Here we describe a development of computer algorithm to simulate the Time Dependent Ginzburg-Landau equation (TDGL) and its application to understand superconducting vortex dynamics in confined geometries. Our initial motivation to get involved in this task was trying to understand better our experimental measurements on dynamics of superconductors with vortices at high frequencies leading to microwave stimulated superconductivity due to presence of vortex (Lara, et al., Scientific Reports, 59187 (2015)).
We have extended Brandt's method for accurate, efficient calculations within Ginzburg-Landau theory for periodic vortex lattices at arbitrary mean induction to lattices of "doubly quantized" vortices.
We investigate the dynamics of magnetic vortices in type II superconductors with normal state pinning sites using the Ginzburg-Landau equations. Simulation results demonstrate hopping of vortices between pinning sites, influenced by external magnetic fields and external currents. The system is highly nonlinear and the vortices show complex nonlinear dynamical behaviour.
The paper deals with the study of superfluidity by a Ginzburg-Landau model that investigates the material by a second order phase transition, in which any particle has simultaneouly a normal and superfluid motion. This pattern is able to describe the classical effects of superfluidity as the phase diagram, the vortices, the second sound and the thermomechanical effect. Finally, the vorticities and turbulence are described by an extension of the model in which the material time derivative is used
We study the properties of the Ginzburg-Laundau model in the self-dual point for a two-dimensional finite system . By a numerical calculation we analyze the solutions of the Euler-Lagrange equations for a cylindrically symmetric ansatz. We also study the self-dual equations for this case. We find that the minimal energy configurations are not given by the Bogomol'nyi equations but by solutions to the Euler Lagrange ones. With a simple approximation scheme we reproduce the result of the numerical calculation.
The Ginzburg-Landau functional for a two-gap superconductor is derived within the weak-coupling BCS model. The two-gap Ginzburg-Landau theory is, then, applied to investigate various magnetic properties of MgB2 including an upturn temperature dependence of the transverse upper critical field and a core structure of an isolated vortex. Orientation of vortex lattice relative to crystallographic axes is studied for magnetic fields parallel to the c-axis. A peculiar 30-degree rotation of the vortex lattice with increasing strength of an applied field observed by neutron scattering is attributed to…
The quantization of magnetic flux in superconductors is usually seen as vortices penetrating the sample. While vortices are unstable in bulk type I superconductors, restricting the superconductor causes a variety of vortex structures to appear. We present a systematic study of giant vortex states in type I superconductors obtained by numerically solving the Ginzburg-Landau equations. The size of the vortices is seen to increase with decreasing film thickness. In type I superconductors, giant vortices appear at intermediate thicknesses but they do not form a well-defined vortex lattice. In the …
Taking into account both the orbital and the paramagnetic depairing effects we derive a simple analytic formula for the temperature dependence of the Ginzburg-Landau parameter valid in vicinity of field dependent critical temperature in a type-II superconductor.
We study two superconducting systems using the Landau-Ginzburg equations. The first is a superconducting half-space with an applied magnetic field parallel to the surface. We calculate the maximum applied field that still supports superconductivity in the material by solving the Landau-Ginzburg equations analytically in asymptotic regimes of the Landau-Ginzburg parameter, kappa. These results are then checked against numerical studies. The other system is a thin, current-carrying strip. Here we do the first systematic study of nucleation of superconductivity in a normal strip and of the motion…
The Landau potential in the general Ginzburg-Landau theory with two order parameters and all possible quadratic and quartic terms cannot be minimized with the straightforward algebra. Here, a geometric approach is presented that circumvents this computational difficulty and allows one to get insight into many properties of the model in the mean-field approximation.
Using the Ginzburg-Landau theory extended to the next-to-leading order we determine numerically the healing lengths of the two order parameters at the two-gap superconductor/normal metal interface. We demonstrate on several examples that those can be significantly different even in the strict domain of applicability of the Ginzburg-Landau theory. This justifies the use of this theory to describe relevant physics of two-gap superconductors, distinguishing them from their single-gap counterparts. The calculational degree of complexity increases only slightly with respect to the conventional Ginz…
We formulate the time-dependent Ginzburg-Landau theory, with the assumption of local equilibrium made in the reference frame floating with normal electrons. This theory with floating nucleation kernel is applied to the far infrared (FIR) conductivity in the Abrikosov vortex lattice. It yields better agreement with recent experimental data [PRB {\bf 79}, 174525 (2009)] than the customary time-dependent Ginzburg-Landau theory.
Long-standing discrepancies within determinations of the Ginzburg-Landau parameter $κ$ from supercritical field measurements on superconducting microspheres are reexamined. The discrepancy in tin is shown to result from differing methods of analyses, whereas the discrepancy in indium is a consequence of significantly differing experimental results. The reanalyses however confirms the lower $κ$ determinations to within experimental uncertainties.
