Instability of j=3/2 Bogoliubov Fermi surfaces

Exotic quantum phases including topological states and non-Fermi liquids may be realized by quantum states with total angular momentum j = 3/2, as manifested in HgTe and pyrochlore iridates. Recently, an exotic superconducting state with a nonzero density of states of zero-energy Bogoliubov (BG) quasiparticles, the Bogoliubov Fermi surface (BG-FS), was also proposed in a centrosymmetric j = 3/2 system, protected by a Z(2) topological invariant. Here, we consider interaction effects of a centrosymmetric BG-FS and demonstrate its instability by using mean-field and renormalization group analysis. The Bardeen-Cooper-Schrieffer (BCS)-type logarithmical enhancement is shown in fluctuation channels associated with inversion symmetry. Thus, we claim that the inversion-symmetry instability is an intrinsic characteristic of a BG-FS under generic attractive interactions between BG quasiparticles. In drastic contrast to the standard BCS superconductivity, a Fermi surface may generically survive even with the instability. We propose the experimental setup, a second-harmonic-generation experiment with a strain gradient, to detect the instability. Possible applications to iron-based superconductors and heavy-fermion systems, including FeSe, are also discussed.