Critical behavior of plastic depinning of vortex lattices in two dimensions: Molecular dynamics simulations

Abstract

Using molecular dynamics simulations, we report a study of the dynamics of two-dimensional vortex lattices driven over a disordered medium. In strong disorder, when topological order is lost, we show that the depinning transition is analogous to a second order critical transition: the velocity-force response at the onset of motion is continuous and characterized by critical exponents. Combining studies at zero and nonzero temperature and using a scaling analysis, two critical exponents are evaluated. We find v ∼ (F − Fc) β with β = 1.3 ± 0.1 at T = 0 and F > Fc, and v ∼ T 1/δ with δ −1 = 0.75 ± 0.1 at F = Fc, where Fc is the critical driving force at which the lattice goes from a pinned state to a sliding one. Both critical exponents and the scaling function are found to exhibit universality with regard to the pinning strength and different disorder realizations. Furthermore, the dynamics is shown to be chaotic in the whole critical region.

Random organization in periodically driven gliding dislocations

“…The vortices have much longer range interactions than the colloidal particles, and in the reversible state the vortices are still strongly interacting with each other, indicating that the idea of random organization can be extended beyond systems with simple contract interactions. Random organization has also been studied in the context of plastic depinning of colloidal particles and vortices, where a divergent transient time appears at the pinned to sliding transition [12][13][14][15] . An intriguing question is whether there are other systems with long range interactions that can also exhibit a dynamical reversible to irreversible transition under periodic driving, and if there can be reversible states that are not simply random but form patterns or structures that differ from the initial random distributions.…”

Collective Transport Properties of Driven Skyrmions with Random Disorder

“…A wide variety of systems can be effectively modeled as collectively interacting particles moving over quenched disorder, with a transition from a pinned state to a sliding state under an applied drive. Examples include driven incommensurate charge density waves [1,2], Wigner crystals [3,4], colloids on various types of substrates [5][6][7], and vortices in type-II superconductors [8][9][10][11][12]. In many of these systems the particle-particle interactions are repulsive, so that in the absence of disorder a hexagonal crystal of particles forms.…”

“…When an external driving force F D is applied to pinned particles, the particles begin to move above a critical drive value F c known as the depinning threshold. For weak disorder the particles generally depin elastically and retain their original neighbors [1,2,5,7,9], but for strong disorder the depinning becomes plastic with particles continuously changing neighbors over time, forming a fluctuating liquid-like state [4][5][6][9][10][11][12]. When depinning occurs from a disordered pinned state, there can be dynamic structural transitions at drives well above F c , where the particles dynamically order into a moving anisotropic crystal or moving smectic phase [9][10][11][14][15][16][17][18][19][20] when the strong driving reduces the effectiveness of the pinning in the drive direction [10].…”

Transition de dépiégeage élastique de vortex supraconducteurs

“…Néanmoins, la variété d'exposants mesurée dans d'autres systèmes périodiques (voir introduction) semble suggérer que les formes précises des interactions particule-particule et particule-piège jouent un rôle important, ce qui impliquerait que de vastes classes d'universalité n'existent pas pour la transition de dépiégeagé elastique. Des conclusions similairesémergaient pour la transition de dépiégeage plastique [12]. Finalement, notons que les mesuresà température non nulle confirment notre résultat β = 0.27 ± 0.04.…”

“…[10], et pour les phases au seuil de dépiégeage plastique en désordre fort voir Refs. [11,12]. Plusieurs tailles de système ontétéétudiées au voisinage du seuil de dépiégeage et les résultats montrent une transition de phase continue (second ordre).…”