Extended superconducting fluctuation region and 6e and 4e flux-quantization in a Kagome compound with a normal state of 3Q-order

TL;DR

This paper investigates an extended fluctuation region in a Kagome superconductor with 3Q order, revealing unconventional 6e and 4e flux quantization states that influence Little-Parks oscillations.

Contribution

It introduces novel 6e and 4e flux-quantized states in a 3Q superconductor, expanding understanding of flux quantization beyond the usual 2e state.

Findings

Extended fluctuation regime below the mean-field transition temperature.

Observation of 6e and 4e flux quantization states.

Periodic resistivity oscillations indicating unconventional flux states.

Abstract

The superconducting state with the usual 2e-flux quantization formed from a normal state with 3Q charge density or loop-current order is a linear combination of 3 different paired states with an overall gauge invariant phase and two internal phases such that the phases in equilibrium are at $2\pi/3$ with respect to each other. In the fluctuation regime of such a 3-component superconductor, internal phase fluctuations are of the same class as for frustrated classical xy-spins on a triangular lattice. The fluctuation region is known therefore to be abnormally extended below the mean-field or the Kosterlitz-Thouless transition temperature. A 6e-flux and a 4e-flux quantized states can be constructed which are also eigenstates of the BCS Hamiltonian and stationary points of the Ginzburg-Landau free-energy with a transition temperature above that of the renormalized 2e-flux quantized state. Such states have no internal phases and so no frustrating internal phase fluctuations. These state however cannot acquire long-range order because their free-energy is higher than the co-existing fluctuating state of 2e flux-quantization. 6e- as well as 4e- flux-quantized Little-Parks oscillations however occur in which the resistivity increases periodically with field above that of the 2e-fluctuating state in its extended fluctuation regime, as are observed, followed at low temperatures to a condensation of the time-reversal odd 2e-quantized state