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

Chandan Setty
2021 Physical review B  
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) – a contour of zeros of the propagator – instead leads to a quantum critical point (QCP) that separates a non-Fermi liquid (NFL) and superconductor. A surprising and little understood aspect of pair fluctuations at this QCP is that their thermodynamics
more » ... aps 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 blackclose to the LS, and (ii) the enforcement of gauge invariance results in a 1/√(τ) (τ∼ T^-1) behavior of the fluctuation propagator near the QCP, as is a feature of the fundamental SYK fermion.
doi:10.1103/physrevb.103.014501 fatcat:nvqkwfaebveybiny5lhdhb7vl4