Vortex depinning as a nonequilibrium phase transition phenomenon: Scaling of current-voltage curves near the low and the high critical-current states in 2H-NbS_2 single crystals

摘要

The vortex depinning phenomenon in single crystals of 2H-NbS_2 superconductors is used as a prototype for investigating properties of the nonequilibrium (NEQ) depinning phase transition. The 2H-NbS_2 is a unique system as it exhibits two distinct depinning thresholds, viz., a lower critical current I_c~l and a higher one I_c~h. While I_c~l is related to depinning of a conventional, static (pinned) vortex state, the state with I_c~h is achieved via a negative differential resistance (NDR) transition where the velocity abruptly drops. Using a generalized finite-temperature scaling ansatz, we study the scaling of current (I)-voltage (V) curves measured across I_c~l and I_c~h. Our analysis shows that for I > I_c~l, the moving vortex state exhibits Arrhenius-like thermally activated flow behavior. This feature persists up to a current value where an inflexion in the IV curves is encountered. While past measurements have often reported similar inflexion, our analysis shows that the inflexion is a signature of a NEQ phase transformation from a thermally activated moving vortex phase to a free flowing phase. Beyond this inflection in IV, a large vortex velocity flow regime is encountered in the 2H-NbS_2 system, wherein the Bardeen-Stephen flux flow limit is crossed. In this regime the NDR transition is encountered, leading to the high I_c~h state. The IV curves above I_c~h we show do not obey the generalized finite-temperature scaling ansatz (as obeyed near I_c~l). Instead, they scale according to the Fisher's scaling form [Fisher, Phys. Rev. B 31, 1396 (1985)] where we show thermal fluctuations do not affect the vortex flow, unlike that found for depinning near l'c.