Vestigial chirality from fluctuating loop currents on the kagome lattice

Abstract: Multicomponent order can melt in stages, leaving a composite order after its primary constituents become short ranged. We study this possibility for commensurate three-$Q$ loop-current order on the kagome lattice. Large-scale cluster and parallel-tempering Monte Carlo simulations reveal direct and two-stage melting regimes in an effective fixed-amplitude sign model. In the latter regime, translation-sector domain walls proliferate before chirality-changing walls, restoring lattice translational symmetry while preserving long-range time-reversal-odd order. The primary $M$-point correlations are short ranged in this intermediate phase. The two-stage regime begins when the lowest-energy chirality-changing wall is only about $12$--$13\%$ more costly than a same-chirality translation wall. Finite-size scaling of a stable amplitude-resolved Ginzburg--Landau theory shows that the phase survives amplitude relaxation. Our results establish a quantitative domain-wall criterion for vestigial loop-current order and a fluctuation route to time-reversal symmetry breaking without long-range loop-current Bragg order. This separation provides a possible thermodynamic framework for time-reversal-odd responses recently reported above the critical temperature for conventional charge-density-wave ordering in kagome metals.