The ice-like vortex states in a nanostructured superconducting film with a dice lattice of elongated antidots

We study the degeneracy of the superconducting vortex ground state in a dice lattice of elongated antidots within the Ginzburg-Landau (GL) theory. It is found there are two kinds of unit cells in this dice lattice, namely z6 unit cell where six antibars meet and z3 unit cell where three antibars meet. This can result in more complicated vortex arrangements in the unit cells than that in the kagome lattice. We demonstrate that the vortex patterns at specific fractional magnetic fields can be determined by the local constraints, which presented the ice-like vortex configuration based on the degeneracy rules. This is the reason that the vortex system follows the rule of “two vortices in, one vortex out” or “two vortices out, one vortex in” at each vertex of z3 unit cell. The so-called degeneracy rules are explored by considering nearest-neighbor interaction. Thus, it is possible to realize a rich variety of ice-like vortex configurations in a large area of the sample.