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This study explores transitions between states with different winding number in two-band superconducting rings. From the time-dependent Ginzburg-Landau (TDGL) equations for two-component superconductors, we apply linear instability theory and develop a semi-analytical method that provides the critical flux for phase-slip occurrence. The developed method was applied to investigate how the critical flux depends on physical properties, such as band parameters and temperature. Finally, we show the possible existence of a soliton state, in which the phase winding number is different in each condensate., Comment: 12 pages, 11 figures

In this work we study the role of the heat diffusion equation in simulating the resistive state of superconducting films. By analyzing the current-voltage and current-resistance characteristic curves for temperatures close to $T_c$ and various heat removal scenarios, we demonstrate that heat diffusion notably influences the behavior of the resistive state, specially near the transition to the normal state, where heat significantly changes the critical current and the calculated resistance. Furthermore, we show how the efficiency of the substrate has important effects in the dynamics of the system, particularly for lower temperatures. Finally, we investigate the hysteresis loops, the role of the film thickness and of the Ginzburg-Landau parameter, the findings accounting for heat diffusion in accurately modeling the resistive state of superconducting films and provide valuable insights into its complex dynamics. To accomplish these findings, we have used the $3D$ generalized Ginzburg-Landau equation coupled with the heat diffusion equation., Comment: Published in Physica C: Superconductivity and its applications

We propose a superconducting diode device comprising a central superconducting film flanked by two wires carrying an applied DC bias, suitably chosen so as to generate different asymmetric field profiles. Through numerical simulations of the coupled Ginzburg-Landau and heat-diffusion equations, we show that this design is capable of efficiently breaking the reciprocity of the critical current in the central superconductor, thus promoting the diode effect in response to an applied AC current. By adjusting the DC bias in the wires, we find the optimum inhomogeneous field profile that facilitates the entrance of vortices and antivortices in a given polarity of the applied AC current and impede their entrance in the other polarity. This way, the system behaves as an ideal superconducting half-wave rectifier, with diode efficiencies surpassing 70%. Furthermore, we detail the behavior and diode efficiency of the system under different experimental conditions, such as the substrate heat transfer coefficient and the sweep rate of the external current., Comment: 13 pages, 14 figures

By using the full 3D generalized time dependent Ginzbug-Landau equation we study a long superconducting film of finite width and thickness under an applied transport current. We show that, for sufficiently large thickness, the vortices and the antivortices become curved before they annihilate each other. As they approach the center of the sample, their ends combine, producing a single closed vortex. We also determine the critical values of the thickness for which the closed vortex sets in for different values of the Ginzburg-Ladau parameter. Finally, we propose a model of how to detect a closed vortex experimentally., Comment: 9 pages, 10 figures, accepted for publication in Phys. Rev. B

It was recently shown that a chiral topological phase emerges from the coupling of two twisted monolayers of superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ for certain twist angles. In this work, we reveal the behavior of such twisted superconducting bilayers with $d_{x^2-y^2}$ pairing symmetry in presence of applied magnetic field. Specifically, we show that the emergent vortex matter can serve as smoking gun for detection of topological superconductivity in such bilayers. Moreover, we report two distinct skyrmionic states that characterize the chiral topological phase, and provide full account of their experimental signatures and their evolution with the twist angle., Comment: 11 pages, 8 figures

In the description of non equilibrium situations in a superconductor at temperatures far below its critical temperature, the Keldysh-Usadel technique (KUT) is required. However, the non-stationary KUT has not been applied to realistic circuits. Moreover, the stationary KUT has been applied in situations where time independence is not guaranteed. As a plausibility check for this procedure, we resort to a toy model (the Ginzburg-Landau model), in situations that involve very slow evolution. We find that, even in these situations, neglecting the explicit influence of time variation leads to inaccurate or even qualitatively wrong description of phase slips., Comment: Co-author joined

Studies involving vortex dynamics and their interaction with pinning centers are an important ingredient to reach higher critical currents in superconducting materials. The vortex distribution around arrays of engineered defects, such as blind and through holes, may help to improve the superconducting properties. Thus, in this work, we used the time-dependent Ginzburg-Landau theory to investigate the vortex dynamics in superconductors of mesoscopic dimensions with a large central square defect with three different configurations: (i) a hole which passes through the sample (interface with the vacuum); (ii) a superconducting region with lower critical temperature (Tc); and (iii) a region with a more robust superconductivity, i.e., with a higherTc. Such systems can be envisaged as elementary building blocks of a macroscopic decorated specimen. Therefore, we evaluated the influence of different interfaces on the vortex dynamics and their effects in the field-dependent magnetization and time-dependent induced electric potential variation. The results show that the lower critical field is independent from the nature of the defect. However, the currents crowd at the vertices of the through hole producing a lower degradation of the local superconductivity, which may increase the upper critical field. On the other hand, the last type of defect can be used to control the vortex dynamics in the main superconducting region around the defect with more accuracy. Whereas the first two defects are attractive for the vortices, the third type is repulsive for them, being needed several vortices penetrated in the superconducting matrix to have vortices penetrated into it., Comment: 14 pages, 8 figures, preprint version

