Static and dynamic behaviours of multivortex states in a superconducting sample with mesoscopic pinning sites

This preliminary work has focused on the static transitions between the multivortex states interacting with square arrays of the mesoscopic pinning sites in superconducting samples. Our results were obtained from an extensive series of numerical simulations as functions of the magnetic field, pinning radius, and sample size. We have presented a wide range of multivortex configurations from commensurate dimer states to more concentric vortex shells at the matching fields. The stability of these states was also studied by means of the current-voltage V(I) curves which illustrate dynamic phase transitions as a function of applied driving force. These transitions manifested themselves as either a sudden jump in velocity or a nonlinear increase with velocity fluctuations in V(I) curves. We have investigated whether that the phase transitions between the pinned regime and the elastic flow regime are indicative of the stability of the initial vortex states. The variety of intermediate flow phases is attributed to large pinning size (reentrant behavior), strong commensurability and caging effects. In particular, three-shell vortex structures were obtained in the presence of larger pinning sites at adequate matching magnetic fields.     

Vortex configurations in regular arrays of pinning sites

The vortex states interacting with a triangular lattice of pinning sites in a two-dimensional (2D) superconducting sample have been investigated by using a molecular dynamics approach. The Nordborg–Vinokur potential is used to model the interaction between the vortices and the pinning sites. We have found several ordered vortex configurations, such as pentagons, hexagons, and shells depending on two critical parameters of the system, namely pinning radius and vorticity. Our results are in good agreement with the results of Bitter decoration experiments performed on type-II superconductors with blind hole and pillar arrays.     

Shifting and pinning of a magnetic vortex core in a permalloy dot by a magnetic field

Magnetic pinning in thin films seems to be a major research subject in the near future, as it is involved in all switching processes which include a movement of a domain wall or a magnetic vortex. We used Lorentz transmission electron microscopy and vortex pinning at artificial pinning sites to investigate the pinning behavior of magnetic vortices for the first time with high spatial resolution.     

Observation of vortex pinning in Bose-Einstein condensates

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.     

Ordered states and structural transitions in a system of Abrikosov vortices with periodic pinning

A system of Abrikosov vortices in a quasi-two-dimensional HTSC plate is considered for various periodic lattices of pinning centers. The magnetization and equilibrium configurations of the vortex density for various values of external magnetic field and temperature are calculated using the Monte Carlo method. It is found that the interaction of the vortex system with the periodic lattice of pinning centers leads to the formation of various ordered vortex states through which the vortex system passes upon an increase or a decrease in the magnetic field. It is shown that ordered vortex states, as well as magnetic field screening processes, are responsible for the emergence of clearly manifested peaks on the magnetization curves. Extended pinning centers and the effect of multiple trapping of vortices on the behavior of magnetization are considered. Melting and crystallization of the vortex system under the periodic pinning conditions are investigated. It is found that the vortex system can crystallize upon heating in the case of periodic pinning.     

Scanning tunneling microscopy study of pinning-induced vortex lattice distortion in ion-irradiated NbSe2

We observe vortex pinning in 2.2 GeV Au-ion irradiated NbSe₂ by scanning tunneling microscopy (STM) at 3K. The ion irradiation generates columnar defects which act as pinning sites. At various external magnetic fields the vortex arrangement is clearly resolved but shows strong distortion. The location of individual defects is extracted from STM data and compared to the vortex arrangement.     

Dynamics of a pinned magnetic vortex

We observe the dynamics of a single magnetic vortex pinned by a defect in a ferromagnetic film. At low excitation amplitudes, the vortex core gyrates about its equilibrium position with a frequency that is characteristic of a single pinning site. At high amplitudes, the frequency of gyration is determined by the magnetostatic energy of the entire vortex, which is confined in a micron-scale disk. We observe a sharp transition between these two amplitude regimes that is due to depinning of the vortex core from a local defect. The distribution of pinning sites is determined by mapping fluctuations in the frequency as the vortex core is displaced by a static in-plane magnetic field.     

Phase transitions of colloidal monolayers in periodic pinning arrays

We study the phase behavior of two-dimensional paramagnetic colloidal systems on square pinning arrays, the latter being created by a holographic optical tweezer technique. When the particle interaction strength is decreased, a transition from an incommensurate to a commensurate solid is observed. At even smaller pair potentials, the interstitial particles start to melt, whereas the particles at the substrate pinning sites are still localized. Our results are in good agreement with recent numerical studies on vortex melting in periodic pinning arrays.     

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.     

Rectified vortex motion in an Nb film with a spacing-graded array of holes

Superconducting Nb thin films with a spacing-graded array of holes were prepared by electron beam lithography. Two films with different hole gradients were fabricated. The ac-driven vortices were investigated in Nb superconductors with a spacing-graded array of holes. The measurements revealed pronounced rectified voltage when the vortex lattice is driven by an ac injected current. The rectified voltage is mainly caused by the strength of the vortex–vortex interaction. The rectified motion of a vortex is affected by the pinning potential of the spacing-graded array and the applied magnetic field. The vortex–vortex interaction strength changes the effective pinning landscape of the vortices and an asymmetric potential is formed. Vortices depin easily from high concentration to low concentration of pinning sites. In both samples, the ac-driven vortices exhibit a variety of dynamical responses and the rectified voltage is tunable with the applied magnetic field.     

