Mixed symmetry superconductivity in two-dimensional Fermi liquids

TL;DR

This paper investigates the possibility of mixed $s+id$ superconducting states in a 2D Fermi liquid with attractions in both channels, finding that such states occur under certain conditions and involve second-order phase transitions.

Contribution

It demonstrates the realization of mixed $s+id$ symmetry states in 2D Fermi liquids across different coupling regimes and clarifies the absence of stable $s+d$ states.

Findings

Mixed $s+id$ states occur in weak and strong coupling regimes.

Phase transitions between mixed and pure states are second order.

No stable mixed $s+d$ symmetry state exists at any coupling.

Abstract

We consider a 2D isotropic Fermi liquid with attraction in both $s$ and $d$ channels and examine the possibility of a superconducting state with mixed $s$ and $d$ symmetry of the gap function. We show that both in the weak coupling limit and at strong coupling, a mixed $s+id$ symmetry state is realized in a certain range of interaction. Phase transitions between the mixed and the pure symmetry states are second order. We also show that there is no stable mixed $s+d$ symmetry state at any coupling.