The generalized time-dependent Ginzburg-Landau (GTDGL) theory was first proposed to describe better gap superconductors and the phenomenon of thermal phase-slips (PSs) in defect-free systems. However, there is a lack of information about studies involving PSs in mesoscopic superconductors with surface defects. Thus, in this work, we simulated samples with two co-linear surface defects consisting of a lower $T_c$ superconductor narrowing the sample in its central part. The non-linear GTDGL equations were solved self-consistently under variable applied currents and by considering both gapless and gap-like superconductors. In such systems, the currents passing by the constriction induce the appearance of kinematic vortices even in the gapless sample. The dynamics always occur with a pair forming at opposite edges of the sample and annihilating in the center. It is noticed that the resistive state appears at distinct values of the applied current density for different samples, and the critical current presents a tiny difference between gapless and gap-like samples. It is worth mentioning that parameters such as the size of electrical contacts and constriction affect the critical current and the average velocity of the kinematic vortices., Comment: 7 pages, 15 figures, submitted to Physics Letters A

M. Tinkham and P. G. de Gennes, described in their books the existence of an intermediate type-I superconductor as a consequence of an external surface that affects the well known classification of superconductors into type-I and II. Here we consider the mesoscopic superconductor where the ratio volume to area is small and the effects of the external surface are enhanced. By means of the standard Ginzburg-Landau theory the Tinkham-de Gennes scenario is extended to the mesoscopic type-I superconductor. We find new features of the transition at the passage from the genuine to the intermediate type-I. The latter has two distinct transitions, namely, from a paramagnetic to diamagnetic response in descending field and a quasi type-II behavior as the critical coupling is approached in ascending field. The intermediate type-I phase proposed here, and its corresponding transitions, reflect intrinsic features of the superconductor and not its geometrical properties., Comment: Accepted for publication in Physical Review B. 6 pages, 4 figures

Within the framework of the generalized time-dependent Ginzburg-Landau equations, we studied the influence of the magnetic self-field induced by the currents inside a superconducting sample driven by an applied transport current. The numerical simulations of the resistive state of the system show that neither material inhomogeneity nor a normal contact smaller than the sample width are required to produce an inhomogeneous current distribution inside the sample, which leads to the emergence of a kinematic vortex-antivortex pair (vortex street) solution. Further, we discuss the behaviors of the kinematic vortex velocity, the annihilation rates of the supercurrent, and the superconducting order parameters alongside the vortex street solution. We prove that these two latter points explain the characteristics of the resistive state of the system. They are the fundamental basis to describe the peak of the current-resistance characteristic curve and the location where the vortex-antivortex pair is formed., Comment: 9 pages, 6 figures. Accepted for publication in Scientific Reports

Usually, the measurements of electronic and magnetic properties of superconducting samples are carried out under a constant temperature bath. On the other hand, thermal gradients induce local variation of the superconducting order parameter, and the vortex dynamics can present interesting behaviors. In this work, we solved the time-dependent Ginzburg-Landau equations simulating samples under two different thermal gradients, and considering two values of the Ginzburg-Landau parameter, \k{appa}. We find out that both parameters, i.e., \k{appa} and thermal gradients, play an important role on the vortex dynamics and on the magnetization behavior of the samples., Comment: raw manuscript of the accepted one, 9 pages, 7 figures

Em geral, quando a teoria fenomenol\'ogica de Ginzburg-Landau para supercondutores \'e trabalhada, pouco se esclarece aos alunos sobre a origem da mesma. Esta tem como base conceitos termodin\^amicos como fen\^omenos cr\'iticos e transi\c{c}\~oes de fase que, se devidamente tratados, enriquecem de sobremaneira a aula sobre tal assunto. Assim, neste trabalho apresentamos uma sequ\^encia para o desenvolvimento da principal teoria fenomenol\'ogica da supercondutividade. Iniciamos com uma breve introdu\c{c}\~ao aos fen\^omenos cr\'iticos e transi\c{c}\~oes de fase e, ent\~ao, desenvolvemos a teoria de Landau para transi\c{c}\~oes de fase de segunda ordem. Ap\'os isso, expomos a teoria de Ginzburg-Landau, e a teoria de Ginzburg-Landau dependente do tempo. Aplicamos esta \'ultima para o caso de dois sistemas supercondutores mesosc\'opicos, um homog\^eneo e outro com defeitos superficiais. Observa-se que os defeitos interferem de sobremaneira na din\^amica de v\'ortices do sistema. Palavras chave: Ginzburg-Landau, mesosc\'opico, v\'ortice, supercondutor In this work we present a sequence for the development of this major phenomenological theory for superconductors. We will begin with a brief introduction to the criticality and phase transitions phenomena e then we will describe the Landau theory for second order phase transitions. After that, we will introduce the Ginzburg-Landau theory and the time-dependent Ginzburg-Landau theory. As an application of this last one, we will study two mesoscopic systems. One of them a homogeneous sample and the other one a sample with surface defects. We show that the defects strongly influences the vortex dynamics of the system. Keywords: Ginzburg-Landau, mesoscopic, vortex, superconductor, Comment: This paper intends to be a didactic material (in Portuguese) for beginning students. It is constituted by 4 figures and 12 pages

