Superconducting phase transitions in frustrated Josephson-junction arrays on a dice lattice

Transport measurements are carried out on dice Josephson-junction arrays with the frustration index $f=1/3$ and 1/2 which possess, within the limit of the $XY$ model, an accidental degeneracy of the ground states as a consequence of the formation of zero-energy domain walls. The measurements demonstrate that both the systems undergo a phase transition to a superconducting vortex-ordered state at considerably high temperatures. The experimental findings are in apparent contradiction with the theoretical expectation that frustration effects in the $f=1/3$ system are particularly strong enough to suppress a vortex-ordering transition down to near zero temperature. The data for $f=1/2$ are more consistent with theoretical evaluations. The agreement between the experiments and the Monte Carlo simulations of a $XY$ model for $f=1/3$ suggests that the order-from-disorder mechanism for the removal of an accidental degeneracy may still be effective in the $f=1/3$ system. The transport data also reveal that the dice arrays with zero-energy domain walls experience a much slower critical relaxation than other frustrated arrays only with finite-energy walls.