Vortex configurations in thin superconducting equilateral triangles

Abstract

We investigated theoretically vortex configurations in thin mesoscopic superconducting equilateral triangles submitted to an external magnetic field. Analytical expressions for the vortex interactions with the screening current and other vortices were calculated by considering the sample sides much smaller than the effective penetration depth within the London limit. The vortex configurations were obtained by using Langevin dynamics simulations. In most of the configurations, the vortices sit close to the corners, presenting twofold or threefold symmetry. We also determined the dependence on the magnetic field of the equilibrium states. The ground states with larger magnetic field range are those with the number of vortices equal to the triangular numbers [${N}^{\ensuremath{'}}=n(n+1)/2$, with $n$ integer]. A study of different stable configurations with the same number of vortices is also presented.