Superconductivity from Luttinger surfaces: Emergent Sachdev-Ye-Kitaev physics with infinite-body interactions

Abstract

The pairing of two electrons on a Fermi surface due to an infinitesimal attraction between them always results in a superconducting instability at zero temperature (T=0). The equivalent question of pairing instability on a Luttinger surface (LS)—190a contour of zeros of the propagator—instead leads to a quantum critical point (QCP) that separates a non-Fermi liquid and superconductor. A surprising and little understood aspect of pair fluctuations at this QCP is that their thermodynamics maps to that of the Sachdev-Ye-Kitaev (SYK) model in the strong coupling limit. Here, we offer a simple justification for this mapping by demonstrating that (i) LS models share the reparametrization symmetry of the q→∞ SYK model with q-body interactions close to the LS, and (ii) the enforcement of gauge invariance results in a 1τ (τ∼T−1) behavior of the fluctuation propagator near the QCP, as is the feature of SYK conformal Green functions, but leaves the overall form of the free energy map robust.

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