Fermi-Liquid Theory for Anisotropic Superconductors

This article develops a Fermi-liquid theory for superconductors with anisotropic Fermi surfaces, Fermi-liquid interactions, and energy gaps. For d-wave superconductors, the Fermi-liquid interaction effects are found to be classifiable into strong and negligible renormalizaton effects, for symmetric and antisymmetric combinations of the energies of $k\uparrow$ and $-k\downarrow$ quasiparticles, respectively. Furthermore, the leading clean-limit temperature-dependent correction to the superfluid density in a d-wave superconductor is found to be renormalized by a Fermi velocity (or mass) renormalization effect. The question is raised of whether or not the penetration depth in the high temperature superconductor YBa$_2$Cu$_3$O$_{6+x}a$ can be accounted for with physically acceptable parameters within the framework of a quasiparticle model. Fermi-liquid corrections to the spin susceptibility and to the zero-energy magnetic-field-induced density of states are also evaluated.