Intrinsic superconducting instabilities of a solvable model for an incoherent metal

Debanjan Chowdhury,Erez Berg

doi:10.1103/physrevresearch.2.013301

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.

Highlights

The search for high-temperature superconductivity in complex electronic materials continues to be at the heart of modern condensed-matter physics
We have argued in the previous sections that if we start with the description of a low-temperature Fermi liquid and focus on the excitations near the Fermi surface, purely as a result of the strong renormalization of the coherent excitations by the factor of Z ∼ t/J, 6 the predicted TcSC ∼ W ∗ ∼ Tcoh
We would like to emphasize that the superconducting instabilities obtained for models A and B in this work do not rely on the conventional “Cooper-log” arising from the nesting between time-reversed pairs of momenta on the Fermi surface

Summary

INTRODUCTION

The search for high-temperature superconductivity in complex electronic materials continues to be at the heart of modern condensed-matter physics. While not all of the different families of NFL metals display an identical phenomenology, they share a number of peculiar features These include short single-particle lifetimes [4,5], a broad regime of anomalous power-law transport seemingly at odds with expectations in a Fermi liquid [6,7,8,9], and an absence of any characteristic crossovers through the “Mott-Ioffe-Regal” (MIR) limit where the electronic mean free path becomes of the order of the lattice spacing [10]. In a previous paper [27], we constructed a family of models with exact translational symmetry and on-site SYK-like interactions This allowed us to study the fate of electronic quasiparticles and sharply defined Fermi surfaces, in the regime of strong interactions. This will be the topic of our study in the few sections

Bethe-Salpeter equations

MODEL A

MODEL B

Strong-coupling analysis

Explicit example

DISCUSSION AND OUTLOOK