Theory of charge-6e condensed phase in Kagome lattice superconductors

TL;DR

This paper develops a Ginzburg-Landau theory for charge-6e condensed phases in kagome lattice superconductors, revealing novel topological defects and a vestigial phase with charge-6e order, supported by numerical simulations.

Contribution

It introduces a new theoretical framework for charge-6e phases in kagome superconductors, linking topological defects, frustrated XY models, and experimental observations.

Findings

Identification of $1/3$ topological charges on domain wall kinks

Numerical confirmation of a vestigial phase with charge-$6e$ order

Explanation of recent magnetoresistance oscillations in experiments

Abstract

We develop a Ginzburg-Landau theory for commensurate pair density wave (PDW) states in a hexagonal lattice system, relevant to the kagome superconductors $\rm{AV_3Sb_5}$. Compared to previous theoretical frameworks, the commensurate wave vectors permit additional symmetric terms in the free energy, altering the system's ground state and its degeneracy. In particular, we analyze topological defects in the energetically favorable $\psi_{\text{kagome}}$ ground state and find that kinks on domain walls can carry $1/3$ topological charges. We further establish a correspondence between the SC fluctuations in these states and an effective $J_1-J_2$ frustrated XY model on the emergent kagome lattice. By employing a state-of-the-art numerical tensor network method, we rigorously solve this effective model at finite temperatures and confirm the existence of a vestigial phase characterized by $1/3$ vortex-antivortex pairs in low temperatures with the absence of phase coherence of Cooper pairs, which is dual to the charge-$6e$ condensed phase. Our theory provides a potential explanation for the vestigial charge-$6e$ magnetoresistance oscillations observed in recent experiments [J. Ge, et. al., Phys. Rev. X 14, 021025 (2024)].