Studies with mesoscopic superconducting materials have made significant advances on the last decades. One of the applications of such systems is in devices for single photon and single electron detectors. However, depending on the geometry of these systems, crowding current effects take place and, as a consequence, the total critical current could decrease which facilitates the penetration of vortices. This effect could also be responsible for a variety of penetration morphologies of flux avalanches in macroscopic samples. Thus, in this work we used the time-dependent Ginzburg-Landau theory to study the crowding current effects in mesoscopic superconducting systems with an array of antidots. It is demonstrated that the profile of the currents is influenced by the antidots, i.e., in the vertices of the antidots the intensity of the currents increases. On the other hand, the profile of the currents in between the antidots is more affected in the smaller system which presents closer antidots., Comment: 4 pages, 4 figures, presented on ASC 2014 and submitted to IEEE TRANSACTION ON APPLIED SUPERCONDUCTIVITY

The dynamics of the annihilation of a vortex-antivortex pair is investigated. The pair is activated magnetically during the run of a simulated hysteresis loop on a square mesoscopic superconducting cylinder with an antidot inserted at its center. We study the nucleation of vortices and antivortices by first increasing the magnetic field, applied parallel to the axis of the sample, from zero until the first vortex is created. A further increase of the field pulls the vortex in, until it reaches the antidot. As the polarity of the field is reversed, an antivortex enters the scene, travels toward the center of the sample and eventually the pair is annihilated. Depending on the sample size, its temperature, and Ginzburg-Landau parameter, the vortex-antivortex encounter takes place at the antidot or at the superconducting sea around it. The position and velocity of the vortex and antivortex singularities were evaluated as a function of time. The current density, magnetization and order parameter topology were also calculated., Comment: One REVTeX file and 5 EPS figures

In the present paper we develop an algorithm to solve the time dependent Ginzburg-Landau (TDGL) equations, by using the link variables technique, for circular geometries. In addition, we evaluate the Helmholtz and Gibbs free energy, the magnetization, and the number of vortices. This algorithm is applied to a circular sector. We evaluate the superconduting-normal magnetic field transition, the magnetization, and the superconducting density. Furthermore, we study the nucleation of giant and multi-vortex states for that geometry., Comment: One REVTeX file and 8 figures

In the present work we investigate the behavior of a vortex in a long superconducting cylinder near to a columnar defect at the center. The derivations of the local magnetic field distribution and the Gibbs free energy will be carried out for a cylinder and a cavity of arbitrary sizes. From the general expressions, it considered two particular limits: one in which the radius of the cavity is very small but the radius of the superconducting cylinder is kept finite; and one in which the radius of the superconducting cylinder is taken very large (infinite) but the radius of the cavity is kept finite. In both cases the maximum number of vortices which are allowed in the cavity is determined. In addition, the surface barrier field for flux entrance into the cavity is calculated., Comment: 13 pages, 1 figure

In this paper we investigate the elastic properties of the vortex lattice for a superconducting film of finite thickness. We derive an analytic expression for the compression modulus. The shear modulus is evaluated numerically by using both the Pearl interaction potential, valid in the limit of very thin film, and a potential for films of arbitrary thickness. A comparative study of the shear moduli is carried out., Comment: 6 pages, 2 figures, a REVTeX file and two PS figures

In the present work we study an anisotropic layered superconducting film of finite thickness. The film surfaces are considered parallel to the $bc$ face of the crystal. The vortex lines are oriented perpendicular to the film surfaces and parallel to the superconducting planes. We calculate the local field and the London free energy for this geometry. Our calculation is a generalization of previous works where the sample is taken as a semi-infinite superconductor. As an application of this theory we investigate the flux spreading at the superconducting surface., Comment: One REVTeX file containing a figure in it and two PS figures. To appear in Physical Review B

We obtain the vortex configurations, the matching fields and the magnetization of a superconducting film with a finite cross section. The applied magnetic field is normal to this cross section, and we use London theory to calculate many of its properties, such as the local magnetic field, the free energy and the induction for the mixed state. Thus previous similar theoretical works, done for an infinitely long superconducting film, are recovered here, in the special limit of a very long cross section., Comment: Contains a REVTeX file and 4 figures

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 state, 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 state 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., Comment: 11 pages, 3 figures