Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry

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.