Models for enhanced absorption in inhomogeneous superconductors

We discuss the low-frequency absorption arising from quenched inhomogeneity in the superfluid density ρ_s of a model superconductor. Such inhomogeneities may arise in a high-T_c superconductor from a wide variety of sources, including quenched random disorder and static charge density waves such as stripes. Using standard classical methods for treating randomly inhomogeneous media, we show that both mechanisms produce additional absorption at finite frequencies. For a two-fluid model with weak mean-square fluctuations 〈(δρ_s)²〉 in ρ_s and a frequency-independent quasiparticle conductivity, the extra absorption has oscillator strength proportional to the quantity 〈(δρ_s)²〉/ρ_s, as observed in some experiments. Similar behavior is found in a two-fluid model with anticorrelated fluctuations in the superfluid and normal fluid densities. The extra absorption typically occurs as a Lorentzian centered at zero frequency. We present simple model calculations for this extra absorption under conditions of both weak and strong fluctuations. The relation between our results and other model calculations is briefly discussed, and their possible relation to experiment is also discussed.