Abstract
The description of heteropairs like K-40-Li-6 near and in the superconducting state requires a fully self-consistent theory (see Hanai R. and Ohashi Y., Phys. Rev.
A, 90 (2014) 043622). 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 singleparticle 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.