Time-dependent Ginzburg-Landau Model Research Articles

A regularity criterion to the time-dependent Ginzburg-Landau model for superconductivity in [formula omitted

In this paper, we prove a regularity criterion ψ,A∈W:={(ψ,A)|∇ψ∈L2(0,T;Ln), A∈L∞(0,T;Ln)∩L2pp−n(0,T;Lp)} with n<p≤∞, for the nD(n≥3) time-dependent Ginzburg-Landau model in superconductivity. Finally, we show that this criterion holds true when n=3 or 4.

Global well-posedness of axially symmetric weak solutions to the Ginzburg–Landau model in superconductivity

ABSTRACT This paper proves global existence and uniqueness of axially symmetric weak solutions to the 3D time-dependent Ginzburg–Landau model in superconductivity in with initial data and the choice of Lorentz gauge. We are unable to prove a similar result with the Coulomb gauge.

High-Frequency Nonlinear Response of Superconducting Cavity-Grade Nb Surfaces

Nb Superconducting Radio-Frequency (SRF) cavities are observed to break down and lose their high-Q superconducting properties at accelerating gradients below the limits imposed by theory. The microscopic origins of SRF cavity breakdown are still a matter of some debate. To investigate these microscopic issues temperature and power dependent local third harmonic response was measured on bulk Nb and Nb thin film samples using a novel near-field magnetic microwave microscope between 2.9K-10K and 2GHz-6GHz. Both periodic and non-periodic response as a function of applied RF field amplitude are observed. We attribute these features to extrinsic and intrinsic nonlinear responses of the sample. The RF-current-biased Resistively Shunted Junction (RSJ) model can account for the periodic response and fits very well to the data using reasonable parameters. The non-periodic response is consistent with vortex semi-loops penetrating into the bulk of the sample once sufficiently high RF magnetic field is applied, and the data can be fit to a Time-Dependent Ginzburg-Landau (TDGL) model of this process. The fact that these responses are measured on a wide variety of Nb samples suggests that we have captured the generic nonlinear response of air-exposed Nb surfaces.

Dynamics of Domain Walls in a Fulde–Ferrell Superconductor

The mechanism of switching between different states of a quasi-one-dimensional current-carrying superconductor in the Fulde–Ferrell phase has been theoretically studied. It has been shown within the time-dependent Ginzburg–Landau model that switching at a current above a critical value occurs due to the appearance of finite domains with a nonzero electric field at the interface with a normal metal or in a “weak” place inside the superconductor and their motion along the superconductor. It has been found that each such soliton of the electric field corresponds to a moving domain wall that separates the parts of the superconductor with opposite directions of supervelocities and near which the absolute value of the superconducting order parameter is finite. The last property distinguishes such solitons from other well-known solitons in current-carrying superconductors, namely, moving Abrikosov or Josephson vortices.

Phase field modeling of domain dynamics and polarization accumulation in ferroelectric HZO

In this work, we investigate the accumulative polarization (P) switching characteristics in ferroelectric (FE) thin films under the influence of sequential sub-coercive electric-field pulses. Performing the dynamic phase-field simulation (based on time-dependent Landau-Ginzburg model) and experimental measurement on Hf0.4Zr0.6O2 (HZO), we analyze the electric field induced domain-wall (DW) motion and the resultant P accumulation process in FE. According to our analysis, even in the absence of an applied electric field, the DW can potentially undergo spontaneous motion. Such a DW instability leads to spontaneous P-excitation and relaxation processes, which play a pivotal role in accumulative P-switching in an FE grain. We show that the extent of such P accumulation increases with the increase in the applied electric field, increase in excitation time and decrease in relaxation time. Finally, by considering an ensemble of grains with local and global coercive field distributions, we model the P-accumulation process in a large area HZO sample. In such a multi-grain scenario, the dependency of P accumulation on the applied electric field pulse attributes follows similar features as that of a single-grain, although the spontaneous processes (excitation/relaxation) are less prominent in large area sample.

