Interplay of the pseudogap and the BCS gap for heteropairs in $^{40}$K-$^6$Li mixture

TL;DR

This paper develops a self-consistent theory for heteropairs in a $^{40}$K-$^6$Li mixture, revealing how pseudogaps and BCS gaps interact and affect single-particle spectra and density of states.

Contribution

It derives analytic pseudogap Green's functions within the Luttinger-Ward framework, highlighting effects of self-consistency on spectral properties and gap structures.

Findings

Normal state is not a Fermi liquid due to decay of excitations.

Pseudogap exhibits a V shape even with s-wave pairing.

Interference between pseudogap and BCS gap causes slope breaks and in-gap states.

Abstract

The description of heteropairs like $^{40}$K-$^6$Li near and in the superconducting state requires a fully selfconsistent theory [see Hanai and Ohashi, Phys. Rev. A 90, 043622 (2014)]. We derive analytic pseudogap Green's functions for the "normal" and superconducting states from the Luttinger-Ward theory with the T-matrix in the static separable approximation. The self-consistency in the closing loop of self-energy has two pronounced effects on the single-particle spectrum. First, the single-particle excitations decay before the asymptotic quasiparticle propagation is established, therefore the normal state is not a Fermi liquid. Second, the pseudogap has a V shape even for s-wave pairing. The V-shaped pseudogap and the U-shaped BCS gap interfere resulting in slope breaks of the gap walls and the in-gap states in the density of states. Various consequences of an incomplete self-consistency are demonstrated.