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.     

Flux vortices and transport currents in type II superconductors

This article is concerned with the mechanisms by which type II superconductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces. The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed. The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical defects. The theoretical models are compared critically with experimental measurements of pinning forces and other related phenomena, such as flux creep, low amplitude vortex oscillations and vortex lattice defect effects. Finally, the implications for technological materials are assessed.     

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.     

Flux vortices and transport currents in type II superconductors

This article is concerned with the mechanisms by which type II super-conductors can carry currents. The equilibrium properties of the vortex lattice are described and the generalized driving force in gradients of temperature and field is derived using irreversible thermodynamics. This leads to expressions for thermal cross effects which can include pinning forces.

The field distributions which occur in a range of situations are derived and a number of useful solutions of the critical state given. In particular, the distribution in a longitudinal field is obtained, and the conditions under which force-free configurations can break down by the cutting of vortices discussed.

The effects of lattice rigidity on the summation of pinning forces is considered and it is shown that a summation based on statistical arguments uses the same approximations and leads to the same results as a dissipation argument. Theoretical expressions are derived for the vortex pinning interaction to a number of different metallurgical defects. The theoretical models are compared critically with experimental measurements of pinning forces and other related phenomena, such as flux creep, low amplitude vortex oscillations and vortex lattice defect effects. Finally, the implications for technological materials are assessed.     

Symmetry locking and commensurate vortex domain formation in periodic pinning arrays

The spontaneous formation of domains of commensurate vortex patterns near rational fractional matching fields of a periodic pinning array has been investigated with high resolution scanning Hall probe microscopy. We show that domain formation is promoted due to the efficient incorporation of mismatched excess vortices and vacancies at the corners of domain walls, which outweighs the energetic cost of creating them. Molecular dynamics simulations with a generic pinning potential reveal that domains are formed only when vortex-vortex interactions are long range.     

第Ⅱ类超导体中磁通运动的低频电压噪声研究

用有限温度下的分子动力学方法模拟二维无序钉扎磁通系统的低频宽带电压噪声.计算了磁通运动的电压噪声谱密度，研究了宽带噪声（BBN）随驱动电流、钉扎强度和温度的变化规律.BBN随钉扎强度的增加而增大，反映了BBN是磁通运动受体钉扎阻碍而产生的内部耗散. BBN随温度的升高而减小，表明热运动部分抵消了体钉扎以及磁通之间相互作用，软化了磁通线格子，使磁通运动BBN减小.以上结论与实验相符，并能解释磁通运动的微观图像. 关键词： 第Ⅱ类超导体 电压噪声 动力学模拟     

Driving forces and polymer hydrodynamics in the Soret effect

A temperature gradient induces different driving forces on the components of a mixture which translates into their segregation. We show that these driving forces constitute the physical picture behind the thermodiffusion effect, and provide an alternative expression of the Soret coefficient which can be applied to both colloidal suspensions and molecular mixtures. To verify the validity of the formalism, we quantify the related forces in an Eulerian reference frame by non-equilibrium molecular simulations. Furthermore, we present an analytical argument to show that the hydrodynamic interactions need to be accounted for to obtain the proper scaling of the thermophoretic force. This result combined with the presented expression satisfactorily explains the experimentally known size dependence of the thermodiffusion coefficient in dilute polymer solutions.     

Temperature-dependent scaling of pinning force data in Bi-based high-Tc superconductors

The scaling of the normalized volume pinning forces, Fp/Fp,max, versus a reduced field h=Ha/Hscale has proven to be a very informative tool to study the origin of the flux pinning in superconductors. Remarkably, on Bi2Sr2Ca2Cu3O10+ (Bi-2223) and Bi2Sr2CaCu2O8+ (Bi-2212) data were mostly analyzed only in a narrow temperature range around 77 K. Here, we present a study of the pinning forces in various Bi-2223 samples at temperatures between 18 K and 80 K. The measurements clearly reveal that there is an apparent non-scaling of the pinning force data; instead, two clearly different temperature regimes for the scaling can be recognized, which are found to be in direct relation to a second step observed in the m(T) curves obtained upon field-cooling and -warming.     

