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

TL;DR

This paper models the emergence of charge-$6e$ superconductivity in kagome superconductors through fractional vortex condensation, revealing a BKT transition driven by vortex unbinding, and highlights the role of frustration and topology in stabilizing this exotic phase.

Contribution

It introduces a frustrated XY model on an emergent kagome lattice to explain charge-$6e$ superconductivity via fractional vortices, supported by tensor network analysis.

Findings

Identification of a BKT transition at T_c/J ≈ 0.075

Power-law decay of fractional vortex correlations below T_c

Exponential decay of integer vortex correlations

Abstract

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 $\mathrm{CsV_3Sb_5}$, 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, we show that the condensation of fractional vortices with $1/3$ vorticity stabilizes phase coherence in $\exp(i3\theta)$, 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 $T_c/J \simeq 0.075$, where the unbinding of $1/3$ fractional vortex-antivortex pairs transforms the system from the charge-$6e$ SC phase to the normal phase. Below $T_c$, 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.