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 nonzero 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.

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• Superconductivity
• Strongly correlated systems
• Unconventional superconductors
• Large-N expansion in field theory
• Non-Fermi-liquid theory
• Sachdev-Ye-Kitaev model