Superconducting instabilities in a spinful Sachdev-Ye-Kitaev model

TL;DR

This paper introduces a solvable spinful Sachdev-Ye-Kitaev model exhibiting superconducting and non-Fermi liquid phases, revealing a tunable gap ratio, phase transitions, and potential realizations in topological insulators.

Contribution

It presents a new exactly solvable spinful SYK model with a rich phase diagram including superconductivity and non-Fermi liquids, and explores its physical implications.

Findings

Identification of a superconducting phase with enhanced gap ratio

Discovery of a first-order transition between phases

Proposal of a physical platform using topological insulators

Abstract

We introduce a spinful variant of the Sachdev-Ye-Kitaev model with an effective time reversal symmetry, which can be solved exactly in the limit of a large number $N$ of degrees of freedom. At low temperature, its phase diagram 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. These two phases are separated by a first-order transition, in the vicinity of which a gapless superconducting phase, characterized by a non-zero magnetization, is stabilized upon applying a Zeeman field. We study equilibrium transport properties of such superconductors using a lattice construction, and propose a physical platform based on topological insulator flakes where they may arise from repulsive electronic interactions.