Simple theoretical proposal of the dependence of the deGennes extrapolation parameter with the surface temperature of a superconducting sample

The Time-dependent Ginzburg–Landau model (TDGLM) is a robust tool widely used to analyze the magnetization of the single-vortex state of a mesoscopic superconducting sample in presence of a magnetic field. The algorithm implemented in this work is applied to a square geometry surrounded by different kinds of materials simulated by deGennes extrapolation length . The inside of the sample remains at constant temperature , while its boundary remains at temperature . This temperature variation in the sample can be generated by a continuous laser wave injected into all the internal points, except for a thin surface layer in the boundary of the material. We found that the b value at , which mimics the magnetization curve for a corresponding , presents a linear dependence with the temperature. Therefore, although within the domain of validity TDGLM the parameter is to be considered temperature-independent in the vicinity of the bulk critical temperature and that depends on the density of states near the surface, we propose a simple dependence of using a TDGLM.

UNIFORM WELL-POSEDNESS FOR A TIME-DEPENDENT GINZBURG-LANDAU MODEL IN SUPERCONDUCTIVITY

We study the initial boundary value problem for a time-dependent Ginzburg-Landau model in superconductivity. First, we prove the uniform boundedness of strong solutions with respect to diffusion coefficient 0 < $\epsilon$ < 1 in the case of Coulomb gauge. Our second result is the global existence and uniqueness of the weak solutions to the limit problem when $\epsilon=0$.

Coherent order parameter dynamics in SmTe3

We present a combined ultrafast optical pump-probe and ultrafast x-ray diffraction measurement of the CDW dynamics in SmTe$_3$ at 300 K. The ultrafast x-ray diffraction measurements, taken at the Linac Coherent Light Source reveal a $\sim 1.55$ THz mode that becomes overdamped with increasing fluence. We identify this oscillation with the lattice component of the amplitude mode. Furthermore, these data allow for a more clear identification of the frequencies present in the optical pump-probe data. In both, reflectivity and diffraction, we observe a crossover of the response from linear (for small displacements) to quadratic in the amplitude of the order parameter displacement. Finally, a time-dependent Ginzburg-Landau model captures the essential features of the experimental observations.

Time-dependent Ginzburg–Landau model for light-induced superconductivity in the cuprate LESCO

Cavalleri and coworkers have discovered evidence of light-induced superconductivity and related phenomena in several different materials. Here, we suggest that some features may be naturally interpreted using a time-dependent Ginzburg–Landau model. In particular, we focus on the lifetime of the transient state in La1.675Eu0.2Sr0.125CuO4 (LESCO1∕8), which is remarkably long below about 25 K, but exhibits different behavior at higher temperature.

Effect of Background Magnetic Field on Type-II Superconductor under Oscillating Magnetic Field Simulated Using Ginzburg-Landau Model

Cubic superconducting sample was simulated using time-dependent Ginzburg-Landau model under oscillating magnetic field with and without additional background static magnetic field. Vortex dynamics including entrance and exit from the sample was simulated. Magnetization and carrier concentration densities of the sample were studied as a function of external magnetic field variations. Anomalies in carrier concentration density were observed at certain values of the magnetic field which were correlated with the entrance and exit processes of vortices. Area swept by superconductor magnetization with magnetic field was observed to have a hysteresis-like behavior where area representing energy dissipated per cycle. This energy accumulation was suggested to cause instability in superconductor over the number of cycles and may result in thermal quenching. Temporal distribution of energy components showed consistency with the pattern observed for carrier concentration and magnetization under oscillating magnetic field. Rapid phase changes with magnetic oscillations resulted in oscillations in energy components, and irregular peaks and ripples in superconducting energy represent the situation of exit and entry of vortices. While the rise in interaction energy with cycles is referred to vortex relaxation time in a cycle, this energy is expected to accumulate and take other forms (e.g., heat) and is predicted to cause thermal quenching. In the presence of background static magnetic field, this energy dissipation was calculated to increase significantly while superconductor is subjected to oscillating magnetic field.

