Time-dependent Ginzburg Research Articles

Single-Defect-Induced Peculiarities in Inverse Faraday-Based Switching of Superconducting Current-Carrying States near a Critical Temperature

The Inverse Faraday Effect (IFE) is a phenomenon that enables non-thermal magnetization in various types of materials through the interaction with circularly polarized light. This study investigates the impact of single defects on the ability of circularly polarized radiation to switch between distinct superconducting current states, when the magnetic flux through a superconducting ring equals half the quantum flux, Φ0/2. Using both analytical methods within the standard Ginzburg–Landau theory and numerical simulations based on the stochastic time-dependent Ginzburg–Landau approach, we demonstrate that while circularly polarized light can effectively switch between current-carrying superconducting states, the presence of a single defect significantly affects this switching mechanism. We establish critical temperature conditions above which the switching effect completely disappears, offering insights into the limitations imposed by a single defect on the dynamics of light-induced IFE-based magnetization in superconductors.

An investigation of rapid surface melting in nanowires

The investigation into virtual melting phenomena in nanowires holds significant relevance owing to its profound impact on material durability under extreme loading conditions. Thus, the exploration of this pivotal plastic deformation mechanism is undertaken utilizing the phase-field methodology. Employing a monolithic solver, we solve the coupled highly nonlinear time-dependent Ginzburg–Landau equation and dynamic elasticity equation. Our analysis encompasses the consideration of surface tension stress in conjunction with a coherent solid–liquid interface subjected to uniaxial transformation strain, thereby unveiling intriguing facets of melting phenomena. The investigation delves into the influence of transformation strain, kinetic coefficient, and temperature on the thickness of the solid–liquid interface and its corresponding velocity. This analysis is conducted through meticulous comparison with existing experimental data and molecular dynamics simulation. Moreover, employing the phase-field method yields precise descriptions of the system kinetics, capturing virtual melting phenomena in both pristine and flawed nanowire configurations.

Impact of magnetic field variation on thermally annealed tantalum-filled vertical superconducting interconnects for scalable quantum computing systems

Efforts to scale down advanced quantum processors with more numbers of qubits offer challenges since the integration of qubits is a significant obstacle in the path. Superconducting vertical interconnects in 3D IC integration can provide a crucial solution for wiring complexities, as shorter interconnections reduce energy loss when working in cryogenic conditions with better signal fidelity. Using the time-dependent Ginzburg–Landau equation, this simulation study analyzes vertical superconducting interconnects filled with materials like tantalum, niobium, and thermally annealed tantalum. It also investigates how London penetration depth (temperature-dependent) and magnetic fields affect Cooper pair density and, consequently, current density.

Effect of grain size and grain boundary on the energy storage performance of polycrystalline ferroelectrics

Dielectric capacitors based on polycrystalline ferroelectrics have attracted much attention due to their significant power density and fast charge–discharge speed. The energy storage performance of polycrystalline ferroelectrics is highly dependent on the grain size and grain boundary. Here, the effect of grain size and grain boundary on the domain structures and polarization–electric field (P–E) hysteresis loops of polycrystalline ferroelectrics are investigated by using a phase-field model based on the time dependent Ginzburg–Landau (TDGL) equation. It is found that the depolarization field in the grain boundary induces the vortex domain when the grain size is reduced or the grain boundary thickness increases in certain extent, resulting in slender P–E loops, which contributes to an improvement in the energy storage efficiency and density. However, as the grain size further decreases or the grain boundary thickness further increases, the energy storage density decreases, which is attributed to the concurrent reduction in both the remnant and saturation polarizations. This study provides a considerable insight for optimizing the energy storage performance by carefully adjusting the grain size and grain boundary thickness in polycrystalline ferroelectrics.

Angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor

We use time-dependent Ginzburg–Landau theory in a three-dimensional model, including thermal noise, to analyze angle-dependent Hall resistivity and longitudinal resistivity of type-II superconductor. The Hall resistivity and longitudinal resistivity are calculated as functions of temperature, magnetic field and the angle θ between the magnetic field and the ab-plane in the vortex-liquid regime. Our theoretical calculations within a self-consistent fluctuation approximation for MgB2 and HgBa2CaCu2O6 materials are in good agreements with the experimental findings for both below and above the critical temperature Tc. We observe that when the field angle decreases, the transition temperature increases and the magnitude of longitudinal resistivity decreases, which is qualitatively comparable to decrease of the perpendicular field component. However, when the magnetic field direction approaches the layer surface, it shows a clear different effect from that of a perpendicular field with the same normal component.

