Low-frequency optical conductivity in inhomogeneous d-wave superconductors

Motivated by the recent optical conductivity experiments on Bi₂Sr₂CaCu₂O_8+δ 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 ρ_s, it is shown that some spectral weight is removed from ω=0 to finite frequencies and contribute to dissipation. A case where both ρ_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.