Renormalizations in unconventional superconducting states born of normal and singular Fermi liquids

Abstract

The density of low-energy particle-hole excitations is nonanalytic in a singular Fermi liquid, but it is altered on entering a superconducting state in which, in the pure limit, it vanishes asymptotically at the chemical potential and in general is analytic. The single-particle excitations in the superconducting states are then quasiparticles so that a form of Landau theory may be constructed for thermodynamic and transport properties in the superconducting state. In this theory, the renormalization of measurable properties due to quasiparticle interactions, such as specific heat, compressibility, magnetic susceptibility, superfluid density, etc., changes in a temperature dependent fashion from the noninteracting theory. This is illustrated by showing the renormalization of these quantities and the relation between the parameters introduced to account for their temperature dependence. When the renormalizations in the normal state are large or singular, temperature dependence of properties in the superconducting states are then in general not useful for identifying the nodal character or symmetry of the superconducting state except for measurements at very low temperatures, the upper limits of which are specified. The results obtained are expected to be useful in interpreting the experimental results for the temperature dependence of various properties in the superconducting state born of singular Fermi liquids.