Geometrical barriers and the growth of flux domes in thin ideal superconducting disks
John R. Clem
备注：
10 pages, 3 figures, 4 appendices, submitted to the Journal of Superconductivity and Novel Magnetism for an issue commemorating John Bardeen's 100th birthday
发表信息：
Journal of Superconductivity and Novel Magnetism 21, 343-352 (2008)
When an ideal (no bulk pinning) flat type-II superconducting disk is subjected to a perpendicular magnetic field H_a, the first vortex nucleates at the rim when H_a = H_0, the threshold field, and moves quickly to the center of the disk. As H_a increases above H_0, additional vortices join the others, and together they produce a domelike field distribution of radius b. In this paper I present analytic solutions for the resulting magnetic-field and sheet-current-density distributions. I show how these distributions vary as b increases with H_a, and I calculate the corresponding field-increasing magnetization.
Differential magneto-optics are used to study the effect of dc in-plane magnetic field on hysteretic behavior due to geometrical barriers in $Bi_2Sr_2CaCu_2O_{8+δ}$ crystals. In absence of in-plane field a vortex dome is visualized in the sample center surrounded by barrier-dominated flux-free regions. With in-plane field, stacks of Josephson vortices form vortex chains which are surprisingly found to protrude out of the dome into the vortex-free regions. The chains are imaged to extend up to the sample edges, thus providing easy channels for vortex entry and for drain of the dome through geom…
Recent theoretical and experimental research on low-bulk-pinning superconducting strips has revealed striking dome-like magnetic-field distributions due to geometrical edge barriers. The observed magnetic-flux profiles differ strongly from those in strips in which bulk pinning is dominant. In this paper we theoretically describe the current and field distributions of a superconducting strip under the combined influence of both a geometrical edge barrier and bulk pinning at the strip's critical current Ic, where a longitudinal voltage first appears. We calculate Ic and find its dependence upon …
We theoretically investigate the magnetic-field and current distributions for coplanar superconducting strips with slits in an applied magnetic field H_a. We consider ideal strips with no bulk pinning and calculate the hysteretic behavior of the magnetic moment m_y as a function of H_a due solely to geometrical edge barriers. We find that the m_y-H_a curves are strongly affected by the slits. In an ascending field, the m_y-H_a curves exhibit kink or peak structures, because the slits prevent penetration of magnetic flux. In a descending field, m_y becomes positive, because magnetic flux is tra…
Domelike magnetic-flux-density distributions previously have been observed experimentally and analyzed theoretically in superconducting films with edges, such as in strips and thin plates. Such flux domes have been explained as arising from a combination of strong geometric barriers and weak bulk pinning. In this paper we predict that, even in films with bulk pinning, flux domes also occur when vortices and antivortices are produced far from the film edges underneath current-carrying wires, coils, or permanent magnets placed above the film. Vortex-antivortex pairs penetrating through the film …
Dependence of the critical current $I_c$ on the applied magnetic field $H_a$ is theoretically studied for a thin superconducting strip of a rectangular cross section, taking an interplay between the Bean-Livingston and the geometric barriers in the sample into account. It is assumed that bulk vortex pinning is negligible, and the London penetration depth $λ$ is essentially less than the thickness $d$ of the strip. To investigate the effect of these barriers on $I_c$ rigorously, a two-dimensional distribution of the current over the cross section of the sample is derived, using the approach bas…
Superconducting dome due to the Fano-Feshbach shape resonance in artificial high-Tc superlattices
Institute of Crystallography, National Research Council, CNR（意大利国家研究委员会晶体学研究所）；Rome International Center for Materials Science Superstripes RICMASS（罗马国际材料科学超条纹研究中心 RICMASS）；Department of Industrial, Electronic and Mechanical Engineering, Roma Tre University（罗马第三大学工业、电子和机械工程系）；Istituto Nazionale di Fisica Nucleare INFN, Sezione Roma Tre（意大利国家核物理研究所罗马三分部）；National High Magnetic Field Laboratory (NHMFL), Los Alamos National Laboratory (LANL)（洛斯阿拉莫斯国家实验室国家高磁场实验室）；Laboratoire National des Champs Magnétiques Intenses（强磁场国家实验室）；Department of Physics and Astronomy, Baylor University（贝勒大学物理与天文系）；CQM group, School of Pharmacy, Physics Unit, University of Camerino（卡梅里诺大学药学院物理学单元量子物质小组）；Department of Physics, Sapienza University（罗马第一大学物理系）；Max Planck Institute for Solid State Research（马克斯·普朗克固体研究所）
The magnetization behavior of mesoscopic superconducting disks can show hysteretic behavior which we explain by using the Ginzburg-Landau (GL) theory and properly taking into account the de-magnetization effects due to geometrical form factors. In large disks the Bean-Livingston surface barrier is responsible for the hysteresis. While in small disks a volume barrier is responsible for this hysteresis. It is shown that although the sample magnetization is diamagnetic (negative), the measured magnetization can be positive at certain fields as observed experimentally, which is a consequence of th…
Local magnetization hysteresis is among the most extensively studied features of high-temperature superconductors (HTSC). The usual source of hysteresis in superconductors is bulk vortex pinning due to material defects. Two additional known mechanisms of magnetic irreversibility are the Bean-Livingston surface barrier and the geometrical barrier (GB). GB arises due to a competition between the line energy of a vortex penetrating into the sample and the Lorentz force of Meissner currents which focuses vortices in the sample's center to form a dome-shaped vortex distribution. This work demonstra…
The penetration field H_p of Bi_2Sr_2CaCu_2O_{8+delta} crystals is determined from magnetization curves for different field sweep rates dH/dt and temperatures. The obtained results are consistent with theoretical reports in the literature about vortex creep over surface and geometrical barriers. The frequently observed low-temperature upturn of H_p is shown to be related to metastable configurations due to barriers for vortex entry. Data of the true lower critical field H_c1 are presented. The low-temperature dependence of H_c1 is consistent with a superconducting state with nodes in the gap f…
We calculate the magnetic-field dependence of the critical current due to both geometrical edge barriers and bulk pinning in a periodic coplanar array of narrow superconducting strips. We find that in zero or low applied magnetic fields the critical current can be considerably enhanced by the edge barriers, but in modest applied magnetic fields the critical current reduces to that due to bulk pinning alone.
