Grain boundaries in vortex matter

We explore the statistical properties of grain boundaries in the vortex polycrystalline phase of type-II superconductors. Treating grain boundaries as arrays of dislocations interacting through linear elasticity, we show that self-interaction of a deformed grain boundary is equivalent to a nonlocal long-range surface tension. This affects the pinning properties of grain boundaries, which are found to be less rough than isolated dislocations. The presence of grain boundaries has an important effect on the transport properties of type-II superconductors as we show by numerical simulations: our results indicate that the critical current is higher for a vortex polycrystal than for a regular vortex lattice. Finally, we discuss the possible role of grain boundaries in vortex lattice melting. Through a phenomenological theory we show that melting can be preceded by an intermediate polycrystalline phase.

Grain boundaries in vortex matter

We explore the statistical properties of grain boundaries in the vortex polycrystalline phase of type-II superconductors. Treating grain boundaries as arrays of dislocations interacting through linear elasticity, we show that self-interaction of a deformed grain boundary is equivalent to a nonlocal long-range surface tension. This affects the pinning properties of grain boundaries, which are found to be less rough than isolated dislocations. The presence of grain boundaries has an important effect on the transport properties of type-II superconductors as we show by numerical simulations: our results indicate that the critical current is higher for a vortex polycrystal than for a regular vortex lattice. Finally, we discuss the possible role of grain boundaries in vortex lattice melting. Through a phenomenological theory we show that melting can be preceded by an intermediate polycrystalline phase.

Minimum size for the occurrence of vortex matter in a square mesoscopic superconductor

The study of superconducting samples in mesoscopic scale presented a remarkable improvement during the last years. Certainly, such interest is based on the fact that when the size of the samples is close to the order of the temperature dependent coherence length xi(T), and/or the size of the penetration depth lambda(T), there are some significant modifications on the physical properties of the superconducting state. This contribution tests the square cross-section size limit for the occurrence (or not) of vortices in mesoscopic samples of area L-2, where L varies discretely from 1 xi(0) to 8 xi(0).The time dependent Ginzburg-Landau (TDGL) equations approach is used upon taking the order parameter and the local magnetic field invariant along the z-direction. The vortex configurations at the equilibrium can be obtained from the TDGL equations for superconductivity as the system relaxes to the stationary state.The obtained results show that the limit of vortex penetration is for the square sample of size 3 xi(0) x 3 xi(0) in which only a single vortex are allowed into the sample. For smaller specimens, no vortex can be formed and the field entrance into the sample is continuous and the total flux penetration occurs at higher values of H/H-c2(0), where H-c2(T) is the upper critical field. Otherwise, for larger samples different vortices patterns can be observed depending on the sample size. (c) 2007 Elsevier B.V. All rights reserved.

Temperature-dependent vortex matter in a superconducting mesoscopic circular sector

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Depinning and vortex-glass-like transition in Nb with uncorrelated disorder

Studies of the third harmonic of the AC-susceptibility were conducted to detect the boundaries of the linear regime of the magnetic response of granular Nb samples. These studies reveal the extent of the region, on the phase diagram, where the magnetic response is linear, which corresponds to the disordered phase of Vortex Matter. The present work addresses the correlation between a linear response and experimental parameters such as the frequency and the amplitude of the excitation field. The order-disorder border has been extracted from the onset temperature of the third harmonic measured at low-frequencies and low-excitation fields in the presence of dc magnetic fields. © 2008 IOP Publishing Ltd.

Solid-liquid transition in Nb powder determined by third harmonic susceptibility

Measurements of the third harmonic of the AC-susceptibility were employed to determine the boundaries of the linear regime of the magnetic response of Nb powder. Non-linear contributions to the magnetic response reveal the occurrence of a structured phase, disappearing as the vortex lattice melts to the liquid state. A systematic study of the third harmonic was conducted to determine how its onset temperature depends on experimental parameters, such as the frequency and amplitude of the excitation field. The melting line (ML) has been extracted from the onset temperature measured at low-frequencies and low-excitation fields in the presence of DC magnetic fields. The study indicates that the ML can be described by a 3D vortex-glass model, except at lower fields, where the system experiences a depinning crossover, and the best description of the experimental data is provided by a 3D Bose-glass model. (c) 2008 Elsevier B. V. All rights reserved.

Linear arrangement of metallic and superconducting defects in a thin superconducting sample

The vortex matter in a superconducting disk with a linear configuration of metallic and superconducting defects is studied. Effects associated to the pinning (anti-pinning) force of the metallic (superconducting) defect on the vortex configuration and on the thermodynamic critical fields are analyzed in the framework of the Ginzburg Landau theory. We calculate the loop of the magnetization, vorticity and free energy curves as a function of the magnetic field for a thin disk. Due to vortex-defect attraction for a metallic defect (repulsion for a superconducting defect), the vortices always (never) are found to be sitting on the defect position. © 2013.

