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Register a new userBuckling instability in type-II superconductors with strong pinning
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We predict a novel buckling instability in the critical state of thin type-II superconductors with strong pinning. This elastic instability appears in high perpendicular magnetic fields and may cause an almost periodic series of flux jumps visible in the magnetization curve. As an illustration we apply the obtained criteria to a long rectangular strip.
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We study effects of pinning on the dynamics of a vortex lattice in a type II superconductor in the strong-pinning situation and determine the force--velocity (or current--voltage) characteristic combining analytical and numerical methods. Our analysis deals with a small density $n_p$ of defects that act with a large force $f_p$ on the vortices, thereby inducing bistable configurations that are a characteristic feature of strong pinning theory. We determine the velocity-dependent average pinning-force density $langle F_p(v)rangle$ and find that it changes on the velocity scale $v_p sim f_p/eta a_0^3$, where $eta$ is the viscosity of vortex motion and $a_0$ the distance between vortices. In the small pin-density limit, this velocity is much larger than the typical flow velocity $v_c sim F_c/eta$ of the free vortex system at drives near the critical force-density $F_c = langle F_p(v=0)rangle propto n_p f_p$. As a result, we find a generic excess-force characteristic, a nearly linear force--velocity characteristic shifted by the critical force-density $F_c$; the linear flux-flow regime is approached only at large drives. Our analysis provides a derivation of Coulombs law of dry friction for the case of strong vortex pinning.
The current-carrying capacity of type-II superconductors is decisively determined by how well material defect structures can immobilize vortex lines. In order to gain deeper insights into the fundamental pinning mechanisms, we have explored the case of vortex trapping by randomly distributed spherical inclusions using large-scale simulations of the time-dependent Ginzburg-Landau equations. We find that for a small density of particles having diameters of two coherence lengths, the vortex lattice preserves its structure and the critical current $j_c$ decays with the magnetic field following a power-law $B^{-alpha}$ with $alpha approx 0.66$, which is consistent with predictions of strong-pinning theory. For a higher density of particles and/or larger inclusions, the lattice becomes progressively more disordered and the exponent smoothly decreases down to $alpha approx 0.3$. At high magnetic fields, all inclusions capture a vortex and the critical current decays faster than $B^{-1}$ as would be expected by theory. In the case of larger inclusions with a diameter of four coherence length, the magnetic-field dependence of the critical current is strongly affected by the ability of inclusions to capture multiple vortex lines. We found that at small densities, the fraction of inclusions trapping two vortex lines rapidly grows within narrow field range leading to a peak in $j_c(B)$-dependence within this range. With increasing inclusion density, this peak transforms into a plateau, which then smooths out. Using the insights gained from simulations, we determine the limits of applicability of strong-pinning theory and provide different routes to describe vortex pinning beyond those bounds.
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 superconductors 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-NbSe$_2$ 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.
Type-II superconductors owe their magnetic and transport properties to vortex pinning, the immobilization of flux quanta through material inhomogeneities or defects. Characterizing the potential energy landscape for vortices, the pinning landscape (or short, pinscape), is of great technological importance. Besides measurement of the critical current density $j_c$ and of creep rates $S$, the $ac$ magnetic response provides valuable information on the pinscape which is different from that obtained through $j_c$ or $S$, with the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ defining a characteristic quantity well accessible in an experiment. Here, we derive a microscopic expression for the Campbell penetration depth $lambda_{rm scriptscriptstyle C}$ using strong pinning theory. Our results explain the dependence of $lambda_{rm scriptscriptstyle C}$ on the state preparation of the vortex system and the appearance of hysteretic response. Analyzing different pinning models, metallic or insulating inclusions as well as $delta T_c$- and $delta ell$-pinning, we discuss the behavior of the Campbell length for different vortex state preparations within the phenomenological $H$-$T$ phase diagram and compare our results with recent experiments.
Using the time-dependent Ginzburg-Landau equation with the complex relaxation time and the Maxwell equation, we systematically examine transverse motion of vortex dynamics in the presence of pinning disorders. Consequently, in a plastic flow phase in which moving and pinned vortices coexist, we find that the Hall voltage generally changes its sign. The origin of the sign change is ascribed to a fact that moving vortices are strongly drifted by circular current of pinned vortices and the enforced transverse moving direction becomes opposite to that by transport current. This suggests that the Hall sign change is a behavior common in all disordered type-II superconductors.
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