Intrinsic superconducting instabilities of a solvable model for an incoherent metal

Abstract

We construct a family of translationally invariant lattice models with a large number ($N$) of orbitals at every site coupled together via single electron tunneling. By tuning the relative strength of the electronic bandwidth and on-site interactions, that have a modified Sachdev-Ye-Kitaev (SYK) form, we demonstrate a number of unusual features at strong coupling and in the large$-N$ limit. We find examples of (i) an intrinsic non-BCS superconducting instability arising out of an incoherent non-Fermi liquid metal, and, (ii) an instability of an incipient heavy Fermi liquid metal to superconductivity with transition temperatures comparable to its renormalized bandwidth. At strong-coupling, these solvable models display pairing instabilities that are not driven by any special "nesting" properties associated with an underlying Fermi surface.

10 pages, 4 figures

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• Quantum critical Eliashberg theory, the SYK superconductor and their holographic duals
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• SYK Superconductivity: Quantum Kuramoto and Generalized Richardson Models
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• Superconductor--Insulator Transition in a non-Fermi Liquid
• Strange metal from incoherent bosons
• Dynamics and Charge Fluctuations in Large-q Sachdev-Ye-Kitaev Lattices
• Superconductivity of non-Fermi liquids described by Sachdev-Ye-Kitaev models
• Reckoning with the Mother of all non-Fermi liquids: alien bosonization vs predator holography
• SYK does not Transit Gloria Mundi just yet
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• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Orbital selective order and ${\mathbb{Z}}_3$ Potts nematicity from a non-Fermi liquid
• The extended diffusive Sachdev-Ye-Kitaev model as a sort of "strange metal"