Solving numerically the 3D non linear Ginzburg-Landau (GL) equations, we study equilibrium and nonequilibrium phase transitions between different superconducting states of mesoscopic disks which are thinner than the coherence length and the penetration depth. We have found a smooth transition from a multi-vortex superconducting state to a giant vortex state with increasing both the disk thickness and the magnetic field. A vortex phase diagram is obtained which shows, as function of the magnetic field, a re-entrant behavior between the multi-vortex and the giant vortex state. PACS number(s): 74.24. Ha, 74.60.Ec, 73.20.Dx Recently, mesoscopic superconductivity has attracted much attention in view of phase transitions in confined systems with sizes comparable to the coherence (ξ) and penetration (λ) lengths. While the type of bulk superconductors is only determined by the value of the GinzburgLandau parameter κ = λ/ξ, the experimental observations [1] and the numerical simulations [2,3] of magnetization of mesoscopic thin disks have shown that the type and the order of those transitions between different superconducting states and between the superconducting and the normal state depends crucially on the disk radius R and the thickness d. With increasing the disk radius the second-order reversible phase transition observed for small disk radii are replaced by first-order transitions with a jump in the magnetization. In previous theoretical investigations of superconductivity in such mesoscopic disks [2,3] only the giant vortex states with fixed total angular momentum L were considered with an axially symmetric order parameter. It is well known [4] that for type-II superconductors (κ > 1/ √ 2), the triangular Abrikosov vortex lattice is energetically favorable in the range H c1 < H < H c2 . Since the effective London penetration depth Λ = λ 2 /d increases considerably in thin disks with d ≪ λ one would expect the appearance of the Abrikosov multi-vortex state even in disks made from a material with κ < 1/ √ 2, like e.g. the Al disks studied in Refs. [2,3]. By analogy with classical particles confined by an external potential [5], the structure of a finite number of vortices should differ from a simple triangular arrangement and allow for different metastable states. Using the London approximation Fetter [6] calculated the critical field H c1 for flux penetration into a disk. For a superconducting cylinder the multi-vortex clusters, containing up to four vortices, were simulated by Bobel [7]. Using the method of images and the London approximation, Buzdin and Brison [8] have considered vortex structures in small R ≪ Λ disks and found a classical particle ringlike arrangement [5] of vortices. In the present Letter we study the transition from the giant vortex state to this multi-vortex configuration for thin superconducting disks within the nonlinear Ginzburg-Landau (GL) theory.We consider a superconducting disk immersed in an insulator media with a perpendicular uniform magnetic field H 0 . For thin disks (d ≪ ξ...

Theoretical approaches to one-dimensional and quasi-one-dimensional quantum rings with a few electrons are reviewed. Discrete Hubbard-type models and continuum models are shown to give similar results governed by the special features of the one-dimensionality. The energy spectrum of the many-body states can be described by a rotation-vibration spectrum of a 'Wigner molecule' of 'localized' electrons, combined with the spin-state determined from an effective antiferromagnetic Heisenberg Hamiltonian. The persistent current as a function of the magnetic flux through the ring shows periodic oscillations arising from the 'rigid rotation' of the electron ring. For polarized electrons the periodicity of the oscillations is always the flux quantum Φ0. For nonpolarized electrons the periodicity depends on the strength of the effective Heisenberg coupling and changes from Φ0 first to Φ0/2 and eventually to Φ0/N when the ring gets narrower.

