Vortex structure and critical parameters in superconducting thin films with arrays of pinning centers (original) (raw)
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).
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