The superconductivity is understood as a quantum condensation of Cooper pairs. While the Fermi surface usually disappears in the pairing state, they can remain in some superconducting states [1], where the elementary excitations near the Fermi surfaces are composed not of original electrons but of Bogoliubov quasiparticles (bogolons). For the time-reversal symmetry broken system with preserved inversion symmetry, such Bogoliubov-Fermi surfaces are stable as they are topologically protected [2]. Since the bogolons can carry energy, the thermal properties such as specific heat and thermal conductivity are expected to be similar to the conventional Fermi liquid of electrons and are potentially observed in the actual materials [3,4]. However, the bogolons are quasiparticles in the superconducting state, and their physical properties should be different from those of the electrons. Therefore, it is desirable to clarify the difference between the Fermi liquid and the Bogoliubov Fermi liquid, the latter of which is realized for the non-ideal bogolons generically.

We have shown that the impurity and correlation effects on this Bogoliubov Fermi surface generate purely odd-frequency pairing amplitude at low energies, which is a Cooper pair formed only at different time [5]. This property gives a clear distinction from the normal Fermi liquid state of electrons. Furthermore, at sufficiently low temperatures, it is also expected that the system shows a (even-frequency) pairing state of bogolons because of the intrinsic logarithmically divergent pair susceptibility of the Fermi surfaces [6]. In the talk, we will discuss these topics in detail.

[1] G.E. Volovik, Phys. Lett. A 142, 282 (1989).
[2] D.F. Agterberg, P.M.R. Brydon, C. Timm, Phys. Rev. Lett. 118, 127001 (2017).
[3] Y. Sato et al., Proc. Natl. Acad. Sci. 115, 1227 (2018).
[4] C. Setty et al., Nat. Commun. 11, 523 (2020).
[5] T. Miki, S.-T. Tamura, S. Iimura, S. Hoshino, arXiv:2103.02251 (2021) (to appear in Phys. Rev. B).
[6] S.-T. Tamura, S. Iimura, S. Hoshino, Phys. Rev. B 102, 024505 (2020).

Keywords: Bogoliubov Fermi surface, odd-frequency pairing, impurity effect, interaction effect