从FeSe0.5Te0.5的V～I曲线论磁通动力学的诸模型（英文）

高温超导体的发现动摇了支配磁通动力学二十几年的Kim-Anderson模型.于是人们提出了新的涡旋玻璃态模型,集体钉扎模型和U～j对数关系模型来描述高温超导体的磁通动力学.其中,涡旋玻璃态模型已被人们广泛接受.Fe基超导体发现后,人们它行为十分类似于高温超导体.我们实验上仔细研究了FeSe0.5Te0.5单晶的V～I关系曲线,发现上述诸模型均不能很好的解释我们的实验结果,而张的反跳模型恰能很好的拟合实验结果.本文讨论了诸模型对高温超导体磁通动力学描述的适用性并给出合理的解释.     

Dynamical phase transition of a driven vortex lattice with disordered pinning

We have numerically solved the overdamped equation of vortex motion in a two-dimensional driven vortex lattice with disordered pinning, in which the driving Lorentz force, the pinning force due to point defects, the intervortex interacting force, and the thermal fluctuation force are taken into account. It is found that the vortex density and pinning strength are two important factors of affecting the melting transition of a vortex lattice. At low magnetic fields, there exist hysteresis loops of the average vortex velocity and the average pinning force vs. the driving force, from which the feature of a first-order melting transition of the vortex motion can be clearly seen. As the magnetic field is increased beyond a critical value, the hysteresis loops disappear and the melting transition is replaced by a second-order glass transition. We have also studied the influence of intervortex interactions on the vortex melting transition by comparing several forms of repulsive forces between the vortices.     

Equilibrium states of planar vortices in a three-dimensional josephson medium and meaning of the pinning-energy concept

Various ways of specifying the pinning-energy concept for planar vortices in a three-dimensional cellular Josephson medium are analyzed. It is shown that, for values of the pinning parameter I that are not small, a universal characteristic of vortex interaction with the lattice cannot be found, since the displacement of a vortex distorts its shape. At small values of I, the maximum pinning force can be chosen for such a characteristic. Two equilibrium states of a vortex are analyzed for stability. It is revealed that the state of higher energy is not inevitably unstable. A correct analysis of stability must be based on exploring a quadratic form that describes the energy of a current configuration. Such an investigation is performed for the equilibrium state of a vortex. At small values of the pinning parameter, the vortex state of higher energy is quasistable.     

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.     

Vortex pinning in thin superfluid films

We have formulated the theory of vortex pinning for thin film superfluids. The pinning site are closed regions where the superfluid density vanishes locally. Vortex pinning occurs due to vortex creation and annihilation at the boundaries of these regions and dominates pair processes in thicker films because of the cost of creating longer lengths of vortex line.     

Critical vortex line length near a zigzag of pinning centers

A vortex line passes through as many pinning centers as possible on its way from one extremety of the superconductor to the other at the expense of increasing its self-energy. In the framework of the Ginzburg-Landau theory we study the relative growth in length, with respect to the straight line, of a vortex near a zigzag of defects. The defects are insulating pinning spheres that form a three-dimensional cubic array embedded in the superconductor. We determine the depinning transition beyond which the vortex line no longer follows the critical zigzag path of defects.Received: 23 July 2004, Published online: 26 November 2004PACS: 74.80.-g Spatially inhomogeneous structures - 74.25.-q General properties; correlations between physical properties in normal and superconducting states - 74.20.De Phenomenological theories (two-fluid, Ginzburg-Landau, etc.)     

Effect of pinning and driving force on the metastability effects in weakly pinned superconductors and the determination of spinodal line pertaining to order—disorder transition

We explore the effect of varying drive on metastability features exhibited by the vortex matter in single crystals of 2H-NbSe₂ and CeRu₂ with varying degree of random pinning. The metastable nature of vortex matter is reflected in the path dependence of the critical current density, which in turn is probed in a contact-less way via AC-susceptibility measurements. The sinusoidal AC magnetic field applied during AC susceptibility measurements appears to generate a driving force on the vortex matter. In a nascent pinned single crystal of 2H-NbSe₂, where the peak effect (PE) pertaining to the order—disorder phenomenon is a sharp first-order-like transition, the supercooling feature below the peak temperature is easily wiped out by the reorganization caused by the AC driving force. In this paper, we elucidate the interplay between the drive and the pinning which can conspire to make the path-dependent AC-susceptibility response of different metastable vortex states appear identical. An optimal balance between the pinning and driving force is needed to view the metastability effects in typically weakly pinned specimen of low temperature superconductors. As one uses samples with larger pinning in order to differentiate the response of different metastable vortex states, one encounters a new phenomenon, viz., the second magnetization peak (SMP) anomaly prior to the PE. Supercooling/superheating can occur across both the PE and the SMP anomalies and both of these are known to display non-linear characteristics as well. Interplay between the path dependence in the critical current density and the non-linearity in the electromagnetic response determine the metastability effects seen in the first and the third harmonic response of the AC susceptibility across the temperature regions of the SMP and the PE. The limiting temperature above which metastability effects cease can be conveniently located in the third harmonic data, and the observed behavior can be rationalized within the Bean’s critical state model. A vortex phase diagram showing different vortex phases for a typically weakly pinned specimen has been constructed via the AC susceptibility data in a crystal of 2H-NbSe₂ which shows the SMP and the PE anomalies. The phase space of coexisting weaker and stronger pinned regions has been identified. It can be bifurcated into two parts, where the order and disorder dominate, respectively. The former part continuously connects to the reentrant disordered vortex phase pertaining to the small bundle pinning regime, where the vortices are far apart, interaction effects are weak and the polycrystalline form of flux line lattice prevails.     

Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.