Critical behavior of nonequilibrium depinning transitions for vortices driven by current and vortex density

Evidence of second-order transition and critical scaling for the dynamical ordering transition in current-driven vortices

Dynamical ordering from a disordered plastic flow to an anisotropically ordered smectic flow induced by a dc force has been studied in various many-particle systems, including vortices in type-II superconductors. However, it remains unclear whether the dynamical ordering is a true phase transition because of lack of suitable experimental methods. Here, we study the response of vortex flow to the transverse force using a cross-shaped amorphous Mo[Formula: see text]Ge[Formula: see text] film. From transverse current-voltage (force-velocity) characteristics under various longitudinal currents, we find a change of the transverse response in low voltage (velocity) regions from a nonlinear to linear behavior at a well-defined longitudinal current that marks the dynamical ordering transition. We also find the scaling collapse of the transverse current-voltage curves to a universal scaling function, providing evidence of the second-order transition for the dynamical ordering transition.

Kibble-Zurek Mechanism for Dynamical Ordering in a Driven Vortex System

The Kibble-Zurek mechanism describes the formation of topological defects in systems crossing a continuous symmetry-breaking phase transition at a finite quench rate. While this mechanism has been extensively studied for equilibrium transitions, its applicability to nonequilibrium transitions has not yet been fully examined. Recent simulation has shown the applicability of the Kibble-Zurek mechanism to dynamical ordering transitions in particlelike assemblies, including superconducting vortices, driven over random disorder. Here, we experimentally study the configurational order of vortices in the course of dynamical ordering with various quench rates. We verify a power-law scaling of the defect density with the quench rate and an impulse-adiabatic crossover on the ordered side of the transition, which are key predictions of the Kibble-Zurek mechanism. Our results suggest the applicability of the Kibble-Zurek mechanism to other nonequilibrium phase transitions.