Charge-6e order of Kagome superconductor as a generalized XY model

Recent theoretical and experimental studies have suggested the emergence of charge-6e order in Kagome superconductors. In this talk, I will present a Ginzburg–Landau theory derived from a microscopic model for the pair-density-wave (PDW) state in Kagome superconductors. I will show that the pairing instability favors a triple-Q PDW state due to sublattice interference. The effective theory is a generalized XY model with three sublattices(colors), in which the charge-6e order naturally emerges. The three colors are coupled by a frustrated interaction which breaks time-reversal symmetry. We study this generalized XY model using Monte Carlo simulations and obtain its phase diagram. Both charge-2e and charge-6e ordered phases are identified, and surprisingly, due to the frustrated coupling, the phase transition between the charge-6e and charge-2e phases is found to be first order. Our theory might explain the multi-charge flux quantization in experiment.