Odd-frequency pairing inherent in Bogoliubov Fermi liquid

TL;DR

This paper demonstrates that Bogoliubov quasiparticles in a Fermi liquid inherently exhibit odd-frequency pairing due to disorder and interactions, with distinct self-energy structures affecting their spectral properties.

Contribution

It reveals the intrinsic emergence of odd-frequency pairing in Bogoliubov Fermi liquids and characterizes their self-energy structures and spectral signatures.

Findings

Bogolons induce odd-frequency pair amplitudes.

Two types of self-energy solutions: frequency-independent and inverse-frequency.

Connection established between bogolons and electron odd-frequency pairing.

Abstract

The disorder and interaction effects on Bogoliubov-Fermi surfaces with preserved inversion symmetry are studied for a low-energy effective model coupled to bosonic degrees of freedom. It is shown that the non-ideal Bogoliubov quasiparticles (bogolons) generically induce the odd-frequency pair amplitude which reflects a Cooper pairing at different time. The self-energy of bogolons is mainly contributed by the disorder effects in the low frequency limit as in the usual electron liquid. Depending on the choice of the parameters, there are two kinds of solutions: one is frequency-independent (but with sign function of frequency) and the other is proportional to the inverse of the frequency, which exist in both the normal and anomalous parts of the self-energy. These characteristic self-energy structures are clearly reflected in the single-particle spectrum. Since the bogolons are originally composed of electrons, the connection between the two is also sought using the concrete $j=3/2$ fermion model, which reveals that the odd-frequency pairing of bogolons is mainly made of the electrons' odd-frequency pairing.