Commensurate and Incommensurate Vortex States in Superconductors with Periodic Pinning Arrays

TL;DR

This paper investigates vortex lattice configurations in superconductors with periodic pinning arrays, providing formulas to predict matching fields and orientations, aligning well with experimental observations.

Contribution

It introduces formulas for predicting commensurate vortex states and their orientations in superconductors with periodic pinning arrays, enhancing understanding of vortex behavior.

Findings

Matching fields for vortex configurations are accurately predicted.

Vortex lattice orientations are determined relative to pinning arrays.

Results agree with recent experimental imaging studies.

Abstract

As a function of applied field, we find a rich variety of ordered and partially-ordered vortex lattice configurations in systems with square or triangular arrays of pinning sites. We present formulas that predict the matching fields at which commensurate vortex configurations occur and the vortex lattice orientation with respect to the pinning lattice. Our results are in excellent agreement with recent imaging experiments on square pinning arrays [K. Harada et al., Science 274, 1167 (1996)].