Superconducting critical temperature in the extended diffusive SYK model

TL;DR

This paper investigates the extended SYK model with disordered fermions, revealing a critical temperature for non-BCS superconductivity mediated by neutral excitations, and connects it to strange metal behavior and collective modes.

Contribution

It introduces a hydrodynamical approach to the extended SYK model, identifying collective excitations and their role in mediating superconductivity beyond BCS theory.

Findings

Identification of neutral diffusive excitations in the SYK phase.

Discovery of a critical temperature for superconductivity mediated by these excitations.

Analysis of hindered diffusion due to coupling with pseudo Goldstone modes.

Abstract

Models for strongly interacting fermions in disordered clusters forming an array, with electron hopping between sites, reproduce the linear dependence on temperature of the resistivity, typical of the strange metal phase of High Temperature Superconducting materials (Extended Sachdev-Ye-Kitaev (SYK) models). Our hydrodynamical approach to the marginal Fermi liquid emerging out of the interaction, identifies the low energy collective excitations of the system in its coherent phase. These neutral excitations diffuse in the lattice, but the diffusion is heavily hindered by coupling to the pseudo Goldstone modes of the conformal broken symmetry SYK phase, which are local in space. A critical temperature for superconductivity arises in the electron liquid,in case these excitations are assumed to mediate an attractive Cooper-pairing, in the electron liquid, which is not BCS-like.