Time-dependent Ginzburg-Landau Model Research Articles

Solving high-dimensional Fokker-Planck equation with functional hierarchical tensor

This work is concerned with solving high-dimensional Fokker-Planck equations with the novel perspective that solving the PDE can be reduced to independent instances of density estimation tasks based on the trajectories sampled from its associated particle dynamics. With this approach, one sidesteps error accumulation occurring from integrating the PDE dynamics on a parameterized function class. This approach significantly simplifies deployment, as one is free of the challenges of implementing loss terms based on the differential equation. In particular, we introduce a novel class of high-dimensional functions called the functional hierarchical tensor (FHT). The FHT ansatz leverages a hierarchical low-rank structure, offering the advantage of linearly scalable runtime and memory complexity relative to the dimension count. We introduce a sketching-based technique that performs density estimation over particles simulated from the particle dynamics associated with the equation, thereby obtaining a representation of the Fokker-Planck solution in terms of our ansatz. We apply the proposed approach successfully to three challenging time-dependent Ginzburg-Landau models with hundreds of variables.

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.

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

Ultrafast Switching from the Charge Density Wave Phase to a Metastable Metallic State in 1T-TiSe_{2}.

The ultrafast electronic structures of the charge density wave material 1T-TiSe_{2} were investigated by high-resolution time- and angle-resolved photoemission spectroscopy. We found that the quasiparticle populations drove ultrafast electronic phase transitions in 1T-TiSe_{2} within 100fs after photoexcitation, and a metastable metallic state, which was significantly different from the equilibrium normal phase, was evidenced far below the charge density wave transition temperature. Detailed time- and pump-fluence-dependent experiments revealed that the photoinduced metastable metallic state was a result of the halted motion of the atoms through the coherent electron-phonon coupling process, and the lifetime of this state was prolonged to picoseconds with the highest pump fluence used in this study. Ultrafast electronic dynamics were well captured by the time-dependent Ginzburg-Landau model. Our work demonstrates a mechanism for realizing novel electronic states by photoinducing coherent motion of atoms in the lattice.

PyTDGL: Time-dependent Ginzburg-Landau in Python

Time-dependent Ginzburg-Landau (TDGL) theory is a phenomenological model for the dynamics of superconducting systems. Due to its simplicity in comparison to microscopic theories and its effectiveness in describing the observed properties of the superconducting state, TDGL is widely used to interpret or explain measurements of superconducting devices. Here, we introduce pyTDGL, a Python package that solves a generalized TDGL model for superconducting thin films of arbitrary geometry, enabling simulations of vortex and phase dynamics in mesoscopic superconducting devices. pyTDGL can model the nonlinear magnetic response and dynamics of multiply connected films, films with multiple current bias terminals, and films with a spatially inhomogeneous critical temperature. We demonstrate these capabilities by modeling quasi-equilibrium vortex distributions in irregularly shaped films, and the dynamics and current-voltage-field characteristics of nanoscale superconducting quantum interference devices (nanoSQUIDs). Program summaryProgram Title: pyTDGLCPC Library link to program files:https://doi.org/10.17632/t6z7szt9bj.1Developer's repository link:http://www.github.com/loganbvh/py-tdglCode Ocean capsule:https://codeocean.com/capsule/2460583Licensing provisions:MIT LicenseProgramming language: PythonNature of problem:pyTDGL solves a generalized time-dependent Ginzburg-Landau (TDGL) equation for two-dimensional superconductors of arbitrary geometry, enabling simulations of vortex and phase slip dynamics in thin film superconducting devices.Solution method:: The package uses a finite volume adaptive Euler method to solve a coupled TDGL and Poisson equation in two dimensions.

