Strong pinning theory of thermal vortex creep in type-II superconductors

Abstract

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]

Experimental test of strong pinning and creep in current-voltage characteristics of type-II superconductors

“…The barriers U c extracted from the fits can be compared with experiments on persistent current relaxation quantified by the normalized creep rate S = −∂ log j/∂ log t [18]. Assuming that the activation barrier U (j) vanishes with a characteristic exponent α = 3/2, the creep rate is related to the barrier through S ≈ (2/3)(k B T /U c ) 2/3 [5]. Fitting the data of 2H-NbSe 2 for T = 4.8 K yields the barrier U c ≈ 980 K, see Fig.…”

“…Here, we have used the definition of the free flux-flow velocity v c = F c /η at F c . The dynamical equation (5) captures the small vortex velocity at subcritical drives j < j c , the rounding of the characteristic in the critical region, and the (initial part) of the smooth approach to the ohmic region. As v approaches v th , thermal fluctuations become irrelevant and the characteristic joins the excess-current shape.…”

“…Besides setting a focus on the Bean critical state [10] and its log-time decay, the shape of the current-voltage characteristic in the critical region was discussed as well, including an interpolation formula describing the transformation of creep-type to flow-type response of vortices that prevail at low and high drives, respectively [8]. Later, much further work has been devoted to studying creep, particularly in the high-T c superconductors where thermal fluctuations play 8,5.0, 5.2, and 5.5 K (red points). Black lines are fits to the data based on the prediction of strong pinning theory; fits are restricted to the region of applicability of the theory (see text for details).…”

Peak effect due to competing vortex ground states in superconductors with large inclusions

“…The described basic scenario assumed in the majority of theoretical studies [28][29][30][31][32][33][34][35][36][37] is valid if the critical deformation u c is much smaller than the lattice period a . This condition may break for large inclusions at sufficiently strong magnetic field, especially in strongly-anisotropic superconductors.…”

Creep effects on the Campbell response in type II superconductors

“…When including thermal fluctuations in the calculation of the pinning force density F pin , different jumps ∆e pin (t) in the pinning energy become relevant that depend on the time t evolution of the vortex state due to creep. While this relaxational time dependence leads to the decay of the persistent current density j(t), the corresponding velocity dependence leads to a rounding 14,15 of the transition 16 between pinned and dissipative states in the current-voltage characteristic; again the quantitative nature of the strong pinning description allows for a detailed comparison of the temperature-shifted and rounded excess-current characteristic predicted by theory with experimental data on superconducting films 17 .…”