Melting and transverse depinning of driven vortex lattices in the periodic pinning of Josephson junction arrays

We study the nonequilibrium dynamical regimes of a moving vortex lattice in the periodic pinning of a Josephson junction array (JJA) for finite temperatures in the case of a fractional or submatching field. We obtain a phase diagram for the current driven JJA as a function of the driving current I and temperature T. We find that when the vortex lattice is driven by a current, the depinning transition at $T_p\mathrm{}\left(I\right)\mathrm{}$ and the melting transition at $T_M\mathrm{}\left(I\right)\mathrm{}$ become separated even for a field for which they coincide in equilibrium. We also distinguish between the depinning of the vortex lattice in the direction of the current drive, and the transverse depinning in the direction perpendicular to the drive. The transverse depinning corresponds to the onset of transverse resistance in a moving vortex lattice at a given temperature $T_{\mathrm{tr}}.$ For driving currents above the critical current we find that the moving vortex lattice has first a transverse depinning transition at low T, and later a melting transition at a higher temperature $T_M>T_{\mathrm{tr}}.$