Simulation of Dynamics in Two-Dimensional Vortex Systems in Random Media

Dynamics in two-dimensional vortex systems with random pinning centres is investigated using molecular dynamical simulations. The driving force and temperature dependences of vortex velocity are investigated. Below the critical depinning force Fc, a creep motion of vortex is found at low temperature. At forces slightly above Fc, a part of vortices flow in winding channels at zero temperature. In the vortex channel flow region, we observe the abnormal behaviour of vortex dynamics： the velocity is roughly independent of temperature or even decreases with temperature at low temperatures. A phase diagram that describes different dynamics of vortices is presented.     

Depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers

We study, by Langevin simulations, the depinning dynamics of two-dimensional magnetized colloids on a substrate with periodic pinning centers. When the number ratios of pinnings to colloids are 1:1 matching and at finite temperature, we find for the first time crossovers from plastic flow through elastic smectic flow to elastic crystal flow near the depinning with increasing the pinning strength. There exists a power-law scaling relationship between the average velocity of colloids and the external driving force for all the three types of flows. It is found that the critical driving force and the power-law scaling exponent as well as the average intensity of Bragg peaks are invariant basically in the region of elastic smectic flow. We also examine the temperature effect and it reveals that the above dynamic moving phases and their transitions could be attributed to the interplay between thermal fluctuation and pinning potential. At sufficiently low temperature, the thermal fluctuation could be neglected and the colloids near the depinning move in the elastic crystal flow no matter what the pinning strength. In addition, the number of pinning centers is changed and when it is close to the number of colloids, there appears a peak in the critical driving force and a dip in the power-law scaling exponent, respectively. The peak and dip are more pronounced for higher pinning strength.     

Vortex glass transition in a random pinning model

We study the vortex glass transition in disordered high temperature superconductors using Monte Carlo simulations. We use a random pinning model with strong point-correlated quenched disorder, a net applied magnetic field, long-range vortex interactions, and periodic boundary conditions. From a finite size scaling study of the helicity modulus, the rms current, and the resistivity, we obtain critical exponents at the phase transition. The new exponents differ substantially from those of the gauge glass model, but are close to those of the pure three-dimensional XY model.     

The volume pinning force for periodical interaction forces between defects and the flux line lattice

The volume pinning force for some forms of the interaction potential defect-flux line is calculated without restrictions on the vortex lattice distance and the interaction range of defects. It is shown that for larger maximum elementary interaction forces, the direct summation of pinning forces is realistic. However, if the interaction range of the defects is smaller than the vortex lattice distance, one obtains a region (about one order of magnitude) in which Labusch's quadratic dependence of the volume pinning force on the elementary interaction force is valid. In the region where the direct summation of pinning forces occur, the volume pinning force is proportional the vortex lattice distance and one obtains an additional magnetic field dependence of the volume pinning force.     

4He Luttinger liquid in nanopores

We study the low-temperature properties of a 4He fluid confined in nanopores, using large-scale quantum Monte Carlo simulations with realistic He-He and He-pore interactions. In the narrow-pore limit, the system can be described by the quantum hydrodynamic theory known as Luttinger liquid theory with a large Luttinger parameter, corresponding to the dominance of solid tendencies and strong susceptibility to pinning by a periodic or random potential from the pore walls. On the other hand, for wider pores, the central region appears to behave like a Luttinger liquid with a smaller Luttinger parameter, and may be protected from pinning by the wall potential, offering the possibility of experimental detection of a Luttinger liquid.     

Commensurability effects in the critical forces of a superconducting film with Kagomé pinning array at submatching fields

Using molecular dynamics simulations, we find the commensurability force peaks in a two-dimensional superconducting thin-film with a Kagomé pinning array. A transport force is applied in two mutually perpendicular directions, and the magnetic field is increased up to the first matching field. Usually the condition to have pronounced force peaks in systems with periodic pinning is associated to the rate between the applied magnetic field and the first matching field, it must be an integer or a rational fraction. Here, we show that another condition must be satisfied, the vortex ground state must be ordered. Our calculations show that the pinning size and strength may dramatically change the vortex ground state. Small pinning radius and high values of pinning strength may lead to disordered vortex configurations, which fade the critical force peaks. The critical forces show anisotropic behavior, but the same dependence on pinning strength and radius is observed for both driven force directions. Different to cases where the applied magnetic field is higher than the first matching field, here the depinning process begins with vortices weakly trapped on top of a pinning site and not with interstitial vortices. Our results are in good agreement with recent experimental results.     

