Superconducting film with weak pinning centers: Incommensurate vortex lattices (original) (raw)
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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.
Journal of the Physical Society of Japan, 2015
As a function of applied field, we find a rich variety of ordered and partially-ordered vortex lattice configurations in systems with square or triangular arrays of pinning sites. We present formulas that predict the matching fields at which commensurate vortex configurations occur and the vortex lattice orientation with respect to the pinning lattice. Our results are in excellent agreement with recent imaging experiments on square pinning arrays [K. Harada et al., Science 274, 1167 (1996)].
Physical Review B, 2003
The effect of a periodic pinning array on the vortex state in a 2D superconductor at low temperatures is studied within the framework of the Ginzburg-Landau approach. It is shown that attractive interaction of vortex cores to a commensurate pin lattice stabilizes vortex solid phases with long range positional order against violent shear fluctuations. Exploiting a simple analytical method, based on the Landau orbitals description, we derive a rather detailed picture of the low temperatures vortex state phase diagram. It is predicted that for sufficiently clean samples application of an artificial periodic pinning array would enable one to directly detect the intrinsic shear stiffness anisotropy characterizing the ideal vortex lattice.
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).
Physical Review B, 2006
Using the non-linear Ginzburg-Landau (GL) theory, we obtain the possible vortex configurations in superconducting thin films containing a square lattice of antidots. The equilibrium structural phase diagram is constructed which gives the different ground-state vortex configurations as function of the size and periodicity of the antidots for a given effective GL parameter κ *. Giant-vortex states, combination of giant-and multi-vortex states, as well as symmetry imposed vortex-antivortex states are found to be the ground state for particular geometrical parameters of the sample. The antidot occupation number no is calculated as a function of related parameters and comparison with existing expressions for the saturation number ns and with experimental results is given. For a small radius of antidots a triangular vortex lattice is obtained, where some of the vortices are pinned by the antidots and some of them are located between them. Transition between the square pinned and triangular vortex lattices is given for different values of the applied field. The enhanced critical current at integer and rational matching fields is found, where the level of enhancement at given magnetic field directly depends on the vortex-occupation number of the antidots. For certain parameters of the antidot lattice and/or temperature the critical current is found to be larger for higher magnetic fields. Superconducting/normal H − T phase boundary exhibits different regimes as antidots are made larger, and we transit from a plain superconducting film to a thin-wire superconducting network. Presented results are in good agreement with available experiments and suggest possible new experiments.
Influence of artificial pinning on vortex lattice instability in superconducting films
New Journal of Physics, 2012
In superconducting films under an applied dc current, we analyze experimentally and theoretically the influence of engineered pinning on the vortex velocity at which the flux-flow dissipation undergoes an abrupt transition from low to high resistance. We argue, based on a nonuniform distribution of vortex velocity in the sample, that in strongly disordered systems the mean critical vortex velocity for flux-flow instability (i) has a nonmonotonic dependence on magnetic field and (ii) decreases as the pinning strength is increased. These findings challenge the generally accepted microscopic model of Larkin and Ovchinnikov (1979 J. Low. Temp. Phys. 34 409) and all subsequent refinements of this model which ignore the presence of pinning centers.
Pinning-Induced Formation of Vortex Clusters and Giant Vortices in Mesoscopic Superconducting Disks
Physical Review Letters, 2007
are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for the formation of GVs. Using Bitter decoration to visualise vortices in small Nb disks, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below T c and H c2 , in contrast to well-defined shells of individual vortices found in the absence of pinning. Mesoscopic superconductors, i.e., such that they can accommodate only a small number of vortices, are known to exhibit complex and unique vortex structures due to the competition between surface superconductivity and vortex-vortex interactions [see e.g. 1-6]. For mesoscopic disks, theoretical studies found two kinds of superconducting states: a giant vortex (GV), i.e., a circular symmetric state with a fixed value of angular momentum that can carry several flux quanta [1,2] and multivortex states (MVS) with an effective total angular momentum corresponding to the number of vortices in the disk (vorticity L) . Recently, it became possible to experimentally distinguish between a singlecore GV and a MVS composed of singly quantized vortices using the multiple-small-tunnel-junction
Vortex states in nanoscale superconducting squares: The influence of quantum confinement
Physical Review B, 2013
Bogoliubov-de Gennes theory is used to investigate the effect of the size of a superconducting square on the vortex states in the quantum confinement regime. When the superconducting coherence length is comparable to the Fermi wavelength, the shape resonances of the superconducting order parameter have strong influence on the vortex configuration. Several unconventional vortex states, including asymmetric ones, giant multi-vortex combinations, and states comprising giant antivortex, were found as ground states and their stability was found to be very sensitive on the value of kF ξ0, the size of the sample W , and the magnetic flux Φ. By increasing the temperature and/or enlarging the size of the sample, quantum confinement is suppressed and the conventional mesoscopic vortex states as predicted by the Ginzburg-Laudau (GL) theory are recovered. However, contrary to the GL results we found that the states containing symmetry-induced vortex-antivortex pairs are stable over the whole temperature range. It turns out that the inhomogeneous order parameter induced by quantum confinement favors vortex-antivortex molecules, as well as giant vortices with a rich structure in the vortex core-unattainable in the GL domain.
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.