Vortex configurations and critical parameters in superconducting thin films containing antidot arrays: Nonlinear Ginzburg-Landau theory (original) (raw)
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Superconducting films with antidot arrays—Novel behavior of the critical current
Europhysics Letters (EPL), 2006
Novel behavior of the critical current density jc of a regularly perforated superconducting film is found, as a function of applied magnetic field H. Previously pronounced peaks of jc at matching fields were always found to decrease with increasing H. Here we found a reversal of this behavior for particular geometrical parameters of the antidot lattice and/or temperature. This new phenomenon is due to a strong "caging" of interstitial vortices between the pinned ones. We show that this vortex-vortex interaction can be further tailored by an appropriate choice of the superconducting material, described by the Ginzburg-Landau parameter κ. In effective type-I samples we predict that the peaks in jc(H) at the matching fields are transformed into a step-like behavior.
2007
Isolated vortex line 1.5.3 Interaction between vortex lines 1.5.4 Vortex lattices 1.6 Flux pinning 1.6.1 Pinning mechanism 1.6.2 Artificial pinning centers 1.7 Thin superconducting films 1.8 Mesoscopic superconductors 1.9 Details of the numerical approach ii Contents Surface barrier for flux penetration and expulsion in thin mesoscopic superconductors 37 2.1 Introduction 2.2 Theoretical formalism 2.2.1 Ginzburg-Landau theory 2.2.2 London approach and phase of the order parameter 2.3 Superconducting disk 2.3.1 A single vortex: estimation of the H c1 2.3.2 Comparison with London theory 2.3.3 The L = 2 state in the disk 2.3.4 Temperature dependence of the energy barrier 2.4 Superconducting ring 2.5 Superconducting square 2.6 Conclusions 3 A superconducting square with antidots 57 3.1 Introduction 3.2 Theoretical formalism 3.3 Free energy and magnetization 3.4 Stability of different vortex states 3.5 Superconducting/Normal phase transition 3.6 Conclusions 4 Superconducting thin films with an antidot lattice 71 4.1 Introduction 4.2 Theoretical formalism 4.3 Vortex structure in perforated superconducting films 4.3.1 Equilibrium vortex configurations 4.3.2 Influence of temperature on the stability of the vortex-antivortex pairs 4.3.3 The hole occupation number n o 4.4 Vortex structure in effective type-I superconducting film with an antidot array 4.5 Weak pining centers: stability of pinned square and partially pinned vortex structures 4.6 The critical current of patterned superconducting films 4.6.1 Influence of the geometrical parameters 4.6.2 Temperature dependence of the critical current Contents iii 4.7 H − T phase diagram 97 4.8 Conclusions 99 5 Vortex-cavity interaction Summary 153 List of important realizations 157 Outlook 159 iv Contents Samenvatting 161 References 167 Curriculum Vitae 179 List of publications 181 1950s the materials that were developed for use as superconductors include: solid solutions of NbN and NbC with T c = 17.8 K; V 3 Si with T c = 17 K; Nb 3 Sn with T c =18 K; NbTi with T c =9 K. Later (1973) Nb 3 Ge was added to this list with the highest T c of all, at 23.2 K, a record that lasted until 1986. The history of the development of T c is shown in Fig. 1.1 [4]. MgB 2 superconductor. Superconductivity in MgB 2 was discovered as late as 2001 [5], with T c at 39 K, a record by far in ordinary metallic compounds. This value of T c is close to what has been considered the maximum possible by pairing caused by electron-phonon interaction. The main disadvantage of early MgB 2 samples is their low critical magnetic field H c2. But H c2 can be increased up to more than 40 T in bulk and up to near 60 T in oriented thin films by Carbon doping. Due to its enhanced mechanical properties, as compared to high-T c superconductors this material is expected to be very promising for applications. Organic superconductors. Superconductivity in a polymer material was first found in (Sn) x in 1975. This was followed by the discovery in 1979 of superconductivity in a molecular salt, (TMTSF) 2 FF 6 under 1.2 Gpa pressure, and with a T c of 0.9 K [6]. Since then, a long list of organic superconductors have been synthesized. T c of those materials remains low, although it has which leads to a temperature dependence of the GL parameter κ = κ(0)/(1+t 2) with t = T /T c0 and κ(0) = λ(0)/ξ(0), agrees better with experiment. 4πλ 2 c ∇ × j + h = zΦ 0 δ(r), (1.31) where z is a unit vector along the vortex and δ(r) a δ-function at the location of the core. Combining Eq. (1.31) with the Maxwell equation ∇ × h = 4π/cj The next configuration very close in energy consists of a square array of vortices (see Fig. 1.8). Here the nearest neighbor distance is given by a = (Φ 0 /H) 1/2. (1.41) Thus, for a given flux density in a homogeneous superconductor, a > a. Taking into account the repulsion of the vortices, it is reasonable that the vortex Consequently, the better the pinning the higher the critical current density J c. The upper limit for the critical current density is the depairing current density H c2 (T) = H c2 (0) |1 − T /T c0 | , (1.54) where H c2 (0) = c /2eξ(0) 2 and T c0 is the critical temperature at zero magnetic field. y +(1 − T) |Ψ j | 2 − 1 Ψ j +f j (t).
