Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model

Abstract

We introduce a spinful variant of the complex Sachdev-Ye-Kitaev model with time reversal symmetry, which can be solved exactly in the limit of a large number N of degrees of freedom. At low temperature, the phase diagram of the model includes a compressible non-Fermi liquid and a strongly-correlated spin singlet superconductor that shows a tunable enhancement of the gap ratio predicted by BCS theory. The two phases are separated by a first-order phase transition, in the vicinity of which a gapless superconducting phase is stabilized. We also discuss time-reversal breaking perturbations that introduce a finite magnetization coexisting with superconductivity.

The extended diffusive Sachdev-Ye-Kitaev model as a sort of "strange metal"

“…The model is originally in 0 + 1 − d dimensions and its fermionic fields are Majorana neutral fermions. This feature, if taken seriously, already implies that the charge and spin degrees of freedom have been dropped out of the model 45 , when describing the electronic carriers. Indeed Majorana Fermions are neutral and interaction J grows to infinity but is fully local and momentum is not conserved.…”

“…The transferred momentum q is a 3 − d vector in the liquid, but it is only defined in two dimensions in the J E −k,−ω J E k,ω term. We overcame the same difficulty in Eq.s (45,47), by considering the convolution (with k− integration) as in Eq. (56) of Subsection III.B, which corresponds to averaging in space, but by assuming that the fluctuation correlations are localized within a volume ∼ ã2 .…”