Solutions of Ginzburg-Landau equations coupled with three-dimensional Maxwell equations reveal an intriguing magnetic response of small superconducting particles, qualitatively different from the twodimensional approximation but in agreement with recent experiments. Depending on the radius and thickness, first or second order transitions are found for the normal to superconducting state. For a sufficiently large radius of the disk, several transitions in the superconducting phase are obtained which correspond to different angular momentum giant vortex states. The incorporation of the finite thickness in the calculation is crucial in order to obtain agreement with the position and the size of these jumps, and the line shape and magnitude of the magnetization curves. [S0031-9007(97)

We have studied the quantum transmission properties of serial stub and loop structures. Throughout we have considered free electron networks and the scattering arises solely due to the geometric nature of the problem. The band formation in these geometric structures is analyzed and compared with the conventional periodic potential scatterers. Some essential differences are pointed out. We show that a single defect in an otherwise periodic structure modifies band properties non trivially. By a proper choice of a single defect one can produce positive energy bound states in continuum in the sense of von Neumann and Wigner. We also discuss some magnetic properties of loop structures in the presence of Aharonov-Bohm

We have considered a system of a metallic ring coupled to two electron reservoirs. We show that in the presence of a transport current, the persistent current can flow in a ring, even in the absence of a magnetic field. This is purely a quantum effect and is related to the current magnification in the loop.These persistent currents can be observed if one tunes the Fermi energy near the antiresonances of the total transmission coefficient or the two-port conductance. Experimental and theoretical research in mesoscopic systems have provided an opportunity of exploring truly quantum-mechanical effects beyond the atomic realm. ' Persistent currents in small metal rings threaded by magnetic Aux are a manifestation of quantum effects in submicrometer systems, and are prominent among the mesoscopic effects. Prior to the experimental observations, Buttiker, Imry, and Landauer suggested the existence of persistent currents in an ordered onedimensional ring threaded by a magnetic Aux. The coherent wave functions extending over the whole circumference of the loop lead to a periodic persistent current. General quantum-mechanical principles require that the wave functions, eigenvalues, and hence all observables be periodic in a Aux (b threaded by the loop with a period Pp Pp= bc/e being the elementary flux quantum.The magnetic field destroys the time-reversal symmetry and, as a consequence, the degeneracy of the states carrying current clockwise and anticlockwise is lifted. Depending on the position of the Fermi level, uncompensated current Rows in either of the directions (diamagnetic or paramagnetic). For an ideal isolated ring without impurities and at zero temperature, the nature of the persistent current depends on the total number N of the electrons and the persistent current exhibits a sawtooth-type behavior as a function of magnetic Aux. For even N, the jump discontinuities occur from the values -(2ev&/L) to (2ev& /L ) at $ = 0, +tbo, and +2$o, and at (b=+Po/2, +3/ /o2, etc. , for odd N. Here v& is the Fermi velocity, and L is the circumference of the ring. Studies have been extended to include multichannel rings, disorder, spin-orbit coupling, and electron-electron interaction effects. ' The persistent current which Rows without dissipation is an equilibrium property of the ring, and is given by a Aux derivative of the total energy of the ring.These currents can also be thought to arise from the competing requirements of minimizing the free energy in the presence of Aux at the same time maintaining the single valuedness of the wave function. Persistent currents are truly mesoscopic effects in the sense that they are strongly suppressed when the ring size exceeds the characteristic dephasing length of the electrons L& (i.e., the length scale over which the electron can be considered to be in a pure state). Theoretical treatments to date have mostly been concentrated on isolated rings. Persistent currents occur not only in the isolated rings but also in rings connected via leads to electron reservoirs, namely in open s...

We have considered an open system consisting of a metallic ring coupled to two electron reservoirs. We have recently shown that in the presence of a transport current, circulating currents can flow in such a ring even in the absence of magnetic field. This is related to the current magnification effect in the ring. In our present work we have studied the effect of impurity on the current magnification. We find that the presence of impurity can enhance the current magnification in the loop significantly and thus lead to large circulating currents in certain range of Fermi energies. This is in contrast to the known fact that impurities can only decrease the persistent currents in a closed ring in the presence of magnetic flux.

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Phase transitions between different (i.e. giant and multi-vortex) superconducting states and between the superconducting-normal state of mesoscopic disks and rings are studied in the presence of an external magnetic field by solving the two nonlinear Ginzburg-Landau equations self-consistently. The flux through a circular disk with a hole in the middle is not quantized.