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

Recent experimental evidence of the charge-6e condensed phase in Kagome superconductors has generated significant interest. This study investigates the unconventional superconductivity in the Kagome superconductor CsV_3Sb_5, 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, the condensation of fractional vortices with 1/3 vorticity stabilizes the phase coherence in \exp(i3\theta), resulting in a charge-6e SC state. Using a tensor network approach tailored for frustrated spin systems, a Berezinskii-Kosterlitz-Thouless transition is identified at T_\rm c/J \simeq 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_\rm c, the 1/3 fractional vortex correlations exhibit a power-law decay, whereas the integer vortex correlations decay exponentially, reflecting the dominance of charge-6e SC in the absence of charge-2e SC. The results provide a theoretical understanding of charge-6e SC in two-dimensional Kagome superconductors, emphasizing the interaction between fractional vortices, frustration, and topology in stabilizing the exotic SC phase.