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

Abstract

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.PACS numbers: 74.81. Fa, 75.10.Hk, 64.60.Cn Vortex matters in Josephson-junction arrays (JJA's) and superconducting wire networks exposed to a magnetic field have been extensively studied in recent years. 1Studies of the systems of a variety of geometries have been concentrated especially on the nature of ordering transitions and excitations in the ordered state. More recently, special attention is given to highly frustrated systems which are unable to simultaneously satisfy the competing interactions and consequently have the highly degenerate ground states. 2,3,4,5,6,7,8,9,10,11,12 Understanding how a highly frustrated system orders or fails to order is one of most challenging problems in current condensed matter physics.The infinite degeneracy of the ground state has been suggested in the systems on the triangular, kagome, honeycomb, or dice lattice with the formation of zero-energy domain walls in the ordered vortex state. 3,4,7,8,11,12 The common cause to lift the accidental degeneracy is thermal fluctuations in the continuous phase variable, that is, spin waves. 3,8,11,12 The difference in free energy of the fluctuations forces many systems to select a particular vortex pattern at finite temperatures. This mechanism of lifting an accidental degeneracy is often referred to as order-from-disorder. Frustrated JJA's on the dice (or T 3 ) lattice have attracted recent attention because of the possibility that the order-from-disorder mechanism for the removal of an accidental degeneracy may not be effective in the systems. Theoretical evaluations 12 on the frustrated XY model, which most closely represents a JJA in a magnetic field, have demonstrated that for the frustration index (defined as the magnetic flux through a rhombus tile in units of flux quantum) f = 1/3, frustration effects on a dice array are particularly large and the system fails to order down to zero tempe...