Vortex-rectification effects in films with periodic asymmetric pinning

We study the transport of vortices excited by an ac current in an Al film with an array of nanoengineered asymmetric antidots. The vortex response to the ac current is investigated by detailed measurements of the voltage output as a function of ac current amplitude, magnetic field, and temperature. The measurements revealed pronounced voltage rectification effects which are mainly characterized by the two critical depinning forces of the asymmetric potential. The shape of the net dc voltage as a function of the excitation amplitude indicates that our vortex ratchet behaves in a way very different from standard overdamped models. Rather, the repinning force, necessary to stop vortex motion, is considerably smaller than the depinning force, resembling the behavior of the so-called inertia ratchets. Calculations based on an underdamped ratchet model provide a very good fit to the experimental data.     

Polaron-like vortices, dissociation transition, and self-induced pinning in magnetic superconductors

Vortices in magnetic superconductors polarize spins nonuniformly and repolarize them when moving. At a low spin relaxation rate and at low bias currents, vortices carrying magnetic polarization clouds become polaron-like and their velocities are determined by the effective drag coefficient that is significantly bigger than the Bardeen-Stephen (BS) one. As the current increases, vortices release polarization clouds and the velocity as well as the voltage in the I–V characteristics jump to values corresponding to the BS drag coefficient at a critical current J _c . The nonuniform components of the magnetic field and magnetization drop as the velocity increases, resulting in weaker polarization and a discontinuous dynamic dissociation depinning transition. Experimentally, the jump shows up as a depinning transition and the corresponding current at the jump is the depinning current. As the current decreases, on the way back, vortices are retrapped by polarization clouds at the current J _r < J _c . As a result, the polaronic effect suppresses dissipation and enhances the critical current. Borocarbides (RE)Ni₂B₂C with a short penetration length and highly polarizable rare earth spins seem to be optimal systems for a detailed study of vortex polaron formation by measuring I–V characteristics. We also propose to use a superconductor-magnet multilayer structure to study polaronic mechanism of pinning with the goal to achieve high critical currents. The magnetic layers should have large magnetic susceptibility to enhance the coupling between vortices and magnetization in magnetic layers while the relaxation of the magnetization should be slow. For Nb and a proper magnet multilayer structure, we estimate the critical current density J _c ～ 10⁹ A/m² at the magnetic field B ≈ 1 T.     

无序超导体磁通运动的两次退钉扎效应和重新进入超导相

考虑平面内和不同平面磁通之间的相互作用力，计算了无序各向异性超导体中磁通运动的平均速度、微分电阻随驱动力F_l的变化规律，用层间关联函数C_z的值来判断2D塑性流动和3D关联流动的运动图像.观察到随着外驱动力的增大微分电阻出现两个尖峰，它对应着磁通运动存在两次退钉扎现象.在一定层间耦合条件下，在微分电阻双峰之间，可观察到重新进入微分电阻为零的钉扎相.这与最近实验上新发现的无序弱钉扎超导体有重新进入超导相的巨大峰值效应相吻合.同时，也可发现随着驱动电流的增大，磁通运动出现由2D塑性流动到3D弹性流动的相变，这一维度的变化对应着微分电阻dV/dI曲线中的二次峰位置. 并证明当层间耦合(即代表磁场的大小)在一定范围时，3D-2D相变对应的临界电流随磁场的增大而增大, 反映了第二磁化峰附近的磁通格子软硬度改变的微观图像. 关键词： 第Ⅱ类超导体 磁通线格子 钉扎 峰值效应     

Critical dynamics associated with dynamic disordering near the depinning transition in different vortex phases

We study a depinning transition based on transient dynamics of vortices driven by a suddenly applied dc current, focusing on whether a difference in the equilibrium vortex phase that can lead to a different vortex flow will change the critical behavior. After preparing an ordered initial vortex configuration, we measure the time evolution of voltage associated with dynamic disordering in three magnetic fields, corresponding to the ordered phase (OP), disordered phase (DP), and coexistence phase. The critical behavior of the depinning transition is commonly observed in these phases, pointing to the universality of the transition. However, the critical behavior is most marked in the coexistence phase, while the suppression of the critical region and that of dynamic disordering are observed in OP and DP, respectively, whose origin is attributed to the different flow states among these phases.     

Metastability and uniqueness of vortex states at depinning

We present results from numerical simulations of the transport of vortices in the zero-field-cooled (ZFC) and the field-cooled (FC) state of a type-II superconductor. In the absence of an applied current I, we find that the FC state has a lower defect density than the ZFC state, and is stable against thermal cycling. On the other hand, by cycling I, surprisingly, we find that the ZFC state is the stable state. The FC state is metastable as manifested by increasing I to the depinning current I(c), in which case the FC state evolves into the ZFC state. We also find that all configurations acquire a unique defect density at the depinning transition independent of the history of the initial states.     

