Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry

TL;DR

This paper demonstrates that in certain multiband superconductors with broken time-reversal symmetry, extended Bogoliubov Fermi surfaces can form, representing a new type of low-energy excitation spectrum beyond traditional nodal classifications.

Contribution

It introduces the concept of topologically protected Bogoliubov Fermi surfaces in multiband superconductors with broken time-reversal symmetry, expanding understanding of possible excitation spectra.

Findings

Bogoliubov Fermi surfaces are generated by inflating point or line nodes.

These Fermi surfaces are topologically protected by a $ ext{Z}_2$ invariant.

Such states can be energetically stable in multiband superconductors.

Abstract

It is commonly believed that in the absence of disorder or an external magnetic field, there are three possible types of superconducting excitation gaps: the gap is nodeless, it has point nodes, or it has line nodes. Here, we show that for an even-parity nodal superconducting state which spontaneously breaks time-reversal symmetry, the low-energy excitation spectrum generally does not belong to any of these categories, instead it has extended Bogoliubov Fermi surfaces. These Fermi surfaces can be visualized as two-dimensional surfaces generated by "inflating" point or line nodes into spheroids or tori, respectively. These inflated nodes are topologically protected from being gapped by a $\mathbb{Z}_2$ invariant, which we give in terms of a Pfaffian. We also show that superconducting states possessing these Fermi surfaces can be energetically stable. A crucial ingredient in our theory is that more than one band is involved in the pairing, since all candidate materials for even-parity superconductivity with broken time-reversal symmetry are multiband systems, we expect these $\mathbb{Z}_2$-protected Fermi surfaces to be ubiquitous.