Phase coherence of charge-6e superconductors via a frustrated Kagome XY antiferromagnet

Recent experimental evidence for the charge-6e condensed phase in kagome superconductors has generated significant interest. We investigate the unconventional superconductivity in the kagome superconductor CsV₃Sb₅, focusing on the emergence of charge-6e superconductivity (SC) at temperatures higher than the conventional charge-2e SC state. By modeling the phase coherence of the SC order parameter using a frustrated antiferromagnetic XY model on an emergent kagome lattice, we show that the condensation of fractional vortices with 1/3 vorticity stabilizes phase coherence in exp(i3θ), giving rise to the charge-6e SC state. Using a tensor network approach tailored for frustrated spin systems, we identify a Berezinskii-Kosterlitz-Thouless transition at T_c/J' ⋍ 0.075, where the unbinding of 1/3 fractional vortex-antivortex pairs transforms the system from the charge-6e SC phase to the normal phase. Below T_c, the 1/3 fractional vortex correlations exhibit power-law decay, while the integer vortex correlations decay exponentially, reflecting the dominance of charge-6e SC in the absence of charge-2e SC. Our results provide a theoretical understanding of the charge-6e SC in two-dimensional kagome superconductors, emphasizing the interplay between fractional vortices, frustration, and topology in stabilizing this exotic SC phase.