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 (q,ω) has been calculated for a wide range of the normal-state collision frequency and the parameter Q=max{‖q⋅‖}, where q is the incident wave vector of the electromagnetic wave and 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 2, assumed to be the maximum energy gap. We find that with a bilevel gap parameter consisting of an in-plane value , a c-axis value of about 1/4 to 1/3 of , 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 , in which q is along the c axis. With ħQ≪ and , the observed data in the region ω<2/ħ 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=2/ħ, must necessarily be large and close to 2.5/ħ. Whether this type of frequency-dependent 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.
- Received 11 January 1991
DOI:https://doi.org/10.1103/PhysRevB.44.300
©1991 American Physical Society