Three-dimensional Ginzburg-Landau Research Articles

Second-order chiral phase transition in three-flavor quantum chromodynamics?

We calculate the renormalization group flows of all perturbatively renormalizable interactions in the three-dimensional Ginzburg-Landau potential for the chiral phase transition of three-flavor quantum chromodynamics. On the contrary to the common belief we find a fixed point in the system that is able to describe a second-order phase transition in the infrared. This shows that long-standing assumptions on the transition order might be false. If the transition is indeed of second order, our results may hint that the axial $U(1)$ symmetry restores at the transition temperature.

Static properties of superconducting pyramidal STM tip in the presence of a vortex

Stationary properties of a superconducting STM tip are studied in the presence of a vortex by applying three-dimensional Ginzburg-Landau formalism. The free energy of the tip is studied in detail to analyze different vortex states. Cooper pairs and corresponding screening current density are studied in the different positions of the tip. Obtained results are important to comprehend the static phenomenon of the STM tip in real-life applications.

Concentration Behavior and Lattice Structure of 3D Surface Superconductivity in the Half Space

We study the three-dimensional Ginzburg-Landau model of superconductivity for strong applied magnetic fields varying between the second and third critical fields. In this regime, it is known from physics that superconductivity should be essentially restricted to a thin layer along the boundary of the sample. This leads to the introduction of a Ginzburg-Landau model on a half-space. We prove that the non-linear Ginzburg-Landau energy on the half-space with constant magnetic field is a decreasing function of the angle $\nu$ that the magnetic field makes with the boundary. In the case when the magnetic field is tangent to the boundary ($\nu=0$), we show that the energy is determined to leading order by the minimization of a simplified 1D functional in the direction perpendicular to the boundary. We also study the geometric behavior of the order parameter near the surface of the sample by constructing formal solutions with lattice properties.

Analysis of minimizers of the Lawrence-Doniach energy for superconductors in applied fields

We analyze minimizers of the Lawrence-Doniach energy for layered superconductors with Josephson constant $ \lambda $ and Ginzburg-Landau parameter $ 1/\epsilon $ in a bounded generalized cylinder $ D = \Omega\times[0, L] $ in $ \mathbb{R}^3 $, where $ \Omega $ is a bounded simply connected Lipschitz domain in $ \mathbb{R}^2 $. Our main result is that in an applied magnetic field $ \vec{H}_{ex} = h_{ex}\vec{e}_{3} $ which is perpendicular to the layers with $ \left|\ln\epsilon\right|\ll h_{ex}\ll\epsilon^{-2} $, the minimum Lawrence-Doniach energy is given by $ \frac{|D|}{2}h_{ex}\ln\frac{1}{\epsilon\sqrt{h_{ex}}}(1+o_{\epsilon, s}(1)) $ as $ \epsilon $ and the interlayer distance $ s $ tend to zero. We also prove estimates on the behavior of the order parameters, induced magnetic field, and vorticity in this regime. Finally, we observe that as a consequence of our results, the same asymptotic formula holds for the minimum anisotropic three-dimensional Ginzburg-Landau energy in $ D $ with anisotropic parameter $ \lambda $ and $ o_{\epsilon, s}(1) $ replaced by $ o_{\epsilon}(1) $.

Geometry-driven vortex states in type-I superconducting Pb nanowires

Hall probe magnetometry has been used to investigate the magnetization of individual cylindrically shaped Pb nanowires grown by electrocrystallization on a highly oriented pyrolytic graphite electrode. These measurements have been interpreted by comparison with three-dimensional Ginzburg-Landau (GL) calculations for nanowires with our sample parameters. We find that the measured superheating field and the critical field for surface superconductivity are strongly influenced by the temperature-dependent coherence length, $\ensuremath{\xi}(T)$ and penetration depth $\ensuremath{\lambda}(T)$ and their relationship to the nanowire diameter. As the temperature is increased toward ${T}_{c}$ this drives a change in the superconductor-normal transition from first order irreversible to first order reversible and finally second order reversible. We find that the geometrical flux confinement in our type-I nanowires leads to the formation of a one-dimensional row of single-quantum vortices. While GL calculations show a quite uniform distribution of vortices in thin nanowires, clear vortex bunching is found as the diameter increases, suggesting a transition to a more classical type-I behavior. Subtle changes in minor magnetization loops also indicate that slightly different flux configurations can form with the same vorticity, which depend on the sample history.

