Local condensation of charge-$4e$ superconductivity at a nematic domain wall

In the fluctuation regime that precedes the onset of pairing in multicomponent superconductors, such as nematic and chiral superconductors, the normal state is generally unstable toward the formation of charge-$4e$ order—an exotic quantum state in which electrons form coherent quartets rather than Cooper pairs. However, charge-$4e$ order is often suppressed by other competing composite orders, such as nematics. Importantly, the formation of nematic domains is unavoidable due to the long-range strains generated, leading to one-dimensional regions where the competing nematic order is suppressed. Here, we employ a real-space variational approach to demonstrate that, in such nematic domain walls, charge-$4e$ order is locally condensed via a vestigial-order mechanism. We explore the experimental manifestations of this effect and discuss materials in which it can be potentially observed.