Solvable model for a charge-$4e$ superconductor

TL;DR

This paper introduces an exactly solvable model for a charge-4e superconductor, revealing its gapless nature, superfluid properties, and phase transition behavior to a charge-2e state.

Contribution

It presents a novel solvable model for charge-4e superconductivity based on a spinful Sachdev-Ye-Kitaev framework with an anomalous quartic interaction.

Findings

Ground state is gapless and resembles a heavy Fermi liquid.

Superfluid density is perturbative in the charge-4e order parameter.

Lowering temperature can induce a first-order transition to charge-2e superconductivity.

Abstract

A charge-$4e$ superconductor forms due to the condensation of quartets of electrons. While in previous works the mechanism for the formation of charge-$4e$ superconductivity has been analyzed in terms of the binding of Cooper pairs in unconventional superconductors, its properties in the fermionic sector have not been studied systematically due to its inherently interacting nature even at the mean-field level. Here we propose a solvable model for a charge-$4e$ superconductor -- a spinful version of the Sachdev-Ye-Kitaev model with an anomalous quartic term. We show that the ground state is gapless and resembles a heavy Fermi liquid. We analytically solve for the superfluid density and show that it is perturbative in the strength of the charge-$4e$ order parameter, in sharp contrast with a regular (charge-$2e$) superconductor. Upon lowering temperature, we show that the correlation between charge-$4e$ order and regular interaction terms can drive a first-order phase transition to a charge-$2e$ superconducting state.