Pairing instability on a Luttinger surface: A non-Fermi liquid to superconductor transition and its Sachdev-Ye-Kitaev dual

Abstract

Superconductivity results from an instability of the Fermi surface—contour of poles of the single-particle propagator—to an infinitesimally small attraction between electrons. Here, we instead discuss the analogous problem on a model Luttinger surface, or contour of zeros of the Green function. At zero temperature (β→∞) and a critical interaction strength (uc∞) characterized by the residue of self-energy pole, we find that the pair susceptibility diverges leading to a superconducting instability. We evaluate the pair fluctuation partition function and find that the spectral density in the normal state has an interaction-driven, power-law 1ω type, van-Hove singularity (vHS), indicating non-Fermi liquid (NFL) physics. Crucially, in the strong coupling limit (βu≫1), the leading-order fluctuation free-energy terms in the normal state of this NFL-SC transition resembles the equivalent O(1) terms of the Sachdev-Ye-Kitaev (SYK) model. This free-energy contribution takes a simple form −βF=βuc∞−γlnβuc∞, where γ is a constant equal to 12. Weak impurity scattering (τ≫β−1) leaves the low-energy spectral density unaffected but leads to an interaction-driven enhancement of superconductivity. Our results shed light on the role played by order-parameter fluctuations in providing the key missing link between Mott physics and strongly coupled toy models exhibiting gravity duals.

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