Emergence of charge-$4e$ superconductivity from 2D nematic superconductors

Charge-$4e$ superconductivity is an exotic state of matter that may emerge as a vestigial order from a charge-$2e$ superconductor with multicomponent superconducting order parameters. Showing its emergence in a microscopic model from numerically-exact large-scale computations has been rare so far. Here, we propose a microscopic lattice model with a nematic superconducting ground state and show that it supports a rich set of vestigial phases at elevated temperature, including a charge-$4e$ phase and a quasi-long-range nematic phase, by performing large-scale Monte Carlo simulations. Combining theoretical analysis with Monte Carlo simulations, we uncover the nature of these phases and show that the phase transitions are governed by the proliferation of distinct topological defects: half superconducting vortices, $(\tfrac{1}{2},\tfrac{1}{2})$ vortices, integer nematic vortices, and domain-wall excitations. In particular, we demonstrate that domain-wall proliferation is crucial for the quasi-nematic phase and should be carefully accounted for in phase transitions associated with vestigial charge-$4e$ order.