with frequencies $\omega\lsim 2\Delta/\hbar$. In this frequency range the response is dominated by order parameter collective modes which are coupled to the vortex-core bound states of Caroli, de Gennes and Matricon. Our calculations show that a vortex core has a more complex and richer dynamics than predicted by previous theories. The {\em ac} field drives an oscillating, nearly homogeneous supercurrent in the direction of the electric field, superimposed with a dissipative current flow which has a dipolar spatial structure. The order parameter response at low frequencies is an approximately rigid collective motion of the vortex structure perpendicular to the external field. This structure becomes strongly deformed at frequencies of order $\omega\gsim 0.5 \Delta /\hbar $. Coupling of the vortex-core bound states to collective modes of the order parameter at low frequencies leads to substantial enhancement of the dissipation near the vortex-center well above that of the normal-state.