Quantum interference on the kagome´ lattice

We study quantum interference effects due to electron motion on the kagome$aa— lattice in a perpendicular magnetic field. These effects arise from the interference between phase factors associated with different electron closed paths. From these we compute, analytically and numerically, the superconducting-normal phase boundary for kagome$aa— 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 (∼10²¹) 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.