Stable implicit numerical algorithm of time-dependent Ginzburg–Landau theory coupled with thermal effect for vortex behaviors in hybrid superconductor systems

Stable implicit numerical algorithm of time-dependent Ginzburg–Landau theory coupled with thermal effect for vortex behaviors in hybrid superconductor systems

Fluctuation effects in superconducting nanowires under electric field

This study applies the time-dependent Ginzburg–Landau (TDGL) theory with thermal noise to analyze the thermoelectric and transport properties of superconducting Sn nanowires, focusing on the thermopower (αxx) and the phase transition characteristics in the S-shaped J-E curves. We observe significant contributions from superconducting Cooper pairs, which remain nonzero above the critical temperature (Tc), indicating residual superconductivity due to strong thermal fluctuations. The S-like shape in the J-E curves is attributed to a dynamical instability transition temperature (T∗) at approximately 2.9 K, where thermal fluctuations dominate. Furthermore, we compare the resistance in the linear response to experimental data for Sn nanowires both below and above Tc. Below Tc, the resistance sharply decreases, reflecting the robust superconducting state, while above Tc, it increases, aligning with normal state behavior. In nonlinear response case, our results indicate that high electric fields can be effectively used to suppress order-parameter fluctuations and the electrical conductivity in superconducting nanowires. The findings provide critical insights into the thermoelectric behavior and phase transitions in Sn nanowires, highlighting the importance of Cooper pair dynamics in shaping the transport properties of one-dimensional superconductors. This understanding is essential for the development of advanced nanoelectronic devices leveraging these unique superconducting properties.

Multi-doping effect on the martensitic transformation behavior of shape memory alloys

Incorporating various elements into host shape memory alloys (SMAs) has proven to be an effective strategy for optimizing their functional properties. However, modeling the complex multi-doping effect is challenging. In the present study, we introduced a phenomenological model based on Ginzburg–Landau theory, wherein each doping element is conceptualized as an internal dilatational stress. This internal stress is represented as a spatial Gaussian distribution characterized by two influential parameters: potency (h) and range (σ). The interaction between doping elements arises from the superposition of these stresses. Utilizing a time-dependent Ginzburg–Landau simulation based on our proposed model, diverse combinations of h and σ replicate the varied experimental outcomes associated with multi-doping effects. This model offers insight into the understanding of the doping impact on martensitic transformation and may contribute to the development of SMAs with tailored properties.

A simple displacement perturbation method for phase-field modeling of ferroelectric thin film

A displacement perturbation method is proposed for phase-field simulations of the ferroelectric domain structures. A temperature-misfit strain phase diagram is computed to validate this method's accuracy, encompassing rhombohedral, orthorhombic, tetragonal, cubic, and mixed phases by comparing with previous phase-field simulations. The change in free energy density surface with temperature and strain distribution is computed to clarify the mechanism of the mixed phase. The phase diagram, ferroelectric hysteresis, and domain structure all demonstrate that the numerical method of displacement discretization is reliable and practical in solving the time-dependent Ginzburg–Landau equation, consistent with previous simulated and experimental results. This new method offers the advantages of simple programming and easy parallelism, paving the way for advancements in phase-field modeling.

Ginzburg–Landau simulations of three-terminal operation of a superconducting nanowire cryotron

Abstract Superconducting nanowire cryotrons (nTrons) are expected to be used as interfaces for super-high-performance hybrid devices in which superconductor and semiconductor circuits are combined. However, nTrons are still under development, and diverse analyses of these devices are needed. Accordingly, we have developed a numerical technique to simulate the three-terminal operation of an nTron by using the finite element method to solve the time-dependent Ginzburg–Landau (TDGL) equation and the heat-diffusion equation. Simulations using this technique offer understanding of the dynamics of the order parameter, the thermal behavior, and the characteristics of three-terminal operation, and the TDGL model reproduces qualitatively the results of nTron experiments conducted at the Massachusetts Institute of Technology. In addition, we investigated how some geometric and physical parameters (the design elements) affect the operation characteristics. The TDGL model has far fewer free parameters compared with the lumped-element electrothermal model commonly used for simulating superconducting devices. Furthermore, the TDGL model provides time-dependent visual information about the superconducting state and the normal state, thereby offering insights into the relationship between nTron geometry and three-terminal operation. These simulation results offer a route to nTron optimization and the development of nTron applications.