The volume pinning force for different shapes of the interaction potential between defects and flux lines

The volume pinning force in superconductors with randomly distributed line defects nearly perpendicular to the flux lines is calculated for model as well as realistic interaction potentials between single defects and single flux lines. Both attractive and repulsive interactions defect — flux line were considered. The line defects were constructed from point defects distributed with constant density on straight lines. The deviations of the results from the theory of Labusch are considerable for small elementary interaction forces between defects and flux lines. The deviations (as well as the differences between repulsive and attractive interaction potentials) are larger for the realistic interaction potential than those for the different model potentials. The threshold values for the flux line distortion (under which no net volume pinning can exist) is also given.     

Origin of reversed vortex ratchet motion

We experimentally demonstrate that the origin of multiply reversed rectified vortex motion in an asymmetric pinning landscape not only is a consequence of the vortex-vortex interactions but also essentially depends on the ratio between the characteristic interaction distance and the period of the asymmetric pinning potential. We study four samples with different periods d of the asymmetric potential. For large d the dc voltage V(dc) recorded under a ac excitation indicates that the average vortex drift is from bigger to smaller dots for all explored positive fields. As d is reduced, a series of sign reversals in the dc response are observed as a function of field. We show that the number of sign reversals increases as d decreases. These findings are in agreement with recent computer simulations and illustrate the relevance of the different characteristic lengths for the vortex rectification effects.     

Research on flux-flow oscillators induced different types of pinning potentials

We have studied dynamics of Josephson vortices in strongly coupled long Josephson junctions stack, such as an intrinsic Josephson junction, by numerical simulations based on coupled sine–Gordon equations considering a periodic pinning potential. In this report, we investigate flux-flow oscillators induced two types of pinning potentials. One is magnetic periodic pinning potential, the other is periodic bias currents. Our results demonstrate that the periodic pinning potential can develop the generated power of flux-flow oscillator in certain condition.     

Modeling of irreversible switching and viscosity phenomena in perpendicular thin films

We have developed a simple numerical model for simulating domains as well as remanence and viscosity curves in the slow dynamics regime, for thin films characterized by perpendicular magnetization and irregular domain configurations due to strong disorder. The physical system is represented as constituted of identical switching units, described by proper switching field distributions and energy barrier laws for pinning and nucleation processes. The model also includes an effective field which accounts for magnetic forces proportional to magnetization, on average. Simulations of DCD curves show that when the reversal of magnetization is governed by pinning, the coercive field depends on the physical size of the film area on which the external field is applied. In the case of viscosity phenomena described by a linear energy barrier law associated with a single predominant reversal process (pinning or nucleation), universal viscosity curves can be generated by properly transforming the DCD curve of the system. We also demonstrate that a reduction of the maximum viscosity coefficient can coexist with a reduction of the energy barrier heights.     

Synchronizability on complex networks via pinning control

It is proved that the maximum eigenvalue sequence of the principal submatrices of coupling matrix is decreasing. The method of calculating the number of pinning nodes is given based on this theory. The findings reveal the relationship between the decreasing speed of maximum eigenvalue sequence of the principal submatrices for coupling matrix and the synchronizability on complex networks via pinning control. We discuss the synchronizability on some networks, such as scale-free networks and small-world networks. Numerical simulations show that different pinning strategies have different pinning synchronizability on the same complex network, and the consistence between the synchronizability with pinning control and one without pinning control in various complex networks.     

Vortex lattice mobility and effective pinning potentials in the peak effect region in YBCO crystals

The peak effect (PE) in the critical current density in both low and high temperature superconductors has been the subject of a large amount of experimental and theoretical work in the last few/several years. In the case of YBCO, crucial discussions describing a dynamic or a static picture are not settled. In that region of field and temperature the mobility of the vortex lattice (VL) is found to be dependent on the dynamical history. Recently we reported evidence that the VL reorganizes and accesses to robust VL configurations (VLCs) with different effective pinning potential wells arising in response to different system histories. One of the keys to understand the nature of the PE is to investigate the VL behavior in the vicinity of the various VLCs in the region of the PE. The stability of these VLCs was investigated and it was found that they have distinct characteristic relaxation times, which may be related to elastic or plastic creep processes. In this paper we review some of these results and propose a scenario to describe the PE in YBCO crystals.