The magnetic field distribution in the barrier of small planar Josephson tunnel junctions is numerically simulated in the case when an external magnetic field is applied perpendicular to the barrier plane. The simulations allow for heuristic analytical solutions for the Josephson static phase profile from which the dependence of the maximum Josephson current on the applied field amplitude is derived. The most common geometrical configurations are considered and, when possible, the theoretical findings are compared with the experimental data.
Critical currents $I_c$ were measured in Superconducting - normal - superconducting SNS c-axis junctions, where S was optimally doped $YBa_2Cu_3O_{7-δ}$ below $T_c$ (90 K) and N was $La_{2-x}Sr_xCuO_4$ above its $T_c$ ($<$25 K) but in the pseudogap regime. $I_c$ was measured versus temperature T in junctions with various N-barrier thicknesses $d$ and doping levels $x$. From the proximity effect relation $I_c(T)\propto exp[-d/ξ_N(T)]$, the normal coherence length $ξ_N(T)$ of N was extracted and plotted versus T. Besides finding a long range proximity effect as reported also by others, we found …
Using an expansion of the order parameter over the eigenfunctions of the linearized first Ginzburg-Landau (GL) equation, we obtain numerically the saddle points of the free energy separating the stable states with different number of vortices. In contrast to known surface and geometrical barrier models, we find that in a wide range of magnetic fields below the penetration field, the saddle point state for flux penetration into a disk does not correspond to a vortex located nearby the sample boundary, but to a region of suppressed superconductivity at the disk edge with no winding of the curren…
We show how to calculate the magnetic-field and sheet-current distributions for a thin-film superconducting annular ring (inner radius a, outer radius b, and thickness d<<a) when either the penetration depth obeys lambda < d/2 or, if lambda > d/2, the two-dimensional screening length obeys Lambda = 2 lambda^2/d << a for the following cases: (a) magnetic flux trapped in the hole in the absence of an applied magnetic field, (b) zero magnetic flux in the hole when the ring is subjected to an applied magnetic field, and (c) focusing of magnetic flux into the hole when a magnetic field is applied b…
We study Andreev reflection in a ballistic one-dimensional channel coupled in parallel to a superconductor via a tunnel barrier of finite length $L$. The dependence of the low-energy Andreev reflection probability $R_A$ on $L$ reveals the existence of a characteristic length scale $ξ_N$ beyond which $R_A(L)$ is enhanced up to unity despite the low interfacial transparency. The Andreev reflection enhancement is due to the strong mixing of particle and hole states that builds up in contacts exceeding the coherence length $ξ_N$, leading to a small energy gap (minigap) in the density of states of …
Evidence of how temperature takes part in the magnetic irreversibility in the intermediate state of a cylinder and various disks of pure type-I superconducting lead is presented. Isothermal measurements of first magnetization curves and magnetic hysteresis cycles are analyzed in a reduced representation that defines an equilibrium state for flux penetration in all the samples and reveals that flux expulsion depends on temperature in the disks but not in the cylinder. The magnetic field at which irreversibility sets in along the descending branch of the hysteresis cycle and the remnant magnetiz…
Using the transport and magnetization measurements the influence of neutron irradiation at a fluence of 5x10$^{17}$ n cm$^{-2}$ on (B0.65C0.35)Ba1.4Sr0.6Ca2Cu3Oz has been investigated. The neutron irradiation was found to decrease critical temperature and transport critical current density, increase the residual and normal state resistivity, and improve the intragranular critical current density with 1.6x10$^{57}$ A/cm$^{2}$ (at 77.3K and in the applied field up to 160 kA m) and ΔMirr/ΔMnonirr ratio (up to factor of 3) at highest field used for investigation. The field dependence of this ratio…
A one-dimensional equation describing the distribution of the effective vector potential $\bar A(y)$ across a film width, which holds for thin ($d<λ$) and thick ($d>λ$) films alike, is derived based on the analysis of a 2D Maxwell-Londons equation for superconducting films in a perpendicular magnetic field. The validity of this equation for a finite-thickness film is verified by a numerical analysis. An approximation dependence $\bar A(y)$, finite (with all of its derivatives) across the entire film width, is found for films, being in the Meissner state. The flux-entry field is evaluated for a…
