Structure of the superconducting state in a fully frustrated wire network with dice lattice geometry

The superconducting state in a fully frustrated wire network with the dice lattice geometry is investigated in the vicinity of the transition temperature. We express the projection of the Ginzburg-Landau free-energy functional on its unstable subspace in terms of variables defined on the triangular sublattice of sixfold coordinated sites. For the resulting effective model, we construct a large class of degenerate equilibrium configurations, which are in one-to-one correspondence with ground states of the fully frustrated XY model with a dice lattice. The entropy of this set of states is proportional to the linear size of the system. Finally, we show that magnetic interactions between currents provide a degeneracy lifting mechanism and find the structure of the periodic state selected by these interactions.