The presence of multiple bands qualitatively changes the nodal structure of an inversion-symmetric time-reversal symmetry-breaking superconductor. Instead of point or line nodes, the gap exhibits extended nodal pockets, called Bogoliubov Fermi surfaces [1-4]. These surfaces originate from the “inflation” of point and line nodes in the absence of time-reversal symmetry breaking. In this work we study a paradigmatic model for Bogoliubov-Fermi surfaces, the Luttinger-Kohn Hamiltonian of spin $j=3/2$ fermions for the cubic point group, and investigate the thermodynamic stability of a time-reversal symmetry-breaking superconducting state with Bogoliubov-Fermi surfaces compared to a time-reversal symmetry-preserving one without as a function of the multiband character of the electronic band structure. We formulate a mean-field theory and minimize the free energy to find the self-consistent superconducting gap as a function of band parameters. The multiband nature gives rise to a rich phase diagram. We also study some basic spectroscopic properties and the influence of cubic anisotropy.
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