Thermodynamic properties of superconductors with Bogoliubov Fermi surfaces

Recent theoretical works have shown that Bogoliubov quasiparticles can form Fermi surfaces in time-reversal symmetry-breaking superconductors in which the paired electrons have additional degrees of freedom besides spin. While one of the defining properties of these states with Bogoliubov Fermi surfaces (BFS) is a non-zero density of states, experimentally it is challenging to determine whether thermodynamic signatures consistent with a non-zero density of states arise from BFS or from more trivial sources, such as impurity states or normal-state disordered regions inside the superconductor. In this regard, a key distinguishing feature of the BFS with respect to regular metals is that their volume changes significantly with the magnitude of the gap, and hence with small changes in temperature. Here, we exploit this effect to determine unambiguous experimental manifestations of BFS. First, we use group theory to construct an effective low-energy model for superconductors with BFS that can be solved self-consistently. We then employ it to derive the low-temperature behavior of several thermodynamic quantities, such as the specific heat and the superfluid density, searching for unique fingerprints of the BFS.