Physical modeling of HZO-based ferroelectric field-effect transistors with a WOx channel

The quasistatic and transient transfer characteristics of Hf0.57Zr0.43O2 (HZO)-based ferroelectric field-effect transistors (FeFETs) with a WOx channel are investigated using a 2-D time-dependent Ginzburg-Landau model as implemented in a state-of-the-art technology computer aided design tool. Starting from an existing FeFET configuration, the influence of different design parameters and geometries is analyzed before providing guidelines for next-generation devices with an increased “high (RH) to low (RL)” resistance ratio, i.e., RH/RL. The suitability of FeFETs as solid-state synapses in memristive crossbar arrays depends on this parameter. Simulations predict that a 13 times larger RH/RL ratio can be achieved in a double-gate FeFET, as compared to a back-gated one with the same channel geometry and ferroelectric layer. The observed improvement can be attributed to the enhanced electrostatic control over the semiconducting channel thanks to the addition of a second gate. A similar effect is obtained by thinning either the HZO dielectric or the WOx channel. These findings could pave the way for FeFETs with enhanced synaptic-like properties that play a key role in future neuromorphic computing applications.

Current Crowding in Nanoscale Superconductors within the Ginzburg-Landau Model

The current density in a superconductor with turnarounds or constrictions is nonuniform due to a geometrical current-crowding effect. This effect reduces the critical current in the superconducting structure compared to a straight segment and is of importance when designing superconducting devices. We investigate the current-crowding effect in numerical simulations within the generalized time-dependent Ginzburg-Landau (GTDGL) model. The results are validated experimentally by measuring the magnetic field dependence of the critical current in superconducting-nanowire structures, similar to those employed in single-photon detector devices. Comparing the results with London theory, we conclude that the reduction in critical current is significantly smaller in the GTDGL model. This difference is attributed to the current redistribution effect, which reduces the current density at weak points of the superconductor and counteracts the current-crowding effect. We numerically investigate the effect of the fill factor on the critical current in a meander and conclude that the reduction of the critical current is low enough to justify fill factors higher than 33% for applications where the detection efficiency is critical. Finally, we propose a meander design that can combine a high fill factor and low current crowding.

Hybrid Time-Dependent Ginzburg-Landau Simulations of Block Copolymer Nanocomposites: Nanoparticle Anisotropy.

Block copolymer melts are perfect candidates to template the position of colloidal nanoparticles in the nanoscale, on top of their well-known suitability for lithography applications. This is due to their ability to self-assemble into periodic ordered structures, in which nanoparticles can segregate depending on the polymer–particle interactions, size and shape. The resulting coassembled structure can be highly ordered as a combination of both the polymeric and colloidal properties. The time-dependent Ginzburg–Landau model for the block copolymer was combined with Brownian dynamics for nanoparticles, resulting in an efficient mesoscopic model to study the complex behaviour of block copolymer nanocomposites. This review covers recent developments of the time-dependent Ginzburg–Landau/Brownian dynamics scheme. This includes efforts to parallelise the numerical scheme and applications of the model. The validity of the model is studied by comparing simulation and experimental results for isotropic nanoparticles. Extensions to simulate nonspherical and inhomogeneous nanoparticles are discussed and simulation results are discussed. The time-dependent Ginzburg–Landau/Brownian dynamics scheme is shown to be a flexible method which can account for the relatively large system sizes required to study block copolymer nanocomposite systems, while being easily extensible to simulate nonspherical nanoparticles.

Observation of banded spherulite in a pure compound by rhythmic growth

Banded spherulitic growth of crystals is observed in some materials with spherically symmetric growth front and periodic radial variation of birefringence. This variation of birefringence in quasi-two-dimensional geometry produces concentric interference color bands when viewed through crossed polarizers. In most materials, the banded spherulites are found to be formed by radially oriented periodically twisted fibrillar crystallites. Here, we report the formation of banded spherulites due to the rhythmic growth of concentric crystallite-rich and crystallite-poor bands for a pure compound consisting of strongly polar rodlike molecules. The compound exhibits coexistence of untwisted fibrillar crystallites and an amorphous phase in its most stable solid state. On sufficient supercooling of the sample from its melting point, the banded spherulites are formed with a periodic variation of composition of untwisted radially aligned fibrillar crystallites and an amorphous solid phase. We have developed a time-dependent Ginzburg-Landau model to account for the observed banded spherulitic growth.