Collisions between spinning and nonspinning co-axial three-dimensional Ginzburg-Landau solitons

We report results of the first analysis of collisions between stable fundamental (alias spinless) and vortical (spinning) three-dimensional dissipative solitons in a model of a laser cavity. The systematic analysis is carried out for values S=1 and S=2 of the vorticity of the latter soliton. With the increase of the collision momentum, Χ, the same generic scenarios are observed in either case: merger into a single fundamental soliton at both small and relatively large values of Χ, and the formation of two fundamental solitons in an intermediate interval of variation of the collision momentum Χ. At very large values of Χ, the collision seems quasi-elastic, but the vortex soliton eventually splits into two nonspinning fragments.

Collisions between counter-rotating solitary vortices in the three-dimensional Ginzburg-Landau equation

We report results of collisions between coaxial vortex solitons with topological charges +/-S in the complex cubic-quintic Ginzburg-Landau equation. With the increase of the collision momentum, merger of the vortices into one or two dipole or quadrupole clusters of fundamental solitons (for S=1 and 2, respectively) is followed by the appearance of pairs of counter-rotating "unfinished vortices," in combination with a soliton cluster or without it. Finally, the collisions become elastic. The clusters generated by the collisions are very robust, while the "unfinished vortices," eventually split into soliton pairs.

Self-stabilized spatiotemporal dynamics of dissipative light bullets generated from inputs without spherical symmetry in three-dimensional Ginzburg-Landau systems

In order to meet experimental conditions, the generation, evolution, and self-stabilization of optical dissipative light bullets from non-spherically-symmetric input pulses is studied. Steady-state solutions of the $(3+1)$-dimensional complex cubic-quintic Ginzburg-Landau equation are computed using the variational approach with a trial function asymmetric with respect to three transverse coordinates. The analytical stability criterion is extended to systems without spherical symmetry, allowing determination of the domain of dissipative parameters for stable solitonic solutions. The analytical predictions are confirmed by numerical evolution of the asymmetric input pulses toward stable dissipative light bullets. Once established, the dissipative light bullet remains surprisingly robust.

Three-dimensional Ginzburg-Landau simulation of a vortex line displaced by a zigzag of pinning spheres

A vortex line is shaped by a zigzag of pinning centers and we study here how far the stretched vortex line is able to follow this path. The pinning center is described by an insulating sphere of coherence length size such that in its surface the de Gennes boundary condition applies. We calculate the free energy density of this system in the framework of the Ginzburg-Landau theory and study the critical displacement beyond which the vortex line is detached from the pinning center.

Effective lowest Landau level treatment of demagnetization in superconducting mesoscopic disks

Demagnetization, which is inherently present in the magnetic response of small finite-size superconductors, can be accounted for by an effective $\kappa$ within a two-dimensional lowest Landau level approximation of the Ginzburg-Landau functional. We show this by comparing the equilibrium magnetization of superconducting mesoscopic disks obtained from the numerical solution of the three-dimensional Ginzburg-Landau equations with that obtained in the ``effective'' LLL approximation.

Critical fluctuations at the superconducting transition of TmBa 2Cu 3O 7−δ thin films in transverse and longitudinal magnetic fields

We report an investigation of the resistive transition from the normal to the mixed state of TmBa 2Cu 3O 7−δ thin films in different orientations of magnetic fields up to 13 T. The broadening of the transition and its specific shape obscures the superconducting phase transition line T c( B). Using the renormalized theory for critical superconducting fluctuations in the anisotropic three-dimensional Ginzburg-Landau model by R. Ikeda we obtained and excellent description of the upper part of the resistive transition in transverse magnetic fields. In the longitudinal orientation, the broadening of the superconducting transition in a magnetic field is significantly smaller, in qualitative agreement with theory.