Dynamic critical phenomena in two-dimensional fully frustrated Coulomb gas model with disorder

The dynamic critical phenomena near depinning transition in two-dimensional fully frustrated square lattice Coulomb gas model with disorders was studied using Monte Carlo technique. The ground state of the model system with disorder σ=0.3 is a disordered state. The dependence of charge current density J on electric field E was investigated at low temperatures. The nonlinear J-E behavior near critical depinning field can be described by a scaling function proposed for three-dimensional flux line system [M.B. Luo, X. Hu, Phys. Rev. Lett. 98 (2007) 267002]. We evaluated critical exponents and found an Arrhenius creep motion for field region Ec/2<E<Ec. The scaling law of the depinning transition is also obtained from the scaling function.     

Vortex motion in superconducting ladders

We study vortex motion in superconducting ladders. Since the single-vortex excitation energy is finite in this system, even in the absence of an external magnetic field there may exist excess vortices that are stabilized by external currents. The motion of the excess vortices induces localized voltage drops, given by a nonlinear power law, at currents less than the critical current of the junctions. The localized voltage drop moves with constant velocity and its amplitude is proportional to the velocity. Above the critical current of the junctions there is continuous creation and annihilation of vortex-antivortex pairs.     

Absence of correlated flux pinning by columnar defects in irradiated epitaxial Bi2Sr2CaCu2O8 thin films

Using heavy-ion irradiation, we produced columnar defects of different density and orientation in epitaxial Bi₂Sr₂CaCu₂O₈ thin films. Although this increases the normal state resistivity and the critical temperature is reduced proportionally to the volume fraction of damaged material, pinning-related quantities like critical current density, activation energy and depinning field are enhanced in external magnetic fields. Transport measurements in dependence of the magnetic field and its orientation consistently indicate two-dimensional pinning of pancake vortices at the columnar defects. We observe the absence of correlated flux pinning by columnar defects and compare to heavy-ion-irradiated single crystals and tapes, where line-like correlations have been observed.     

Critical currents in quasiperiodic pinning arrays: chains and Penrose lattices

We study the critical depinning current Jc versus the applied magnetic flux Phi, for quasiperiodic (QP) chains and 2D arrays of pinning centers placed on the nodes of a fivefold Penrose lattice. In QP chains, the peaks in Jc(Phi) are determined by a sequence of harmonics of the long and short segments of the chain. The critical current Jc(Phi) has a remarkable self-similarity. In 2D QP pinning arrays, we predict analytically and numerically the main features of Jc(Phi), and demonstrate that the Penrose lattice of pinning sites provides an enormous enhancement of Jc(Phi), even compared to triangular and random pinning site arrays. This huge increase in Jc(Phi) could be useful for applications.     

Peak Effect and the Phase Diagram of Moving Vortices in FexNi1-xZr2 Superconducting Glasses

In the mixed state of type II superconductors, vortices penetrate the sample and form a correlated system due to the screening of supercurrents around them. Interestingly, we can study this correlated system as a function of density and driving force. The density, for instance, is controlled by the magnetic field B, whereas a current density j acts as a driving force F=j x B on all vortices. To minimize the pinning strength, we study a superconducting glass in which the depinning current is 10 to 1000 times smaller than in previous studies, which enables us to map out the complete phase diagram in this new regime. The diagram is obtained as a function of B, driving current, and temperature, and leads to a remarkable set of new results, which includes a huge peak effect, an additional reentrant depinning phase, and a driving force induced pinning phase.     

AC response of vortices subjected to pinning by columnar defects in Tl2Ba2CaCu2O8 epitaxial films

A micro-Hall-probe-based ac susceptometer is used to study the dynamics of vortices in Tl₂Ba₂CaCu₂O₈ (Tl-2212) epitaxial films with and without correlated disorder in a low field (<6 kG) and high temperature (T>60 K) regime. The Bean critical state model for a thin superconducting disc in perpendicular magnetic field is used to extract the critical current density of the films. The temperature and frequency dependence of the irreversibility field (B_irr) is compared for samples with and without the linear defects. The B_irr(T) curve shows a distinct discontinuity at B≈B_φ. The frequency dependence of the screening current density J(ω), extracted from the inphase component (T^′_H) of the fundamental transmittivity, has been analyzed in the framework of Bose glass dynamics. This analysis shows that the vortex depinning temperature is ≈24 K for this Tl-2212 film and the depinning process starts via excitations of half-loops. The angle dependent studies of the susceptibility further suggest that these half-loops consist of many pancake vortices.     

Dependence of current and field driven depinning of domain walls on their structure and chirality in permalloy nanowires

A magnetic domain wall (DW) injected and pinned at a notch in a permalloy nanowire is shown to exhibit four well-defined magnetic states, vortex and transverse, each with two chiralities. These states, imaged using magnetic force microscopy, are readily detected from their different resistance values arising from the anisotropic magnetoresistance effect. Whereas distinct depinning fields and critical depinning currents in the presence of magnetic fields are found, the critical depinning currents are surprisingly similar for all four DW states in low magnetic fields. We observe current-induced transformations between these DW states below the critical depinning current which may account for the similar depinning currents.     

