Vortex depinning as a nonequilibrium phase transition phenomenon: Scaling of current-voltage curves near the low and the high critical-current states in 2H−NbS2 single crystals

The vortex depinning phenomenon in single crystals of $2H\text{\ensuremath{-}}\mathrm{Nb}{\mathrm{S}}₂$ superconductors is used as a prototype for investigating properties of the nonequilibrium (NEQ) depinning phase transition. The $2H\text{\ensuremath{-}}\mathrm{Nb}{\mathrm{S}}₂$ 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 $2H\text{\ensuremath{-}}\mathrm{Nb}{\mathrm{S}}₂$ 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 ${I}_c^l$.