Analytic proposal for p + ip coupling in three-band Ginzburg-Landau model

In this contribution, we propose a theoretical Josephson coupling for a superconducting system in the three-component time-dependent Ginzburg-Landau model. We study a system with three superconducting bands ψ 1, ψ 2, and ψ 3 in the superconducting condensate. The coupling between bands is of the form γ 12, γ 13 and γ 23, taking into account couplings of each of the bands with the other two. We show the mathematical development of the final form of the complete set of acopled non-linear time-dependent Ginzburg-Landau differential equations, considering the coupling between the three bands, also we show that this coupling imposes a phase difference between the different components of the superconducting order parameter.

Weak-very weak uniqueness to the time-dependent Ginzburg–Landau model for superconductivity in [formula omitted

In this paper, we consider the n(n≥3) dimensional time-dependent Ginzburg–Landau model for superconductivity. First, we obtain a global existence of very weak solutions. Finally we prove a result of weak-very weak uniqueness.

Local affection of weak gravitational field from supercondensates

We study the mutual interaction between a superconducting sample and the weak, static Earth’s gravitational field, exploiting the gravito-Maxwell formalism combined with the time-dependent Ginzburg-Landau model. We will also determine the appropriate conditions to enhance the desired gravity/superfluid interplay, analysing the effects of thermal fluctuations and optimizing the superconductor parameters and sample geometry.

Inverse Faraday Effect for Superconducting Condensates.

The Cooper pairs in superconducting condensates are shown to acquire a temperature-dependent dc magnetic moment under the effect of the circularly polarized electromagnetic radiation. The mechanisms of this inverse Faraday effect are investigated within the simplest version of the phenomenological dynamic theory for superfluids, namely, the time-dependent Ginzburg-Landau (GL) model. The light-induced magnetic moment is shown to be strongly affected by the nondissipative oscillatory contribution to the superconducting order parameter dynamics, which appears due to the nonzero imaginary part of the GL relaxation time. The relevance of the latter quantity to the Hall effect in the superconducting state allows us to establish the connection between the direct and inverse Faraday phenomena.

Spin-polarized superconductivity: Order parameter topology, current dissipation, and multiple-period Josephson effect

We discuss transport properties of fully spin-polarized triplet superconductors, where only electrons of one spin component (along a certain axis) are paired. Due to the structure of the order parameter space, wherein phase and spin rotations are intertwined, a configuration where the superconducting phase winds by $4\pi$ in space is topologically equivalent to a configuration with no phase winding. This opens the possibility of supercurrent relaxation by a smooth deformation of the order parameter, where the order parameter remains non-zero at any point in space throughout the entire process. During the process, a spin texture is formed. We discuss the conditions for such processes to occur and their physical consequences. In particular, we show that when a voltage is applied, they lead to an unusual alternating-current Josephson effect whose period is an integer multiple of the usual Josephson period. These conclusions are substantiated in a simple time-dependent Ginzburg-Landau model for the dynamics of the order parameter. One of the potential applications of our analysis is for moir\'e systems, such as twisted bilayer and double bilayer graphene, where superconductivity is found in the vicinity of ferromagnetism.

Electronic and fluctuation dynamics following a quench to the superconducting phase

We investigate the dynamics of superconducting fluctuations in the attractive three-dimensional Hubbard model after a quench from the disordered phase to the ordered regime. While the long time evolution is well understood in terms of dissipative time-dependent Ginzburg-Landau models with unstable potentials, early times are more demanding due to the inseparable dynamics of the pairing fluctuations and the electronic quasiparticles. Our simulation using the time-dependent fluctuation exchange approximation treat both degrees of freedom on the same footing and reveal a non-thermal electronic regime causing a non-monotonous growth of the fluctuations. This feature is not directly captured from the Ginzburg-Landau theory, but nevertheless remains observable beyond the thermalization time of the electrons. We further explore how the growth of the order parameter fluctuations leads to an opening of a pseudo-gap in the electronic spectrum, and identify Andreev reflections as the dominant mechanism behind the gap opening.

