We report on measurements of the magnetic moment in superconducting MgB2 single crystals. We find µ0H c c2 (0) = 3.2 T, µ0H ab c2 (0) = 14.5 T, γ = 4.6, µ0Hc(0) = 0.28 T, and κ(Tc) = 4.7. The standard Ginzburg-Landau and London model relations lead to a consistent data set and indicate that MgB2 is a clean limit superconductor of intermediate coupling strength with very pronounced anisotropy effects.PACS numbers: 74.25. Ha, 74.60.Ec, 74.70.Ad The recent discovery of superconductivity in MgB 2 [1] has attracted a lot of attention. Especially the rather high transition temperature of nearly 40 K in such a simple compound is of interest for applications, but also for an analysis of the physical mechanism leading to superconductivity. Several experiments indicate a phonon mediated s -wave BCS mechanism [2,3]. Different models are proposed to explain the particular properties of MgB 2 [4,5]. Their correctness has to be checked by experiments, but only a few results are available on single crystals [6,7,8,9,10,11,12].We report in this Letter on magnetization measurements on single crystalline MgB 2 in magnetic fields applied parallel and perpendicular to the uniaxial crystallographic (≡ c) axis. A detailed evaluation allows us to obtain the temperature dependence of the most important reversible mixed state parameters, such as the critical magnetic fields, the characteristic lengths, the Ginzburg-Landau (GL) parameter and the anisotropy. We will show that MgB 2 is a clean limit superconductor of intermediate coupling strength with very pronounced anisotropy effects.Several single crystals of MgB 2 were grown using high pressure cubic anvils. Details of the process will be published elsewhere [13]. Two crystals (sample A:3 ) were investigated by magnetic methods. The transition temperature (T c ) of each sample was obtained from the ac -susceptibility measured in a 1 T quantum interference device (SQUID) magnetometer. Sample A shows an onset of T c at 38 K and a rather broad transition of about 1 K. A linear fit of H c c2 vs. T near T c indicates a "bulk transition temperature" of 37.5 K (see inset of fig. 1a). In sample B we find T c = 38.3 K, ∆ T c = 0.3 K and a "bulk T c " of 38.2 K. A simple analysis [14] of the slope of the magnetic moment after reversing the applied field demonstrates that the size of the domain, in which the supercurrents flow without impedance, is identical to the sample size. Furthermore, a comparison of the calculated and the measured magnetization in the Meissner regime indicates a superconducting volume fraction of about 100 %. The further evaluation of the mixed state parameters did not show significant differences between these two crystals.The measurements of the magnetic moment were carried out in the 1 T and in an 8 T (SHE) SQUID magnetometer (for details, cf. [15]). Fig. 1a shows the upper critical field of MgB 2 for applied fields H a c (H c c2 ) and H a ab (H ab c2 ). H c2 (T ) is determined either from the onset of the superconducting signal in the m(T ) curve ("T c (H a )") or ...

The influence of anisotropy on the transport current in MgB2 polycrystalline bulk samples and wires is discussed. A model for the critical current density is proposed, which is based on anisotropic London theory, grain boundary pinning and percolation theory. The calculated currents agree convincingly with experimental data and the fit parameters, especially the anisotropy, obtained from percolation theory agree with experiment or theoretical predictions.

Two-band superconductivity has become an important topic over the last ten years. Extensive experimental and theoretical studies started with MgB2 and are now focused on the iron-based and other new superconductors. In this review, I describe how important thermodynamic, reversible mixed-state, and other superconducting properties are changed by two-band and, for comparison, by other effects such as anisotropy in a single-band material or an energy gap structure different from the conventional s-wave symmetry. The work consists of three main parts, in which I review (i) theoretical models and what they predict for experimentally accessible properties in the two-band and other scenarios, (ii) experimental methods applied for investigating superconducting properties and the results obtained in potential two-band materials, and (iii) materials, for which two-or multi-band superconductivity has been suggested. It is shown that two-band effects appear in most of the analyzed properties and that they can be quite significant but usually fade away as interband interactions increase. Anisotropy often leads to similar modifications in single-band superconductors, which is why the distinction of two-band and anisotropy effects is usually difficult, particularly when the temperature dependence of the quantities is examined. In contrast, the field dependent effects are more often different and thus more often allow a reliable distinction between the models. CONTENTS

Early postoperative and long-term follow-ups showed effective and stable correction of astigmatism after implantation of a foldable toric posterior chamber silicone IOL.

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