A Comparative Computational Study of the Solidification Kinetic Coefficients for the Soft-Sphere BCC-Melt and the FCC-Melt Interfaces

Using the non-equilibrium molecular dynamics (NEMD) simulations and the time-dependent Ginzburg–Landau (TDGL) theory for solidification kinetics, we study the crystal-melt interface (CMI) kinetic coefficients for both the soft-sphere (SS) BCC-melt and the FCC-melt interfaces, modeled with the inverse-power repulsive potential (n=8). The collective dynamics of the interfacial liquids at four equilibrium CMIs are calculated and employed to eliminate the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. The speedup of the two modes of the interfacial liquid collective dynamics (at wavenumbers equal to the principal and the secondary reciprocal lattice vector of the grown crystal) at the equilibrium FCC CMI is observed. The calculated local collective dynamics of the SS BCC CMIs are compared with the previously reported data for the BCC Fe CMIs, validating a hypothesis proposed recently that the density relaxation times of the interfacial liquids at the CMIs are anisotropic and material dependent. With the insights provided by the improved application of the TDGL solidification theory, an attempt has been made to interpret the variation physics of the crystal-structure dependence of the solidification kinetic coefficient.

The local rupture of the superconductivity and the curvature of the mesoscopic sample

In this article we revisit a well-known effect in superconductors, which is the penetration of the magnetic field by regions of greater radius of curvature (Tinkham, 2008; De Gennes, 1966). This is exposed in the literature but without a quantitative solution. Here we solve this problem by two distinct numerical simulations. We calculate the superconducting current density using numerical simulations via the London theory in the Meissner state and numerical simulations using the time-dependent Ginzburg–Landau (TDGL) theory for the vortex state. In both simulations, the results obtained are in agreement, as could not be otherwise. We show that in the Meissner state the current density increases much faster in the region where the radius of curvature is larger, thus reaching the critical value first in this location, and therefore local breakdown of superconductivity occurs. In the vortex state, our simulations, using TDGL, show that the vortices penetrate through exactly the same location pointed out by the previous simulation. For this study we worked with a superconducting needle with an ellipsoidal mesoscopic cross section.

Asymmetric fracture behavior in ferroelectric materials induced by flexoelectric effect

Ferroelectric materials are widely used in actuators, exciters, and memory devices due to their excellent electromechanical properties. However, the instinctive brittleness of ferroelectric materials makes them easy to fracture under external load. Since giant strain gradient can be easily generated near the crack tip, the flexoelectric effect is indispensable in the research of fracture properties of ferroelectric materials. With the combination of time-dependent Ginzburg–Landau theory and phase-field model, the electromechanical behavior of PbTiO3 in the vicinity of the crack tip is determined in this work. The simulation results demonstrate that the domain structure near the crack tip becomes asymmetric with the flexoelectric effect. The polarization switching-induced toughening, which is characterized by the J-integral, depends on the direction of the crack relative to the original polarization orientation. Furthermore, the longitude flexoelectric coefficient f11 has more significant impact on the fracture toughness than that of the transverse flexoelectric coefficient f12 and the shear flexoelectric coefficient f44. The results of the present work suggest that the flexoelectric effect must be considered in the reliable design of ferroelectric devices.

Effect of defects on flux expulsion of pure niobium superconducting radio frequency cavities via spatial temperature gradient

Since flux vortices are easily pinned by defects in superconducting radio frequency (SRF) cavities, trapped magnetic flux increases the surface resistance of the SRF cavity. It has been experimentally demonstrated that trapped magnetic flux can be expelled by cooling down a superconducting cavity under a large spatial temperature gradient. In this paper, we use the time-dependent Ginzburg–Landau (TDGL) theory to theoretically investigate the effect of defects on the flux expulsion ability of pure niobium superconducting cavities with an applied spatial temperature gradient. It is shown that the residual flux vortex density displays a notable stepwise decreasing trend with increasing temperature gradient at smaller residual fields, while it shows a stepwise rising with increasing defect size. Both larger defect number and size make vortices difficult to be expelled. Moreover, long cooling time is beneficial for vortices to be expelled, and the cooling time has nearly no significant effect on flux expulsion under conditions of large cooling times. The results in this paper provide some theoretical guidelines for improving the performance of superconducting cavities in practical situations.