On the properties of a single vortex solution of Ginzburg–Landau model of superconductivity

We closely examine a single vortex formation in an infinitely long cylinder with a rectangular crossection through field-cooling process with Temperature and Time-dependent Ginzburg–Landau model. We identify a solution for which components of vector potential and order function display a certain symmetry, which we name symmetric vortex solution. Furthermore, we observe that single vortex formation is associated with a jump discontinuity in all components of solution and associated observables, and illustrate graphically dynamics of transition. We carry out simulations in a vectorial algorithm using a variable order stiff ODE integration scheme of MATLAB.

Nucleation and growth of cholesteric collagen tactoids: A time-series statistical analysis based on integration of direct numerical simulation (DNS) and long short-term memory recurrent neural network (LSTM-RNN)

HypothesisLiquid-crystalline phase separation by nucleation and growth (NG) is a crucial step in the formation of collagen-based biomaterials. However, the fundamental mechanisms are not completely understood for chiral lyotropic colloidal mesogens such as collagen. MethodologyTo capture the dynamics of NG under a quenching process into the biphasic equilibrium zone, we use direct numerical simulation based on the time-dependent Ginzburg-Landau model allowing minimization of the total free energy comprised of five key contributions: phase separation (Flory-Huggins), ordering (Landau-de Gennes), chiral orientational elasticity (Frank-Oseen-Mermin), interfacial and coupling effects. LSTM-RNN is applied as a surrogate model to greatly enrich the results. Significant correlations are established using Symbolic Regression. FindingsWe quantify the NG boundaries existing in the collagen phase diagram that has recently been developed and validated by our thermodynamic model (Khadem and Rey, 2019 [1]). We characterize the three NG stages (induction, nucleation, and coarsening) in terms of tactoids’ shape, morphology, growth laws, and population across the NG zone. Wide-range generic correlations are developed, revealing the quench depth dependence of NG characteristics and connecting the sequential NG stages. We confirm experimental observations on time-dependent growth law exponent changes from an initial n≈0.5 for the mass transfer limited regime to n≈1 for the volume-driven phase ordering regime upon increasing quench depth during the nucleation period and having exclusively a value of n≈0.5 for the coarsening period regardless of quench depth. We lastly uncover the underlying physics behind the NG phenomena.

Existence and uniqueness for a Ginzburg-Landau system for superconductivity

We prove the existence of a unique solution for a time-dependent Ginzburg-Landau model in superconductivity under the Coulomb gauge. Also we prove the uniform-in-\(\epsilon\) well-posedness of the solution, where \(\epsilon\) is the coefficient of the double-well potential energy.
 For more information see https://ejde.math.txstate.edu/Volumes/2020/17/abstr.html

A note on the time-dependent Ginzburg–Landau model for superconductivity in [formula omitted

In this work, we prove the global well-posedness of strong solutions to the time-dependent Ginzburg–Landau model for superconductivity in Rn with 5≤n≤17.

Dynamics of a Persistent Insulator-to-Metal Transition in Strained Manganite Films.

Transition metal oxides possess complex free-energy surfaces with competing degrees of freedom. Photoexcitation allows shaping of such rich energy landscapes. In epitaxially strained La_{0.67}Ca_{0.33}MnO_{3}, optical excitation with a sub-100-fs pulse above 2 mJ/cm^{2} leads to a persistent metallic phase below 100K. Using single-shot optical and terahertz spectroscopy, we show that this phase transition is a multistep process. We conclude that the phase transition is driven by partial charge-order melting, followed by growth of the persistent metallic phase on longer timescales. A time-dependent Ginzburg-Landau model can describe the fast dynamics of the reflectivity, followed by longer timescale in-growth of the metallic phase.