Fermi-Liquid Theory for Unconventional Superconductors

TL;DR

This paper develops a Fermi-liquid based Ginzburg-Landau theory for unconventional superconductors, analyzing how Fermi surface anisotropy, impurities, and pairing symmetry influence superconducting phases, with applications to UPt3.

Contribution

It extends Fermi-liquid theory to derive Ginzburg-Landau functionals for unconventional superconductors, highlighting the effects of anisotropy and symmetry on superconducting states.

Findings

Spontaneous time-reversal symmetry breaking in zero-field equilibrium states.

Gradient energies are sensitive to orbital symmetry and Fermi surface anisotropy.

Predictions specific to two-dimensional representations of hexagonal symmetry group.

Abstract

Fermi liquid theory is used to generate the Ginzburg-Landau free energy functionals for unconventional superconductors belonging to various representations. The parameters defining the GL functional depend on Fermi surface anisotropy, impurity scattering and the symmetry class of the pairing interaction. As applications I consider the basic models for the superconducting phases of UPt$_3$. Two predictions of Fermi liquid theory for the two-dimensional representations of the hexagonal symmetry group are (i) the zero-field equilibrium state exhibits spontaneously broken time-reversal symmetry, and (ii) the gradient energies for the different 2D representations, although described by a similar GL functionals, are particularly sensitive to the orbital symmetry of the pairing state and Fermi surface anisotropy.