Charge-$4e$ superconductivity from multi-component nematic pairing: Application to twisted bilayer graphene

TL;DR

This paper predicts a charge-4e superconducting phase in nematic superconductors with multi-component order parameters, especially in twisted bilayer graphene, driven by lattice symmetries and strain effects.

Contribution

It introduces the concept of a charge-4e vestigial superconducting phase supported by lattice symmetries and strain, applicable to systems like twisted bilayer graphene.

Findings

Charge-4e state is nearly degenerate with nematic state.

Random strain favors charge-4e superconductivity.

Twisted bilayer graphene is a promising platform.

Abstract

We show that unconventional nematic superconductors with multi-component order parameter in lattices with three-fold and six-fold rotational symmetries support a charge-$4e$ vestigial superconducting phase above $T_c$. The charge-$4e$ state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is non-superconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-$4e$ state over the nematic phase, as it acts as a random-mass to the former but as a random-field to the latter. Thus, we propose that two-dimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-$4e$ superconducting phase.