Inomogeneidades estruturais em amostras nanoscópicas de supercondutores de alta temperatura crítica

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

K-Rb Fermi-Bose mixtures: Vortex states and sag

We study a confined mixture of bosons and fermions in the quantal degeneracy regime with attractive boson-fermion interaction. We discuss the effect that the presence of vortical states and the displacement of the trapping potentials may have on mixtures near collapse, and investigate the phase stability diagram of the K-Rb mixture in the mean-field approximation supposing in one case that the trapping potentials felt by bosons and fermions are shifted from each other, as it happens in the presence of a gravitational sag, and in another case, assuming that the Bose condensate sustains a vortex state. In both cases, we have obtained an analytical expression for the fermion effective potential when the Bose condensate is in the Thomas-Fermi regime, that can be used to determine the maxima of the Fermionic density. We have numerically checked that the values one obtains for the location of these maxima using the analytical formulas remain valid up to the critical boson and fermion numbers, above which the mixture collapses.

Critical frequency for vortex nucleation in Bose-Fermi mixtures in optical lattices

We investigate within mean-field theory the influence of a one-dimensional optical lattice and of trapped degenerate fermions on the critical rotational frequency for vortex line creation in a Bose-Einstein condensate. We consider laser intensities of the lattice such that quantum coherence across the condensate is ensured. We find a sizable decrease of the thermodynamic critical frequency for vortex nucleation with increasing applied laser strength and suggest suitable parameters for experimental observation. Since 87Rb-40K mixtures may undergo collapse, we analyze the related question of how the optical lattice affects the mechanical stability of the system.

Énergie des vortex dans un modèle abélien de Higgs en 2+1 dimensions avec un potentiel d’ordre six

Dans ce travail, j’étudierai principalement un modèle abélien de Higgs en 2+1 dimensions, dans lequel un champ scalaire interagit avec un champ de jauge. Des défauts topologiques, nommés vortex, sont créés lorsque le potentiel possède un minimum brisant spontanément la symétrie U(1). En 3+1 dimensions, ces vortex deviennent des défauts à une dimension. Ils ap- paraissent par exemple en matière condensée dans les supraconducteurs de type II comme des lignes de flux magnétique. J’analyserai comment l’énergie des solutions statiques dépend des paramètres du modèle et en particulier du nombre d’enroulement du vortex. Pour le choix habituel de potentiel (un poly- nôme quartique dit « BPS »), la relation entre les masses des deux champs mène à deux types de comportements : type I si la masse du champ de jauge est plus grande que celle du champ sca- laire et type II inversement. Selon le cas, la dépendance de l’énergie au nombre d’enroulement, n, indiquera si les vortex auront tendance à s’attirer ou à se repousser, respectivement. Lorsque le flux emprisonné est grand, les vortex présentent un profil où la paroi est mince, permettant certaines simplifications dans l’analyse. Le potentiel, un polynôme d’ordre six (« non-BPS »), est choisi tel que le centre du vortex se trouve dans le vrai vide (minimum absolu du potentiel) alors qu’à l’infini le champ scalaire se retrouve dans le faux vide (minimum relatif du potentiel). Le taux de désintégration a déjà été estimé par une approximation semi-classique pour montrer l’impact des défauts topologiques sur la stabilité du faux vide. Le projet consiste d’abord à établir l’existence de vortex classi- quement stables de façon numérique. Puis, ma contribution fut une analyse des paramètres du modèle révélant le comportement énergétique de ceux-ci en fonction du nombre d’enroulement. Ce comportement s’avèrera être différent du cas « BPS » : le ratio des masses ne réussit pas à décrire le comportement observé numériquement.

Interaction potential between vortex lines for uniaxial superconductors in the London approximation

Two distinct expressions of the interaction potential between arbitrarily oriented curved vortex lines with respect to the crystal c axis are derived within the London approximation. One of these expressions is used to compute the eigenvalues of the elasticity matrix. We examine the elastic properties of the vortex chain lattice, recently proposed, concerning shearing deformation.

Vortex lattice and matching fields for a long superconducting wire

We investigate the flux penetration patterns and matching fields of a long cylindrical wire of circular cross section in the presence of an external magnetic field. For this study we write the London theory for a long cylinder both for the mixed and Meissner states, with boundary conditions appropriate for this geometry. Using the Monte Carlo simulated annealing method, the free energy of the mixed state is minimized with respect to the vortex position and we obtain the ground state of the vortex lattice for N=3 up to 18 vortices. The free energy of the Meissner and mixed states provides expressions for the matching fields. We find that, as in the case of samples of different geometry, the finite-size effect provokes a delay on the vortex penetration and a vortex accumulation in the center of the sample. The vortex patterns obtained are in good agreement with experimental results.

Free expansion of attractive and repulsive Bose-Einstein condensed vortex states

A numerical study of the time-dependent Gross-Pitaevskii equation for an axially symmetric trap to obtain insight into the free expansion of vortex states of BEC is presented. As such, the ratio of vortex-core radius to radia rms radius xc/xrms(<1) is found to play an interesting role in the free expansion of condensed vortex states. the larger this ratio, the more prominent is the vortex core and the easier is the possibility of experimental detection of vortex states.