Non equilibrium phase diagrams of current driven Josephson junction arrays

We present a review of our previous numerical studies on non equilibrium vortex dynamics in Josephson Junction arrays (JJA) driven by a dc current. Dynamical phase diagrams for different magnetic fields, current directions and varying temperature are discussed and compared. First, the effect of thermal fluctuations in a current driven diluted vortex lattice (VL) is analyzed. The case of f = 1/25 (where f is the fraction of flux quanta per plaquette in the array) is considered and the phase diagram as a function of the driving current and temperature is analyzed. In equilibrium, this system has a weakly first-order melting transition of the vortex lattice, which coincides with a depinning transition. When a low current is applied, the “longitudinal” depinning transition occurs at a temperature lower than the melting transition. More interestingly, for large currents (well above the critical current) there is an analogous sequence of transitions but for the transverse response of a fast moving VL. There is a transverse depinning temperature below the melting transition of the moving VL. We also discuss the dependence with the direction of the applied dc current of the transport properties of diluted vortex arrays on a square JJA at low temperatures. We show that orientational pinning phenomenon leads to a finite transverse critical current when the bias current is applied in the directions of high symmetry and it leads to an anomalous transverse voltage when vortices are driven away from the favorable directions. In addition, the effect of disorder in the transport properties of square JJA with a dc current applied in the “diagonal direction” ([11] direction) is analyzed and a finite transverse voltage is also observed in this case. The case of a fully frustrated square JJA, corresponding to f = 1/2, driven by a dc current and with thermal fluctuations is also discussed. In equilibrium, the low temperature phase has two broken symmetries: the U(1) symmetry, corresponding to superconducting coherence, and the Z2 symmetry corresponding to the periodic order of the VL, which forms a “checkerboard pattern”. At high currents (well above the critical current) two well separated transitions are observed. The order of the checkerboard vortex lattice (discrete Z2 symmetry) is destroyed at a much lower temperature than the transverse superconducting coherence (continuous U(1) symmetry).