Harmonic analysis of ferroelectric polarization dynamics simulated by a second-order Landau model

By using a second-order time-dependent Ginzburg–Landau model, we simulate the polarization hysteresis behavior of a ferroelectric system subjected to a sinusoidal electric field. We examine polarization hysteresis loop structure as a function of both field amplitude and field frequency. Departing from previous work, the relationship between these field parameters and loop structure is quantified by considering the Fourier transform spectra of the time series of polarization. These spectra are used to determine deforming factors that measure the amplitude- and frequency-dependent distortions of hysteresis loop structures from ellipticity. Our results agree with experimental observations, thus validating the model.

Kagome–Honeycomb structure produced using a wave laser in a conventional superconductor

Magnetization and Shubnikov-state in a mesoscopic superconducting sample (disk and square) with a Honeycomb–Kagome structure in regions with suppressed superconductivity, produced in the sample increasing the local temperature Td by using a continuous wave laser that emits a beam with a controlled heat output, are studied. The simple time-dependent Ginzburg–Landau model is used to describe the interaction of light with the superconducting sample, where the defects are include through the spatially-dependent-temperature. The quantized magnetic flux (vortices or Shubnikov-state) are located first in the depressed-superconducting regions (defects), in which is considered that Tc > Td > T (Tc is the critical temperature of the sample and T the temperature of the thermal bath in which the sample is immersed). Different signatures on the magnetization and the Shubnikov-state are observed in the presence of defects with different sizes rd and Td. Thus it is possible to control the magnetic response of the sample and to manipulate the vortex configuration without any structural changes that could include another kind of material.

Pico pulse response analysis of Josephson weak-link using time-dependent Ginzburg-Landau model

The pulse wave whose width is picosecond is called the pico pulse. In this paper, the pico pulse response analysis of high Tc superconducting Josephson weak-link made of Bi2Sr2Ca2Cu3O10 in the Terahertz (THz) region is reported. Since the photon energy of the THz radiation is greater than the energy gap of high Tc superconductor, the one dimensional time-dependent Ginzburg–Landau (TDGL) equation is used and the TDGL model as the equivalent circuit of Josephson weak-link instead of the Resistively-Shunted-Junction model is derived by use of the TDGL equation. It is found that the peak value of pulse response decreases when the pulse width decreases.

Uniform regularity for a 3D time-dependent Ginzburg–Landau model in superconductivity

In this paper, we prove the uniform-in-σ regularity for 3D time-dependent Ginzburg–Landau model in superconductivity in the case of Coulomb gauge. Here σ is the normal conductivity of the superconducting material.

Global Well-posedness of Weak Solutions to the Time-dependent Ginzburg-Landau Model for Superconductivity

We prove the global existence and uniqueness of weak solutions to the time dependent Ginzburg-Landau system in superconductivity with Coulomb gauge.

Dynamics of superconducting order parameter through ultrafast normal-to-superconducting phase transition in Bi2Sr2CaCu2O8+δ from multipulse polarization-resolved transient optical reflectivity

A systematic temperature dependent study of the femtosecond optical superconducting (SC) state destruction and recovery in Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ cuprate superconductor by means of the all-optical polarization-sensitive multi-pulse spectroscopy is presented. At low temperatures and a partial SC state suppression an anisotropic SC-gap recovery-timescale is suggested by the data. The SC state destruction and recovery dynamics are compared to the recent TR-ARPES-inferred SC-gap dynamics and a qualitative agreement is found. Using a phenomenological response function the experimental data are also compared to time dependent Ginzburg-Landau model simulations.

