Bogoliubov Fermi surfaces in topological superconductors

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Superconductors have an energy gap towards quasiparticle excitations. In unconventional superconductors, this gap can go to zero for certain momenta of these quasiparticles. These zeros of the gap are called nodes. We have recently shown that in multiband superconductors that spontaneously break time-reversal symmetry, these nodes are generically two dimensional. They can be understood as Fermi surfaces of Bogoliubov quasiparticles. This is interesting since Fermi surfaces are typically thought of as a hallmark of normal conductors. Two directions of research are now pressing and will be pursued in this project: the time-reversal-symmetry-breaking pairing states have to be put on a microscopic basis and possible experimental signatures of the Fermi surfaces have to be worked out.The main objective in the first part of this project is to obtain time-reversal-symmetry-breaking states that show Bogolibov Fermi surfaces starting from microscopic models with a pairing interaction. The goal is to understand the conditions for such pairing states to be favored over conventional ones. The spatial structure of these superconducting states, in particular close to a surface, will also be studied. This is crucial for the description of surface-sensitive probes. Furthermore, it is now important to suggest experimental probes and to derive predictions for them. Our goal is to understand how the Bogoliubov Fermi surfaces and the concomitant magnetic order affect standard probes of superconducting states, in particular photoemission, tunneling, thermodynamic quantities, the magnetic penetration depth, the magnetization, nuclear probes, and the optical conductivity. Moreover, we have preliminary arguments that quantum oscillations should exist in spite of the fact that the Bogoliubov quasiparticles are electrically neutral on average. For all quantities, we will elucidate their dependences on temperature and applied magnetic field, which are expected to be characteristic for the pairing state and the Bogoliubov Fermi surfaces.