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A nonperturbative method for evaluation of thermodynamic scaling functions in the critical region of type-II superconductors, appropriate for high-temperature superconductors, is extended for the case of external magnetic fields with arbitrary angles with respect to the c axis for the case of three-dimensional anisotropic superconductors. An explicit scaling function for the magnetization is presented, discussed, and compared with experimental data from measurements with applied fields along the ab planes.

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In the framework of the Ginzburg-Landau (GL) theory in the limit of a GL parameter much larger than unity, we study theoretically the critical behavior of a mesoscopic superconducting ring with negligible width in the presence of a magnetic field applied perpendicularly to the ring plane. It is assumed that the inner ring edge is in contact with a material whose properties are accounted in the de Gennes boundary condition with a parameter b (de Gennes extrapolation length), while the outer edge is in contact with vacuum. Special attention is devoted to the influence of the different materials contacting the inner ring edge of the superconductor on the features of the phase diagram, as well as the effect of the confinement on such thermodynamic property.

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We study the effect of geometric confinement on the electron states in a concentric double quantum ring. We calculate the energy of the electron ground state for both symmetric and asymmetric double quantum rings as a function of the radius of the inner and outer rings, the barrier height and as a function of an applied magnetic field. We found that the probability amplitude for the electron state is approximately the same in the inner and outer wells of the structure when the width of the wells is the same, but there is a noticeable change in the probability amplitude in the well regions when the width of the inner well is slightly different from the outer one (asymmetric rings). As a result the carrier energy changes considerably from one situation to the other. On the other hand the barrier width between the inner and outer ring plays an important role in the definition of the energy of the electron ground state up to the extent that for certain values of the barrier and well widths, the energy of the ground state does not depend any more on the barrier width.1 Introduction Semiconductors quantum rings (QR) are structures in which quantum confinement produces levels of discrete energy, which have been seen in low-temperature photoluminescence studies. The difference between a quantum dot (QD) and a quantum ring is due to the hole in the center of the ring. Semiconductor QR can be fabricated in a variety of sizes and shapes by using different techniques, like Self-assembled growth, Molecular Beam Epitaxy, chemical synthesis, chemical etching and other techniques as it is mentioned by Petroff et al. [1]; however, well-controlled methods for fabricating such structures remain a challenge. Although is not possible to determine the profile form of the radial confinement potential directly from these methods, Petroff et al. [1] showed that for a self-assembled QR the confinement potential profile is parabolic. On the other hand McCarthy [2] proposed that the radial confinement profile for an etched ring is a finite deep square potential well. Song and Ulloa [3], showed the behavior of the magneto-exciton binding energy and magnetic susceptibility as function of the ring width and the magnetic field, for a 2D QR using a parabolic profile as radial confinement potential. Mano et al. [4] demonstrate the self-assembled formation of concentric double quantum rings formation with high uniformity and rotational symmetry using the droplet epitaxy technique. They show that varying the growth process conditions can control the size of each ring. Photoluminescence spectra emitted from an individual quantum ring complex show quantized levels, signature of the carrier orbital state. Making use of a droplet-epitaxial technique Kuroda et al. [5], investigated within the local spin density approximation the state structure of few-electron concentric double quantum ring (DQR). These authors explore the role of the coupling inter ring distances finding that the energy structure of low lying electron states is essentially that of sin...