Solvable model for a charge-$4e$ superconductor

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.

24 pages, 3 figures

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• Cascade of vestigial orders in two-component superconductors: nematic, ferromagnetic, s-wave charge-4e, and d-wave charge-4e states
• Vestigial singlet pairing in a fluctuating magnetic triplet superconductor: Applications to graphene moiré systems
• Charge-4$e$ Superconductivity in a Hubbard model
• Andreev reflection in normal metal/charge-4e superconductor junctions
• Local condensation of charge-$4e$ superconductivity at a nematic domain wall
• Vestigial $d$-wave charge-$4e$ Superconductivity from Bidirectional Pair Density Waves
• Upper bound on $T_c$ in a strongly coupled electron-boson superconductor