We study thermal effects on pinning and creep in type-II superconductors where vortices interact with a low density np of strong point-like defects with pinning energy ep and extension ξ, the vortex core size. Defects are classified as strong if the interaction between a single pin and an individual vortex leads to the appearance of bistable solutions describing pinned and free vortex configurations. Extending the strong pinning theory to account for thermal fluctuations, we provide a quantitative analysis of vortex depinning and creep. We determine the thermally activated transitions between bistable states using Kramer's rate theory and find the non-equilibrium steady-state occupation of vortex states. The latter depends on the temperature T and vortex velocity v and determines the current-voltage (or force-velocity) characteristic of the superconductor at finite temperatures. We find that the T = 0 linear excess-current characteristic v ∝ (j − jc) Θ(j − jc) with its sharp transition at the critical current density jc, keeps its overall shape but is modified in three ways due to thermal creep: a downward renormalization of jc to the thermal depinning current density j dp (T ) < jc, a smooth rounding of the characteristic around j dp (T ), and the appearance of thermally assisted flux flow (TAFF) v ∝ j exp(−U0/kBT ) at small drive j jc, with the activation barrier U0 defined through the energy landscape at the intersection of free and pinned branches. This characteristic emphasizes the persistence of pinning of creep at current densities beyond critical. arXiv:1903.09083v2 [cond-mat.supr-con]
Pinning and thermal creep determine the response of numerous systems containing superstructures, e.g., vortices in type II superconductors, domain walls in ferroics, or dislocations in metals. The combination of drive and thermal fluctuations lead to the superstructure's depinning and its velocity v determines the electric, magnetic, or mechanical response. It is commonly believed that pinning and creep collapse above the critical drive Fc, entailing a sharp rise in the velocity v. We challenge this perception by studying the effects of thermal fluctuations within the framework of strong vortex pinning in type-II superconductors. In fact, we show that pinning and thermal creep persist far beyond the critical force. The resulting force-velocity characteristic largely maintains its zero-temperature shape and thermal creep manifests itself by a downward renormalisation of the critical drive. Such characteristics is in agreement with Coulomb's law of dry friction and has been often observed in experiments.
Pinning and creep determine the current-voltage characteristic of a type II superconductor and thereby its potential for technological applications. The recent development of strong pinning theory provides us with a tool to assess a superconductor's electric properties in a quantitative way. Motivated by the observation of typical excess-current characteristics and field-scaling of critical currents, here, we analyze current-voltage characteristics measured on 2H-NbSe2 and a-MoGe type II superconductors within the setting provided by strong pinning theory. The experimentally observed shift and rounding of the voltage-onset is consistent with the predictions of strong pinning in the presence of thermal fluctuations. We find the underlying parameters determining pinning and creep and discuss their consistency.
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