We study driven vortices lattices in superconducting thin films. Above the critical force Fc we find two dynamical phase transitions at Fp and Ft, which could be observed in simultaneous noise measurements of the longitudinal and the Hall voltage. At Fp there is a transition from plastic flow to smectic flow where the voltage noise is isotropic (Hall noise = longitudinal noise) and there is a peak in the differential resistance. At Ft there is a sharp transition to a frozen transverse solid where the Hall noise falls down abruptly and vortex motion is localized in the transverse direction.The study of the collective motion of vortex lattices in superconductors has brought new concepts in the nonequilibrium statistical physics of driven disordered media [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. The prediction [1] of a dynamical phase transition upon increasing drive, from a fluidlike plastic flow regime [2-4] to a coherently moving solid [1], has motivated an outburst of recent theoretical [5][6][7], experimental [8][9][10][11], and simulation [12][13][14][15][16][17][18] work. The relevant physics of the high velocity driven phase is controlled by the transverse displacements (in the direction perpendicular to the driving force) [5], leading to a new class of driven systems characterized by anisotropic spatial structures with transverse periodicity [5][6][7]. Recently, these moving anisotropic vortex structures have been observed experimentally by Pardo et al. [11], and their different features have been studied in 2D [12][13][14][15][16] and 3D [17,18] simulations. In this letter, we show that a better insight on the moving phases can be obtained from studying the anisotropic temporal fluctuations. We find two dynamical phase transitions which could be observed experimentally by measuring voltage noise [19,20] both in the longitudinal and transversal directions. In the transverse direction, where the system is not driven, we can study diffusion, from which we define an effective temperature in analogy with equilibrium physics [1,7].The equation of motion of a vortex in position r i is:where r ij = |r i − r j | is the distance between vortices i, j, r ip = |r i − r p | is the distance between the vortex i and a pinning site at r p , η = Φ0Hc2d c 2 ρn is the Bardeen-Stephen friction and F = dΦ0 c J × z is the driving force due to an applied current J. A two-dimensional superconductor is realized in thin films of thickness d where d ≪ λ, which have an effective penetration depth Λ = 2λ 2 /d. Since Λ is of the order of the sample size (Λ ≈ 200µm in [9]), the vortex-vortex interaction is logarithmic:The vortices interact with a random uniform distribution of attractive pinning centers with U p (r) = −A p e −(r/ξ) 2 with ξ being the coherence length. We normalize length scales by ξ, energy scales by A v , and time is normalized by τ = ηξ 2 /A v . We consider N v vortices and N p pinning centers in a rectangular box of size L x × L y , and the normalized vortex density isWe study the dynamical re...

We study the steady state of driven elastic strings in disordered media below the depinning threshold. In the low-temperature limit, for a fixed sample, the steady state is dominated by a single configuration, which we determine exactly from the transition pathways between metastable states. We obtain the dynamical phase diagram in this limit. At variance with a thermodynamic phase transition, the depinning transition is not associated with a divergent length scale of the steady state below threshold, but only of the transient dynamics. We discuss the distribution of barrier heights, and check the validity of the dynamic phase diagram at small but finite temperatures using Langevin simulations. The phase diagram continues to hold for broken statistical tilt symmetry. We point out the relevance of our results for experiments of creep motion in elastic interfaces.

We study the steady-state low-temperature dynamics of an elastic line in a disordered medium below the depinning threshold. Analogously to the equilibrium dynamics, in the limit T→0, the steady state is dominated by a single configuration which is occupied with probability 1. We develop an exact algorithm to target this dominant configuration and to analyze its geometrical properties as a function of the driving force. The roughness exponent of the line at large scales is identical to the one at depinning. No length scale diverges in the steady-state regime as the depinning threshold is approached from below. We do find a divergent length, but it is associated only with the transient relaxation between metastable states

We report a comparative study of magnetic field driven domain wall motion in thin films made of different magnetic materials for a wide range of field and temperature. The full thermally activated creep motion, observed below the depinning threshold, is shown to be described by a unique universal energy barrier function. Our findings should be relevant for other systems whose dynamics can be modeled by elastic interfaces moving on disordered energy landscapes.