Vortex-Antivortex Lattices in Superconducting Films with Magnetic Pinning Arrays
Journal of Low Temperature Physics, 2005
Novel vortex structures are found when a thin superconducting film (SC) is covered with a lattice of out-of-plane magnetized magnetic dots (MDs). The stray magnetic field of the dots confines the vortices to the MD regions, surrounded by antivortices which "crystallize" into regular lattices. First and second order transitions are found as magnetic array is made sparser or MD-magnetization larger. For sparse MD-arrays fractional vortex-antivortex states are formed, where the crystalsymmetry is combined with a non-uniform "charge" distribution. We demonstrate that due to the (anti)vortices and the supercurrents induced by the MDs, the critical current of the sample actually increases if exposed to a homogeneous external magnetic field, contrary to conventional SC behavior. PACS numbers: 74.78.-w, 74.25.Op, 74.25.Qt, 74.25.Dw.
Superconducting film with weak pinning centers: Incommensurate vortex lattices
Physical Review B, 2007
Vortex configurations in a superconducting film with a square array of small antidots are studied within the Ginzburg-Landau ͑GL͒ theory. We find that in addition to the conventional vortex structures at the matching fields, a variety of vortex states can be stabilized by decreasing the pinning strength of the antidots, including ͑i͒ the triangular vortex lattice where some vortices are pinned by the antidots and others are located between them, ͑ii͒ vortex line structures, and ͑iii͒ a lattice of vortex cluster structures around the empty pinning centers. Although these partially pinned vortex structures are obtained more frequently in field cooled experiments than the square pinned vortex lattice, they are not the lowest energy states, i.e., the ground state, contrary to the results from a London approach. This result can be understood as due to the presence of a broad local minimum in the GL free energy which keeps the vortices away from the pinning centers. Our results can also be related to recent experiments on macroscopic metallic particles that move in a plane in the presence of a weak electrostatic pinning potential.
Novel Commensurability Effects in Superconducting Films with Antidot Arrays
Physical Review Letters, 2006
Vortex configurations in superconducting films with regular arrays of antidots (holes) are calculated within the nonlinear Ginzburg-Landau theory. In addition to the well-established matching phenomena, we predict (i) the nucleation of giant-vortex states between the antidots, (ii) the combination of giant-and multivortices at rational matching fields, and (iii) for particular values of the vorticity, symmetry imposed creation of vortex-antivortex configurations.
Vortex configurations in high-{Tc} superconducting films
1992
This article addresses the Ginzburg-Landau (GL) model for high-temperature superconductivity in thin lms (two-dimensional periodic domains). A new gauge is de ned to reduce the coupling between the equations for the nonzero components of the vector potential. The GL equations are written in a novel form by means of continuous link variables; this form is symmetric and has particular advantages for numerical analysis. The continuous GL model is approximated by a discrete model, which is shown to be second-order accurate. Two methods are used for the numerical solution of the discrete model|a modi ed Newton's method, in combination with a sweeping algorithm for the solution of the linear system, and a time-like integration method based on gradient ow. Numerical experiments demonstrate that the discrete GL model leads to asymmetric solutions in the plane; symmetry is recovered only in the limit as the mesh size goes to zero. The results of computational experiments to nd the upper critical eld and establish an empirical power law for vortex interactions are given. AMS(MOS) subject classi cation. Primary 81J05. Secondary 82A25, 65N05, 35J60.
On Ginzburg–Landau Vortices of Superconducting Thin Films
Acta Mathematica Sinica, English Series, 2006
In this paper, we discuss the vortex structure of the superconducting thin films placed in a magnetic field. We show that the global minimizer of the functional modelling the superconducting thin films has a bounded number of vortices when the applied magnetic field h ex < H c 1 + K log | log ε| where H c 1 is the lower critical field of the film obtained by Ding and Du in SIAM J. Math. Anal., 2002. The locations of the vortices are also given.
Multi-vortex versus interstitial vortices scenario in superconducting antidot arrays
Physica C: Superconductivity, 2010
In superconducting thin films, engineered lattice of antidots (holes) act as an array of columnar pinning sites for the vortices and thus lead to vortex matching phenomena at commensurate fields guided by the lattice spacing. The strength and nature of vortex pinning is determined by the geometrical characteristics of the antidot lattice (such as the lattice spacing a 0 , antidot diameter d, lattice symmetry, orientation, etc) along with the characteristic length scales of the superconducting thin films, viz., the coherence length (ξ) and the penetration depth (λ). There are at least two competing scenarios: (i) multiple vortices sit on each of the antidots at a higher matching period, and, (ii) there is nucleation of vortices at the interstitial sites at higher matching periods. Furthermore it is also possible for the nucleated interstitial vortices to reorder under suitable conditions. We present our experimental results on NbN antidot arrays in the light of the above scenarios.
Superconductor …, 2005
Measurements of the critical current density dependence on the direction of the external magnetic field vector H have been performed on Nb/CuMn multilayers with and without a regular square lattice of submicrometre antidots. (i) At small angles between H and the surface of the sample, the presence of the antidot array strongly influences the topology of the flux lines. In the multilayers without the antidot array the vortex topology is mainly due to the anisotropy of the system with the formation of kinked vortices in the samples with higher values of the anisotropy parameter. In antidotted samples, the presence of kinked vortices is not related to the anisotropy of the system but to the geometry of the antidot array. (ii) At large angles between H and the surface of the sample, the dimensions of the antidots determine the pinning mechanism, with the prevalence of edge pinning when the antidot diameter is larger than the magnetic penetration depth λ and the presence of electromagnetic pinning when the diameter is comparable to λ. A phenomenological expression for the angular dependence of the pinning force at intermediate and large angles is proposed, satisfactorily describing the experimental data.
Vortex dynamics in superconductors with an array of triangular blind antidots
2003
We report on numerical studies of the DC vortex transport properties, including V (I) curves and vortex trajectories, in triangular pinning arrays of triangular blind antidots. The asymmetric geometry of the pinning sites produces a significant influence on the vortex motion depending on the direction of the applied Lorentz force FL.