Non-uniform vestigial charge-4e phase in the Kagome superconductor CsV₃Sb₅

Pair density wave state and its vestigial charge-4e and 6e superconducting phases have been reported in the Kagome superconductor CsV₃Sb₅. By treating the charge density waves that are ordered at high temperatures as static backgrounds, we notice that all pair density waves have the same wavevector in the folded 2D Brillouin zone. This wavevector is at a high symmetry point and preserves time-reversal symmetry. The PDW state is thus neither ‘FF’-like nor ‘LO’-like. With this non-degenerate pair density wave, we illustrate the resulting necessity for the vestigial charge-4e phase to be non-uniform. We will also highlight the importance of disorder in stabilizing vestigial phases in a commensurate system.