Flux confinement in mesoscopic superconductors

We report on flux confinement effects in superconducting submicron line, loop and dot structures. The main idea of our study was to vary the boundary conditions for confinement of the superconducting condensate by taking samples of different topology and, through that, modifying the lowest Landau level E_LLL(H). Since the critical temperature versus applied magnetic field T_c(H) is, in fact,E_LLL (H) measured in temperature units, it is varied as well when the sample topology is changed. We demonstrate that in all the submicron structures studied the shape of theT_c (H) phase boundary is determined by the confinement topology in a unique way.     

Relaxation processes in mesoscopic superconductors

We investigate the possibility of a novel kind of optical pump probe spectroscopy where the two laser pulses are focused on different areas of the sample. The response to the destruction of the superconducting state in a large part of a mesoscopic ring is studied numerically. We use the time dependent Ginzburg-Landau equations with periodic boundary conditions and external magnetic field. We evaluate the relaxation rates of the superconducting order parameter as well as the voltage induced by the charge imbalance. Computer simulations confirm that the perturbation of superconductivity on one part of the ring induces a voltage which decelerates the superconducting electrons on the other part of the ring. This deceleration results in the decrease of the superconducting current and the superfluid density. The relaxation times are of the order of the picosecond, the induced voltage of few millivolts and the variation of the superconducting gap of 10% which we believe to be suitable for time resolved femtosecond optical spectroscopy.     

Vortex states in mesoscopic superconductors

The results of theoretical investigations of the electronic structure and transport properties of vortex states in mesoscopic superconductors with sizes of several coherence lengths are reviewed. The features of the electronic spectra of multiquantum vortices and vortex molecules, as well as mechanisms of thermal transport along vortex lines, are considered by taking into account boundary effects.     

Critical currents of type ii superconductors in non-transversal magnetic fields

The force on flux lines near narrow defects elongated in the direction of the transport current is calculated. This force, together with the maximum interaction forcek _m on the central flux line element, gives the volume pinning forceF _p on the flux line lattice. The dependence ofk _m (and of the critical current densityj _c ) on the angle between the magnetic field and the transport current is calculated for different defect dimensions (with respect to the coherence length of the superconductor) and compared with the experimental results. We obtainj _c sin^–n , where 1n3 in dependence on the defect dimensions and on the angle interval. The possibility of testing theF _p k _m ² dependence of the statistical theory of pinning is proposed.     

Suppression of superconductivity in mesoscopic superconductors

We propose a new boundary-driven phase transition associated with vortex nucleation in mesoscopic superconductors (of size of the order of, or larger than, the penetration depth). We derive the rescaling equations and we show that boundary effects associated with vortex nucleation lower the conventional transition temperature in mesoscopic superconductors by an amount which is a function of the size of the superconductor. This result explains recent experiments in small superconductors where it was found that the transition temperature depends on the size of the system and is lower than the critical Berezinsk?-Kosterlitz-Thouless temperature.     

Nucleation of superconductivity in mesoscopic star-shaped superconductors

We study the phase transition of a star-shaped superconductor, which covers smoothly the range from zero to two dimensions with respect to the superconducting coherence length . Detailed measurements and numerical calculations show that the nucleation of superconductivity in this device is very inhomogeneous: the superconducting order parameter is strongly enhanced and mostly robust in regions close to multiple boundaries. The strong inhomogeneity of the order parameter results in a rich structure of the superconducting transition as a function of temperature and magnetic field.Received: 26 February 2003, Published online: 4 August 2003PACS: 74.78.-w Superconducting films and low-dimensional structures - 74.78.Na Mesoscopic and nanoscale systems - 74.20.De Phenomenological theories D.A. Dikin: On leave from: Institute for Low Temperature Physics and Engineering, 61164 Kharkov, UkraineV.R. Misko: On leave from: Institute of Applied Physics, 2028 Kishinev, Republic of MoldovaV.M. Fomin: On leave from: State University of Moldova, 2009 Kishinev, Republic of Moldova; Also at: Technische Universiteit Eindhoven, 5600 MB Eindhoven, The NetherlandsJ.T. Devreese: Also at: Universiteit Antwerpen (RUCA), B-2020 Antwerpen, Belgium and Technische Universiteit Eindhoven, 5600 MB Eindhoven, The Netherlands     

Giant oscillations of energy levels in mesoscopic superconductors

The interplay of geometrical and Andreev quantization in mesoscopic superconductors leads to giant mesoscopic oscillations of energy levels as functions of the Fermi momentum and/or sample size. Quantization rules are formulated for closed quasiparticle trajectories in the presence of normal scattering at the sample boundaries. Two generic examples of mesoscopic systems are studied: (i) one-dimensional Andreev states in a quantum box and (ii) a single vortex in a mesoscopic cylinder.     

Critical voltage of a mesoscopic superconductor

We study the influence of a voltage-driven nonequilibrium of quasiparticles on the properties of short mesoscopic superconducting wires. We employ a numerical calculation based upon the Usadel equation. Going beyond linear response, we find a nonthermal energy distribution of the quasiparticles caused by the applied bias voltage. It is demonstrated that this nonequilibrium drives the system from the superconducting state to the normal state, at a current density far below the critical depairing current density.     