Parallel magnetic field suppresses dissipation in superconducting nanostrips

The motion of Abrikosov vortices in type-II superconductors results in a finite resistance in the presence of an applied electric current. Elimination or reduction of the resistance via immobilization of vortices is the "holy grail" of superconductivity research. Common wisdom dictates that an increase in the magnetic field escalates the loss of energy since the number of vortices increases. Here we show that this is no longer true if the magnetic field and the current are applied parallel to each other. Our experimental studies on the resistive behavior of a superconducting Mo0.79Ge0.21 nanostrip reveal the emergence of a dissipative state with increasing magnetic field, followed by a pronounced resistance drop, signifying a reentrance to the superconducting state. Large-scale simulations of the 3D time-dependent Ginzburg-Landau model indicate that the intermediate resistive state is due to an unwinding of twisted vortices. When the magnetic field increases, this instability is suppressed due to a better accommodation of the vortex lattice to the pinning configuration. Our findings show that magnetic field and geometrical confinement can suppress the dissipation induced by vortex motion and thus radically improve the performance of superconducting materials.

Ferroelectric system dynamics simulated by a second-order Landau model

By using a second-order time-dependent Ginzburg–Landau model, we simulate the dynamic polarization hysteresis behavior of a ferroelectric system subjected to a sinusoidal electric field. We examine polarization hysteresis loop structure as a function of both field amplitude and field frequency. The relationship between the latter and hysteresis loop area, i.e., hysteresis dispersion, is calculated. Departing from previous work that established that the considered model produces experimentally expected hysteresis dispersion in the low-frequency regime, we demonstrate that (i) this model also produces experimentally expected hysteresis dispersion in the high-frequency regime; (ii) this dispersion implies, in agreement with experimental observations, that system relaxation is characterized by an effective characteristic time which is inversely proportional to field amplitude when the latter is sufficiently high; and (iii) the considered model predicts a symmetry-breaking transition that depends on both field frequency and field amplitude.

Numerical Simulations of Directed Self-Assembly in Diblock Copolymer Films using Zone Annealing and Pattern Templating

Bulk fabrication of surface patterns with sub-20 nm feature sizes is immensely desirable for many existing and emerging technologies. Directed self-assembly (DSA) of block copolymers (BCPs) has been a recently demonstrated approach to achieve such feature resolution over large-scale areas with minimal defect populations. However, much work remains to understand and optimize DSA methods in order to move this field forward. This paper presents large-scale numerical simulations of zone annealing and chemo-epitaxy processing of BCP films to achieve long-range orientational order. The simulations utilize a Time-Dependent Ginzburg-Landau model and parallel processing to elucidate relationships between the magnitude and velocity of a moving thermal gradient and the resulting BCP domain orientations and defect densities. Additional simulations have been conducted to study to what degree orientational order can be further improved by combining zone annealing and chemo-epitaxy techniques. It is found that these two DSA methods do synergistically enhance long-range order with a particular relationship between thermal gradient velocity and chemical template spacing.

The out of plane a.c. fluctuation conductivity of superconductor under magnetic field

The time-dependent Ginzburg-Landau model with thermal noise is used to calculate the out of plane a.c. fluctuation conductivity of type-II superconductor under magnetic field. We assume that thermal fluctuations, represented by the Langevin white noise, are strong enough to melt the Abrikosov vortex lattice created by the magnetic field into a moving vortex liquid. The nonlinear interaction term in the time-dependent Ginzburg-Landau equation is treated within the self-consistent Gaussian approximation. The real and imaginary parts of the out of plane a.c. fluctuation conductivity formula are summation over all Landau levels to treat arbitrary magnetic fields. Our results indicate that high frequencies can be effectively used to suppress the out-of-plane a.c. fluctuation conductivity in high-temperature superconductors. The results also have refined analytical form and are fitted well to experimental data on high-Tc superconductor. The results in two-dimensional and three-dimensional limits are directly inferred from the corresponding result of the layered model.