Effects of gap anisotropy on the electromagnetic response of high-T_c superconductors

Abstract

We study the nature of the electromagnetic absorption in a superconductor with an anisotropic energy gap and a nonspherical Fermi surface that is either completely closed or open along the direction of the c axis of the crystal. The real part of the electromagnetic conductivity σ_μν(q,ω) has been calculated for a wide range of the normal-state collision frequency ω_c and the parameter Q=max{||q.V_F||}, where q is the incident wave vector of the electromagnetic wave and V_F is quasiparticle velocity at the Fermi surface. For simplicity, the model gap parameter Δ(k) is assumed to vary only with the angle θ between the direction k^ of the quasiparticle wave vector and the c axis of the crystal (chosen to be the z direction). We employ a formulation for calculating the linear conductivity in which the collision frequency is directly related to the imaginary part of the single-particle self-energy resulting from various elastic and inelastic collisions. In the presence of gap anisotropy, there is finite absorption below the in-plane gap 2Δ_ab, assumed to be the maximum energy gap. We find that with a bilevel gap parameter consisting of an in-plane value Δ_ab, a c-axis value of about ¼ to 1/3 of Δ_ab, and a sharp transition between them at ||cosθ||~0.5, we are able to fit quite well the experimental infrared absorption data for the single crsytal YBa₂Cu₃O₇, in which q is along the c axis. With hQ << Δ_ab and ω_c, the observed data in the region ω<2Δ_ab/h can be fitted even with a low normal-state collision frequency derived from the normal-state dc conductivity. However, we find that to get a good fit in the region beyond ω=2Δ_ab/h, ω_c must necessarily be large and close to 2.5Δ_ab/h. Whether this type of frequency-dependent ω_c implies electron-electron collision effects in the normal state beyond the normal Fermi-liquid picture or wether this is merely due to the existence of another inelastic scattering channel in the system with a low threshold, cannot be resolved unambiguously.