Charge-$4e$ superconductivity from nematic superconductors in 2D and 3D

TL;DR

This paper proposes that charge-4e superconductivity can emerge as a vestigial phase above the nematic superconducting transition in 2D and 3D systems, driven by vortex proliferation and competing orders.

Contribution

It demonstrates a mechanism for charge-4e phase emergence in nematic superconductors through vortex proliferation and theoretical analysis of competing orders.

Findings

Charge-4e phase can arise above nematic superconductivity.

Nematic vortices favor charge-4e order when nematic stiffness is low.

A sizable regime exists where charge-4e order is energetically favored.

Abstract

Charge-$4e$ superconductivity as a novel phase of matter remains elusive so far. Here we show that charge-$4e$ phase can arise as a vestigial order above the nematic superconducting transition temperature in time-reversal-invariant nematic superconductors. On the one hand, the nontrivial topological defect -- nematic vortex -- is energetically favored over the superconducting phase vortex when the nematic stiffness is less than the superfluid stiffness; consequently the charge-$4e$ phase emerges by proliferation of nematic vortices upon increasing temperatures. On the other hand, the Ginzburg-Landau theory of the nematic superconductors has two distinct decoupling channels to either charge-$4e$ orders or nematic orders; by analyzing the competition between the effective mass of the charge-$4e$ order and the cubic potential of the nematic order, we find a sizable regime where the charge-$4e$ order is favored. These two analysis consistently show that nematic superconductors can provide a promising route to realize charge-$4e$ phases, which may apply to candidate nematic superconductors such as PbTaSe$_2$ and twisted bilayer graphene.