Anisotropic ac dissipation at the surface of mesoscopic superconductors

In this work we study the ac dissipation of mesoscopic superconductors at microwave frequencies using the time dependent Ginzburg-Landau equations. Our numerical simulations show that the ac dissipation is strongly dependent on the orientation of the ac magnetic field (h_ac) relative to the dc magnetic field (H_dc). When h_ac is parallel to H_dc we observe that each vortex penetration event produces a significant suppression of the ac losses because the imaginary part of the ac susceptibility as a function of H_dc increases before the penetration of vortices, and then it decreases abruptly after vortices have entered into the sample. In the second case, when h_ac is perpendicular to H_dc, we observe that the jumps in dissipation occur at the same values of H_dc but are much smaller than in the parallel configuration. The behavior of the dissipation in the perpendicular configuration is similar to previous results obtained in recent microwave experiments using mesoscopic lithographed squares of Pb [A.D. Hernández, O. Arés, C. Hart, D. Domínguez, H. Pastoriza, A. Butera, J. Low Temp. Phys. 135 (2004) 119].     

Local density of states of vortex state in mesoscopic superconductors

We study local density of states (LDOS) of vortex state in mesoscopic square superconductors with Bogoliubov-de Gennes (BdG) equation. We develop one effective numerical method based on the finite element method to self-consistently solve the BdG equation. The LDOS for various vortex states is obtained. Our results about the single vortex show that the LDOS has the particle-hole asymmetry and the results for one- and two-vortex state agree very well with the experimental observation. Besides, we predict the LDOS of multi-vortex states, which is crucial for the further STM/STS experimental study of vortex state in mesoscopic superconducting system.     

Effects of geometrical symmetry on the vortex in mesoscopic superconductors

We first systematically study the multivortex states in mesoscopic superconductors via self-consistent Bogoliubov-de Gennes equations. Our work focuses on how the geometrical symmetry affects the penetration and arrangement of vortices in mesoscopic superconductors and find that the key parameter determining the entrance of the vortex is the current density at the hot spots on the edge of sample. Through determining the spatial distribution of hot spots, the geometrical symmetry of the superconducting sample influences the nucleation and entrance of vortices. Our results propose one possible experimental approach to control and manipulate the quantum states of mesoscopic superconductors with their topological geometries, and they can be easily generalized to the confined superfluids and Bose-Einstein condensates.     

Critical behavior in type-II superconductors

The high-field critical behavior of type-II superconductors with weak disorder is dominated by the Landau levels of Cooper pairs. The macroscopic degeneracy of Landau manifolds suppresses phase coherence and eliminates the Abrikosov transition in dimensions two and three. A novel phase transition, unrelated to the conventional Abrikosov transition, is predicted to take its place. At this transition the normal state is unstable to the charge-density wave of Cooper pairs. The nature of this new state is discussed. This phase should be most readily observable in layered materials at fields > 1–10T.     

Critical fluctuations in a mesoscopic superconducting ring

The nonlocal magnetoconductivity fluctuations in a superconducting submicron ring, with radius comparable to the Ginzburg-Landau coherence length, are studied. The order parameter mode separation yields to the solution of the time-dependent Ginzburg-Landau equation and the paraconductivity Fourier components are calculated in the vicinity of the critical temperature, including the critical fluctuation region. The homogeneous component has a logarithmic singularity at T(c) while the other components are found to be not singular.     

Transverse electric fields in mesoscopic normal rings

A quantum mechanical estimate of the electric field within a normal metal ring is made. In the clean limit, the voltage drop across a ring threaded by Aharonov-Bohm flux contains a large flux-independent part and a small flux-periodic part. The results agree with the Bernoulli theorem.     

Flux flow in current driven mesoscopic superconductors: size effects

Flux-flow phenomena in a superconducting mesoscopic stripe submitted to an appliedcurrent and external magnetic field is studied. The time-dependent Ginzburg-Landauequations are solved numerically to obtain the electric and magnetic response of thesystem. It is shown that the I-V curves, for the wider strips, present a universalbehaviour. The dependence of the flux-flow resistivity on the magnetic field and widthallow us to propose a criterion characterizing, both, the macroscopic and mesoscopicregimes. The power spectrum of the average voltage permits identifying the effect ofsurface currents in vortices movement. Based on the maximum value of the power spectrumfirst harmonic we propose a geometric condition for matching between the sample dimensionsand the vortex lattice parameter.     

Critical temperature of transition-metal alloy superconductors

We calculate the critical temperature T_c of a superconducting transition-metal alloy using an ansatz of Kerker and Bennamann, but in contrast to that of Kerker and Bennamann our approximation does not violate the time reversal and spin rotation symmetries.     

Iron-based superconductors in high magnetic fields

Here we review measurements of the normal and superconducting state properties of iron-based superconductors using high magnetic fields. We discuss the various physical mechanisms that limit superconductivity in high fields, and the information on the superconducting state that can be extracted from the upper critical field, but also how thermal fluctuations affect its determination by resistivity and specific heat measurements. We also discuss measurements of the normal state electronic structure focusing on measurement of quantum oscillations, particularly the de Haas–van Alphen effect. These results have determined very accurately, the topology of the Fermi surface and the quasi-particle masses in a number of different iron-based superconductors, from the 1111, 122 and 111 families.