Quantum Interference on the Kagom\'e Lattice

TL;DR

This paper investigates quantum interference effects on the Kagomé lattice under a magnetic field, analyzing how electron phase factors influence the superconducting-normal phase boundary through extensive path summation.

Contribution

It provides an analytical and numerical study of interference effects on the Kagomé lattice, including exact path summation and phase boundary analysis, linking quantum interference to lattice structure.

Findings

Computed phase boundary for Kagomé superconducting networks.

Identified the origin of fine and overall structure in the phase diagram.

Predicted experimental signatures of quantum interference effects.

Abstract

We study quantum interference effects due to electron motion on the Kagom\'e lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed-paths. From these we compute, analytically and numerically, the superconducting-normal phase boundary for Kagom\'e superconducting wire networks and Josephson junction arrays. We use an analytical approach to analyze the relationship between the interference and the complex structure present in the phase boundary, including the origin of the overall and fine structure. Our results are obtained by exactly summing over one thousand billion billions ($\sim 10^{21}$) closed paths, each one weighted by its corresponding phase factor representing the net flux enclosed by each path. We expect our computed mean-field phase diagrams to compare well with several proposed experiments.