Low-frequency optical conductivity in inhomogeneousd-wave superconductors

Abstract

Motivated by the recent optical conductivity experiments on ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ films, we examine the possible origin of low-frequency dissipation in the superconducting state. In the presence of spatial inhomogeneity of the local phase stiffness ${\ensuremath{\rho}}_{s},$ it is shown that some spectral weight is removed from $\ensuremath{\omega}=0$ to finite frequencies and contribute to dissipation. A case where both ${\ensuremath{\rho}}_{s}$ and the local normal-fluid density are inhomogeneous is also considered. We find an enhanced dissipation at low frequency if the two variations are anticorrelated.