Dynamics of two-dimensional vortex system in a strong square pinning array at the second matching field

We study the dynamics of a two-dimensional vortex system in a strong square pinning array at the second matching field. Two kinds of depinning behaviors, a continuous depinning transition at weak pinning and a discontinuous one at strong pinning, are found. We show that the two different kinds of vortex depinning transitions can be identified in transport as a function of the pinning strength and temperature. Moreover, interstitial vortex state can be probed from the transport properties of vortices.     

Delocalization in two-dimensional disordered Bose systems and depinning transition in the vortex state in superconductors

We investigate a two-dimensional (2D) Bose system with the long range interactions in the presence of disorder. Formation of the bound states at strong impurity sites gives rise to a depletion of the superfluid density. We predict the intermediate superfluid state where the condensate and localized bosons are present simultaneously. We find that interactions suppress localization and that with the increase of the boson density the system experiences a sharp delocalization crossover into a state where all bosons are delocalized. We map our results onto a 3D system of vortices in type II superconductors in the presence of columnar defects; the intermediate superfluid state maps to an intermediate vortex liquid where vortex liquid neighbors pinned vortices. We predict the depinning crossover within the vortex liquid and depinning induced vortex lattice-Bose glass melting.     

Dynamics of vortices in type-II superconductors with periodic square columnar pins

The dynamics of a two-dimensional vortex system with strong periodic square columnar pins is investigated. For the case vortex number matching pinning number, we find that the vortex liquid is frozen into square lattice via a continuous transition, and the freezing (melting) temperature T_m is the same as the thermal depinning temperature of vortices, which are different from the first-order phase transition at weak pinning. The zero-temperature critical depinning force F_c0 is exactly the same as the maximum pinning force, and the depinning property at T = 0 can be expressed by scaling v ～ (F ? F_c0)^β with the exponent β close to 0.5. The v–F curves at temperatures below T_m show that vortices are pinned at small driving force.     

Collective Cooper-pair transport in the insulating state of Josephson-junction arrays

We investigate collective Cooper-pair transport of one- and two-dimensional Josephson-junction arrays. We derive an analytical expression for the current-voltage characteristic revealing thermally activated conductivity at small voltages and threshold voltage depinning. The activation energy and the related depinning voltage represent a dynamic Coulomb barrier for collective charge transfer over the whole system and scale with the system size. We show that both quantities are nonmonotonic functions of the magnetic field. We propose that formation of the dynamic Coulomb barrier and its size scaling are consequences of the mutual Josephson phase synchronization across the system. We apply the results for interpretation of experimental data in disordered films near the superconductor-insulator transition.     

Why an ac magnetic field shifts the irreversibility line in type-II superconductors

We show that for a thin superconducting strip placed in a transverse dc magnetic field--the typical geometry of experiments with high-T(c) superconductors--the application of a weak ac magnetic field perpendicular to the dc field generates a dc voltage in the strip. This voltage leads to the decay of the critical currents circulating in the strip, and eventually the equilibrium state of the superconductor is established. This relaxation is not due to thermally activated flux creep but to the "walking" motion of vortices in the two-dimensional critical state of the strip with in-plane ac field. Our theory explains the shaking effect that was used for detecting phase transitions of the vortex lattice in superconductors.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

Resistive state of superconducting structures with fractal clusters of a normal phase

The effect of morphologic factors on magnetic flux trapping and critical currents in a superconducting structure, which presents a type II percolation superconductor with pinning centers, is considered. The role of pinning centers is played by fractal clusters of the normal phase. The properties of these clusters are analyzed in detail: their statistics is studied, the distribution of critical currents of depinning is found, and the depen-dences of the main statistical parameters on the fractal dimension are obtained. The effect of fractal clusters of the normal phase on the electric field caused by the motion of the magnetic flux after the vortices have been broken away from pinning centers is considered. The current-voltage characteristics of superconducting structures in a resistive state are obtained for an arbitrary fractal dimension. It is found that the fractality of the boundaries of normal-phase clusters forces magnetic flux trapping, thereby increasing the critical current.     

Current-induced voltage oscillations in superconducting Y<Subscript>1</Subscript>Ba<Subscript>2</Subscript>Cu<Subscript>3</Subscript>O<Subscript>7-δ</Subscript>

We investigated influence of bidirectional square wave current with long periods and dc current on the evolution of the voltage-time (V - t) curves in superconducting polycrystalline bulk Y₁Ba₂Cu₃O_7-δ (YBCO) material at the temperatures near the critical temperature. In a well-defined range of amplitudes and periods of driving current, and temperatures, novel type of non-linear dynamic responses was observed by means of the V-t curves. It was seen that such a non-linear response to bidirectional square wave current sometimes reflects itself as regular sinusoidal-like voltage oscillations. The sinusoidal-like and non-sinusoidal oscillations were discussed mainly in terms of the dynamic competition between pinning and depinning and significant relaxation effects which appear in this competing process. The density fluctuations associated with the current induced self-magnetic flux (SMF) lines and semi-elastic coupling of SMF lines with the pinning centers were also considered as possible physical mechanisms in the interpretation of the experimental results.