Vortex rivers and multiple voltage transitions in superconducting MgB$_2$ thin films

Abstract

Vortex dynamics govern the dissipation and magneto-resistive properties of type-II superconductors. At large transport currents, the current-voltage ($I$-$V$) characteristics of a superconductor in the mixed state usually exhibit a nonlinear upturn followed by an abrupt jump occurring due to a flux-flow instability. However, other transition behaviors are also possible, including the formation of phase-slip lines and normal domains. Which mechanism dominates depends on the sample uniformity, its dimensions relative to the coherence length and penetration depth, and the rates of electron energy relaxation and heat removal. Here, based on the time-dependent Ginzburg-Landau equation, we present the results of numerical modeling of the $I$-$V$ curves of superconducting films with various types of disorder. For a grain-boundary defect mesh, we find multiple voltage transitions overlaid with a nonlinear upturn of the $I$-$V$ curves. For randomly arranged elongated defects, the $I$-$V$ curves exhibit voltage steps, whereas for L-shaped defects oriented perpendicular to the transport current, the $I$-$V$ curves show extended linear regimes separated by voltage transitions. We analyze the evolution of the order parameter along the $I$-$V$ curves and discuss the experimental accessibility of the revealed dynamics regimes.