Stability of Bogoliubov Fermi Surfaces within BCS Theory

TL;DR

This paper demonstrates within BCS theory that time-reversal-symmetry-breaking superconducting states with Bogoliubov Fermi surfaces can be stable over broad parameters, and introduces a fast, robust method to analyze such states.

Contribution

It shows the stability of Bogoliubov Fermi surfaces in multiband superconductors within BCS theory and presents a new efficient method to solve the inverse gap equation.

Findings

Time-reversal-symmetry-breaking states are stabilized at weak coupling.

A fast, convergence-free method for solving the inverse BCS gap equation.

Bogoliubov Fermi surfaces can be stable over broad parameter ranges.

Abstract

It has recently been realized that the gap nodes of multiband superconductors that break time-reversal symmetry generically take the form of Fermi surfaces of Bogoliubov quasiparticles. However, these Fermi surfaces lead to a nonzero density of states (DOS) at the Fermi energy, which typically disfavors such superconducting states. It has thus not been clear whether they can be stable for reasonable pairing interactions or are in practice preempted by time-reversal-symmetric states with vanishing DOS. In this Letter, we show within BCS theory applied to a paradigmatic model that the time-reversal-symmetry-breaking states are indeed stabilized over broad parameter ranges at weak coupling. Moreover, we introduce a fast method that involves solving the inverse BCS gap equation, does not require iteration, does not suffer from convergence problems, and can handle metastable solutions.