In this paper, we provide the different types of bifurcation diagrams for a superconducting cylinder placed in a magnetic field along the direction of the axis of the cylinder. The computation is based on the numerical solutions of the Ginzburg-Landau model by the finite element method. The response of the material depends on the values of the exterior field, the Ginzburg-Landau parameter and the size of the domain. The solution branches in the different regions of the bifurcation diagrams are analyzed and open mathematical problems are mentioned.
We present an analysis of the Ginzburg-Landau equations for the description of a two-dimensional superconductor in a bounded domain. Using the properties of a special integrability point of these equations which allows vortex solutions, we obtain a closed expression for the energy of the superconductor. The role of the boundary of the system is to provide a selection mechanism for the number of vortices. A geometrical interpretation of these results is presented and they are applied to the analysis of the magnetization recently measured on small superconducting disks. Problems related to the i…
Using Ginzburg-Landau theory, we have performed detailed studies of vortices in the presence of artificial defect arrays, for a thin film geometry. We show that when a vortex approaches the vicinity of a defect, an abrupt transition occurs in which the vortex core develops a ``string'' extending to the defect boundary, while simultaneously the supercurrents and associated magnetic flux spread out and engulf the defect. Current induced depinning of vortices is shown to be dominated by the core string distortion in typical experimental situations. Experimental consequences of this unusual depinn…
In these notes we discuss the topological nature of some problems in condensed matter physics. We adopt the language of differential geometry to present this subject and our aim is to develop some intuition towards concepts like curvature, fiber bundles, connexions, characteristic classes and topological invariants. The lectures end with a theoretical analysis of recent experimental results obtained on mesoscopic superconducting films.
In a class of two-component Ginzburg-Landau models (TCGL) with a U(1)$\times$U(1) symmetric potential, vortices with a condensate at their core may have significantly lower energies than the Abrikosov-Nielsen-Olesen (ANO) ones. On the example of liquid metallic hydrogen (LMH) above the critical temperature for protons we show that the ANO vortices become unstable against core-condensation, while condensate-core (CC) vortices are stable. For LMH the ratio of the masses of the two types of condensates, $M=m_2/m_1$ is large, and then as a consequence the energy per flux quantum of the vortices, $…
We study the interaction between the vortices in multi components superconductors based on the Jacobs and Rebbi variation method using Ginzburg-Landau theory. With one condensation, we get attraction interaction between the vortices for type I and repulsion for type II superconductors. With two condensation states such as Mg B_{2} superconductors the behavior is quite different. There is attraction at large distances and repulsion when the vortices are close to each other. A stability point at distance 2.7/λ_{1} is obtained. In the case of three condensation states such as iron based supercond…
We succeed to build up a straightforward theoretical model for spin-triplet p-wave superconductors by introducing in Ginzburg-Landau theory a second order parameter and a suitable interaction between the two mean fields.
Motivated by recent experimental progress in the critical regime of high-$T_c$ superconductors we show how the tricritical point in a superconductor can be derived from the Ginzburg-Landau theory as a consequence of vortex fluctuations. Our derivation explains why usual renormalization group arguments always produce a first-order transition, in contrast to experimental evidence and Monte Carlo simulations.
Under holographic prescription for Schwinger-Keldysh closed time contour for non-equilibrium system, we consider fluctuation effect of the order parameter in a holographic superconductor model. Near the critical point, we derive the time-dependent Ginzburg-Landau effective action governing dynamics of the fluctuating order parameter. In a semi-analytical approach, the time-dependent Ginzburg-Landau action is computed up to quartic order of the fluctuating order parameter, and first order in time derivative.
The Ginzburg-Landau theory of a trapped Fermi gas with a BEC-BCS crossover is derived by the path-integral method. In addition to the standard Ginzburg-Landau equation, a second equation describing the total atom density is obtained. These two coupled equations are necessary to describe both homogeneous and inhomogeneous systems. The Ginzburg-Landau theory is valid near the transition temperature $T_c$ on both sides of the crossover. In the weakly-interacting BEC region, it is also accurate at zero temperature where the Ginzburg-Landau equation can be mapped onto the Gross-Pitaevskii (GP) equa…
A boundary condition for the Ginzburg-Landau wave function at surfaces biased by a strong electric field is derived within the de Gennes approach. This condition provides a simple theory of the field effect on the critical temperature of superconducting layers.
In a recent paper we give the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Here we present our results in the simplified case of a one-dimensional system of particles interacting via a delta-potential.
We give a straightforward generalization of the Ginzburg-Landau theory for superconductors where the scalar phase field is replaced by an antisymmetric Kalb-Ramond field. We predict that at very low temperatures, where quantum phase effects are expected to play a significant role, the presence of vortices destroys superconductivity.