Combined FEM and phase field method for reliability design of forward degradation in SiC bipolar device

The reliability of 4H-SiC bipolar devices is compromised by the expansion of single Shockley stacking faults (SSFs) during forward-current operation. Because SSF expansion is governed by multiphysical aspects, including electrical, thermal, and stress states, analysis of the mounted structure is important for improving power module design. We propose a practical design method that analyzes the critical condition due to SSF expansion using a combined method with a multiphysical finite element method (FEM) and phase field model based on the time-dependent Ginzburg–Landau equation. In preliminary studies, the thermal deformation of the demonstration module and the variation of threshold current of a bar-shaped SSF were verified from experimental and reference data. Estimating the SSF expansion rate on the constructed response surface under the mutiphysical inputs from FEM, the proposed design method can be used effectively in the design process by changing the various design variables.

A phase-field model for ferroelectric materials—Based on the multiphase-field method

A novel phase-field model is developed to investigate the domain structure in ferroelectric materials subjected to an external field. Differing from the time-dependent Ginzburg–Landau (TDGL) theory that describes domain structures based on the spatial and temporal evolution of polarization, our model utilizes the multiphase-field approach to calculate domain structures by minimizing the total energy functional with respect to the multiphase-field order parameter ϕ. The energy functional in the proposed model comprises the general multiphase interfacial energy and the phase-dependent bulk energy, accounting for the contributions from domain walls, and mechanical as well as electric fields. By considering the interplay between the different energy components, the model provides insights into the complex domain structure of ferroelectric materials and their response to external stimuli. This comprehensive approach is validated through simulations of both single-crystal and polycrystalline structures. The approach presented in this study simplifies the computational coefficients required to analyze the domain structure in ferroelectric materials, compared to the TDGL approach, by disregarding the Landau potential. This makes it possible to analyze the domain structure of materials without Landau coefficients. Furthermore, the proposed model serves as a reference for applying the multiphase-field concept to ferroelectric materials.

Helicity-controlled switching of superconducting states by radiation pulse

We provide a theoretical analysis of the possibility of using circularly polarized radiation to switch between two different quantum states of a superconducting nanoring subjected to the half quantum flux. Numerical modeling, performed in the framework of the time-dependent Ginzburg–Landau equation, reveals the condition for on-demand switching between current-carrying states with different helicities with 100% probability. An experimental demonstration of this effect will be unambiguous evidence of the inverse Faraday effect in superconductors and pave the way for the design of light-operated superconducting devices.

On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity

On the numerical stability and transitional stages of time-dependent Ginzburg–Landau model of superconductivity

Disorder enhanced dynamical heterogeneity in strain glass alloys.

An open question related to strain-glass (STG) alloys is whether they process similar dynamical behaviors to other glass systems. In the present work, we investigate the reorientation process of martensite domains in both STG and martensitic alloys. Our results show the presence of highly doped point defects can greatly intensify the dynamical heterogeneity and spatiotemporal correlation in ferroelastic or shape memory alloy systems, which are also two main hallmarks of structural glasses. What's more, we find that such dynamic heterogeneity exists in a different range spanning microscopic to mesoscopic scales, indicated by our molecular dynamic (MD) simulations and time-dependent Ginzburg-Landau (TDGL) modeling. Dopant atoms induced transient strain networks, i.e., spatial correlated local lattice distortion, is a response for such heterogeneous dynamics. The present study thus solidifies strain glass as a new state of matter and may provide guidelines for developing new strain glass alloys.&#xD.

Fast Multigrid Simulations of Pinning in REBCO With Highly Resistive Nanorods

A geometric multigrid method is applied to the frozen-field time-dependent Ginzburg–Landau equations for anisotropic superconductors with spatially varying material properties. This reduces the simulation time for critical current determination in large 3D systems by up to two orders of magnitude compared with a single grid. Critical current density calculations are presented for a model of REBCO tape with nanorod artificial pinning centers. The model consists of an anisotropic superconducting matrix with embedded nanorods which are treated as isotropic highly resistive cylinders. The effects of varying the density, splay, and conductivity of the nanorods are considered. Increasing the resistivity of the nanorods profoundly affects the critical current density in high fields, where current paths are percolative in the vicinity of matrix-pin interfaces and persist well above the upper critical field of the superconducting matrix.