Commensurate and Incommensurate Vortex States Confined in Mesoscopic Triangles of Weak Pinning Superconducting Thin Films

Abstract

We report on the direct observation of vortex states confined in equilateral and isosceles triangular dots of weak pinning amorphous superconducting thin films with a scanning superconducting quantum interference device microscope. The observed images illustrate not only pieces of a triangular vortex lattice as commensurate vortex states, but also incommensurate vortex states including metastable ones. We comparatively analyze vortex configurations found in different sample geometries and discuss the symmetry and stability of commensurate and incommensurate vortex configurations against deformations of the sample shape.The concept of a small number of interacting particles in lateral confinement is found in a variety of physical systems, including electrons confined in semiconductor quantum dots, 1 electron dimples in the liquid-helium surface, 2 and paramagnetic colloids in cavities. 3 Of particular interest is vortex matter in mesoscopic superconductors with different shapes. 4-7In addition to the vortex-vortex repulsion, vortices are subject to the lateral confinement due to the shielding current flowing along the sample boundary. The interplay between the intervortex interaction and the confinement results in unique vortex states with strong features of the sample shape, different from the Abrikosov-triangular lattice in bulk superconductors. 8It is well established that in mesoscopic disks, vortices form circular symmetric shells and obey the specific rules for shell filling with increasing the vorticity L. 9, 10 Meanwhile, in other geometric shapes such as squares [11][12][13] and pentagons, 14 the formation of vortex shells is not well defined as in disks owing to the commensurability between the geometry and the vortex arrangement. In mesoscopic triangles, which we focus on this study, vortices form intrinsically a piece of the triangular lattice since they match the geometric shape with threefold *

Vortex shells in mesoscopic triangles of amorphous superconducting thin films

“…Recently, we have reported the direct observation of multi-vortex states in triangle shaped, mesoscopic dots of weak pinning amorphous thin films with a scanning superconducting quantum interference device (SQUID) microscope [10]. We observed the coexistence of multiple (metastable) patterns at some vorticities.…”

“…The issue of vortex shells would be interesting when vortices are confined in polygonal small superconductors like triangle [8,9,10], square [11,12] and pentagonal shaped dots [13]. These polygonal dots have discrete, natural symmetries that coincide or compete with the configurational symmetry of vortex polygons, depending on vorticity L. In triangle dots, vortices intrinsically form a triangular cluster of which symmetry is commensurate with that of the triangle geometry.…”

Finite-size effect of critical penetration of Pearl vortices in narrow superconducting flat rings

“…2 The interplay between the intervortex interaction and the confinement results in unique vortex states, different from the Abrikosov-vortex lattice in bulk superconductors. These include vortex polygons, 3 concentric vortex shells, 4,5 and vortex fusion, [6][7][8][9] which have been directly observed in imaging experiments on small superconducting discs, 10,11 squares, 12,13 , triangles, 14,15 pentagons, 16 and others. [17][18][19] In recent years there has been renewed interest in vortices trapped in small superconductors as one of the control sources for non-equilibrium excess quasiparticles.…”