A model for variable thickness superconducting thin films

A model for superconductivity in thin films having variable thickness is derived through an averaging process across the film. When the film is of uniform thickness the model is identical to a model for superconducting cylinders as the Ginzburg-Landau parameter tends to ∞. This means that all superconducting materials, whether type I or type II in bulk, behave as type-II superconductors when made into sufficiently thin films. When the film is of non-uniform thickness the variations in thickness appear as spatially varying coefficients in the thin-film differential equations. After providing a formal derivation of the model, some results about solutions of the variable thickness model are given. In particular, it is shown that solutions obtained from the new model are an appropriate limit of a sequence of averages of solutions of the three-dimensional Ginzburg-Landau model as the thickness of the film tends to zero. An application of the variable thickness thin film model to flux pinning is then provided. In particular, the results of a numerical calculation are given that show that the vortex-like structures present in superconductors are attracted to relatively thin regions.

A model for superconducting thin films having variable thickness

A two-dimensional macroscopic model for superconductivity in thin films having variable thickness is derived through an averaging process across the film thickness. The resulting model is similar to the well-known Ginzburg-Landau equations for homogeneous, isotropic materials, except that a function that describes the variations in the thickness of the film now appears in the coefficients of the differential equations. Some results about solutions of the variable thickness model are then given, including existence of solutions and boundedness of the order parameter. It is also shown that the model is consistent in the sense that solutions obtained from the new model are an appropriate limit of a sequence of averages of solutions of the three-dimensional Ginzburg-Landau model as the thickness of the film tends to zero. An application of the variable thickness thin film model to flux pinning is then provided. In particular, the results of numerical calculations are given that show that the vortex-like structures that are present in certain superconductors are attracted re relatively thin regions in a material sample. Finally, extensions of the model to other settings are discussed.

Large-Order Behavior of the Perturbation Series for Superconductors nearHc2

The perturbation series for superconductors near ${H}_{c2}$ are studied in the two- and three-dimensional Ginzburg-Landau model. The large-order behavior is discussed first on a theoretical basis by an instanton method of Lipatov type. The results are compared with an eleventh-order calculation in 2D and a sixth-order one in 3D and show good agreement with the theoretical prediction. The conjectures based upon an Abrikosov lattice configuration seem to be ruled out.

Angular dependence of the upper critical field of Bi2.2Sr2Ca0.8Cu2O8+ delta.

We have measured the electrical resistivity of Bi2.2Sr2Ca0.8Cu2O8+δ in the vicinity of Tc for various angles between the [CuO2]∞ double layers of the crystal and the magnetic field. Defining Tc at the transition midpoints, we have measured values for –dH∥c2/dT=45 T/K and –dH⊥c2/dT=0.75 T/K for the magnetic field parallel and perpendicular to the [CuO2]∞ planes, respectively. This results in an anisotropy of a factor 60. The numerical results are sensitive to the definition of Tc and larger values for the anisotropy cannot be excluded. The results are compared with the anisotropic three-dimensional Ginzburg-Landau theory.

Theory of charge-density-wave dynamics.

A theoretical model is developed to describe the polarization and depinning of charge-density waves (CDW's) in the inorganic linear-chain compounds which exhibit Fr\ohlich sliding conduction. Each individual impurity within the crystal is assumed to pin the CDW phase very strongly at the impurity site, and dc CDW motion is made possible only by phase slip. Simple estimates are obtained for most observed properties of sliding CDW systems with use of a three-dimensional Ginzburg-Landau analysis. These predictions are found to be in excellent quantitative agreement with available experimental data characterizing virtually every aspect of CDW dynamics.