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Register a new userStrong-pinning regimes by spherical inclusions in anisotropic type-II superconductors
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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.
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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.
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.
One of the most promising routes for achieving unprecedentedly high critical currents in superconductors is to incorporate dispersed, non-superconducting nanoparticles to control the dissipative motion of vortices. However, these inclusions reduce the overall superconducting volume and can strain the interlaying superconducting matrix, which can detrimentally reduce $T_c$. Consequently, an optimal balance must be achieved between the nanoparticle density $n_p$ and size $d$. Determining this balance requires garnering a better understanding of vortex-nanoparticle interactions, described by strong pinning theory. Here, we map the dependence of the critical current on nanoparticle size and density in (Y$_{0.77}$,Gd$_{0.23}$)Ba$_2$Cu$_3$O$_{7-delta}$ films in magnetic fields up to 35 T, and compare the trends to recent results from time-dependent Ginzburg-Landau simulations. We identify consistencies between the field-dependent critical current $J_c(B)$ and expectations from strong pinning theory. Specifically, we find that that $J_c propto B^{-alpha}$, where $alpha$ decreases from $0.66$ to $0.2$ with increasing density of nanoparticles and increases roughly linearly with nanoparticle size $d/xi$ (normalized to the coherence length). At high fields, the critical current decays faster ($sim B^{-1}$), suggestive that each nanoparticle has captured a vortex. When nanoparticles capture more than one vortex, a small, high-field peak is expected in $J_c(B)$. Due to a spread in defect sizes, this novel peak effect remains unresolved here. Lastly, we reveal that the dependence of the vortex creep rate $S$ on nanoparticle size and density roughly mirrors that of $alpha$, and compare our results to low-$T$ nonlinearities in $S(T)$ that are predicted by strong pinning theory.
In a class of type II superconductor films, the critical current is determined by the Bean-Livingston barrier posed by the film surfaces to vortex penetration into the sample. A bulk property thus depends sensitively on the surface or interface to an adjacent material. We theoretically investigate the dependence of vortex barrier and critical current in such films on the Rashba spin-orbit coupling at their interfaces with adjacent materials. Considering an interface with a magnetic insulator, we find the spontaneous supercurrent resulting from the Zeeman field and interfacial spin-orbit coupling to substantially modify the vortex surface barrier. Thus, we show that the critical currents in superconductor-magnet heterostructures can be controlled, and even enhanced, via the interfacial spin-orbit coupling. Since the latter can be controlled via a gate voltage, our analysis predicts a class of heterostructures amenable to gate-voltage modulation of superconducting critical currents. It also sheds light on the recently observed gate-voltage enhancement of critical current in NbN superconducting films.
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.
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