Time-dependent Ginzburg-Landau Research Articles

Circularly polarized radiation to control the superconducting states: Stability analysis.

Recently, the use of circularly polarized radiation for on-demand switching between distinct quantum states in a superconducting nanoring exposed to half-quantum magnetic flux has been proposed. However, the effectiveness of this method depends on the system's stability against local variations in the superconducting characteristics of the ring and flux fluctuations. In this study, we utilize numerical simulations based on the time-dependent Ginzburg-Landau (TDGL) equation to evaluate the influence of these inevitable factors on the switching behavior. The results obtained demonstrate that the switching phenomena remain remarkably robust, providing confidence in their experimental observation.

Thermal gradient-induced critical current degradation in mesoscopic superconducting thin film

Abstract Superconducting materials inevitably suffer from the sudden change of temperature in localized areas in practical applications, and the concomitant thermal gradient may be detrimental to their performance. Critical current density is a key factor affecting the performance of superconductors. However, the effect of thermal gradient on the critical current density has not been identified. Here, by combining the time-dependent Ginzburg–Landau equations and the heat transfer equation, the thermal gradient and magnetic field dependence of the critical current density are systematically investigated and rationalized by exploring the behavior of vortex and magnetization. For lower magnetic fields, it is found that the thermal gradients strongly reduce the local surface barriers, which inhibits vortex entry and movement, leading to a rapid deterioration of the current-carrying capability. Under moderate magnetic fields, the critical current density corresponding to higher thermal gradients decreases more slowly with increasing magnetic field, which results from the thermal gradient-induced entry and moving of vortices along the current direction. As the magnetic field continues to increase, the variation of the critical current density transitions into a platform period and even slightly rises. The enhanced critical current is primarily attributed to the excess entry of vortices, which increases the surface barrier of the sample. With the further increase in the magnetic field, the critical current density continues to decrease due to increased magnetic field penetration. These results unveil the fundamental interplay between thermal gradients, external magnetic field, vortex, magnetization and critical current density, and provide a theoretical basis for understanding the heat-induced quenching of mesoscopic superconducting thin films in practical applications.

Dynamics of Vortex Matter in 2D Gapless Superconducting Materials with Impurities.

The recent interest in using ultrafast single-photon detectors in research and commercial applications has garnered significant attention from the scientific community. The dynamic event in the detection process consists of a photon causing local destruction of the order parameter, and then the applied current dissipates heat, bringing the material even more out of the superconducting state and then spiking a voltage peak in a measurement device. We investigated the role of superconducting and thermal parameters of the Generalized Time-Dependent Ginzburg-Landau (GTDGL) theory within the event of the first vortex penetration and the thermal dissipation in superconductors near the critical temperature. Moreover, in the vicinity of the Bogomolny point of the static Ginzburg-Landau theory, where κ ≈ 1/√2 and T → Tc, it has been found severely different vortex profiles. We point out that within the GTDGL theory, the presence of impurities (usual or paramagnetic) influences flux penetration and enhances the dissipation of heat, causing anomalous vortex configurations.

Numerical Modeling of Vortex-Based Superconducting Memory Cells: Dynamics and Geometrical Optimization.

The lack of dense random-access memory is one of the main obstacles to the development of digital superconducting computers. It has been suggested that AVRAM cells, based on the storage of a single Abrikosov vortex-the smallest quantized object in superconductors-can enable drastic miniaturization to the nanometer scale. In this work, we present the numerical modeling of such cells using time-dependent Ginzburg-Landau equations. The cell represents a fluxonic quantum dot containing a small superconducting island, an asymmetric notch for the vortex entrance, a guiding track, and a vortex trap. We determine the optimal geometrical parameters for operation at zero magnetic field and the conditions for controllable vortex manipulation by short current pulses. We report ultrafast vortex motion with velocities more than an order of magnitude faster than those expected for macroscopic superconductors. This phenomenon is attributed to strong interactions with the edges of a mesoscopic island, combined with the nonlinear reduction of flux-flow viscosity due to the nonequilibrium effects in the track. Our results show that such cells can be scaled down to sizes comparable to the London penetration depth, ∼100 nm, and can enable ultrafast switching on the picosecond scale with ultralow energy per operation, ∼10-19 J.

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.

Characteristic Times for Gap Relaxation and Heat Escape in Nanothin NbTi Superconducting Filaments: Thickness Dependence and Effect of Substrate.

We measured the temporal voltage response of NbTi superconducting filaments with varied nanoscale thicknesses to step current pulses that induce non-equilibrium superconducting states governed by a hot spot mechanism. Such detected voltage emerges after a delay time td, which is intimately connected to the gap relaxation and heat escape times. By employing time-dependent Ginzburg-Landau theory to link the delay time to the applied current, we determined that the gap relaxation time depends linearly on film thickness, aligning with the acoustic mismatch theory for phonon transmission at the superconductor-substrate interface. We thereby find a gap relaxation time of 104 ps per nm of thickness for NbTi films on polished sapphire. We further show that interfacial interaction with the substrate significantly impacts the gap relaxation time, with observed values of 9 ns on SiOx, 6.8 ns on fused silica, and 5.2 ns on sapphire for a 50 nm thick NbTi strip at T=5.75 K. These insights are valuable for optimizing superconducting sensing technologies, particularly the single-photon detectors that operate in the transient regime of nanothin superconducting bridges and filaments.

A quantitative theory and atomistic simulation study on the soft-sphere crystal-melt interfacial properties. I. Kinetic coefficients.

By employing non-equilibrium molecular dynamics (NEMD) simulations and time-dependent Ginzburg-Landau (TDGL) theory for solidification kinetics [Cryst. Growth Des. 20, 7862 (2020)], we predict the kinetic coefficients of FCC(100) crystal-melt interface (CMI) of soft-spheres modeled with an inverse-sixth-power repulsive potential. The collective dynamics of the local interfacial liquid phase at the equilibrium FCC(100) CMIs are calculated based on a recently proposed algorithm [J. Chem. Phys. 157, 084 709 (2022)] and are employed as the resulting parameter that eliminates the discrepancy between the predictions of the kinetic coefficient using the NEMD simulations and the TDGL solidification theory. A 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) is observed. With the insights provided by the quantitative predictive theory, the variation of the solidification kinetic coefficient along the crystal-melt coexistence boundary is discussed. The combined methodology (simulation and theory) presented in this study could be further applied to investigate the role of the inter-atomic potential (e.g., softness parameter s = 1/n of the inverse-power repulsive potential) in the kinetic coefficient.

Emergent symmetry in TbTe3revealed by ultrafast reflectivity under anisotropic strain.

We report ultrafast reflectivity measurements of the dynamics of the order parameter of the charge density wave (CDW) in TbTe3under anisotropic strain. We observe an increase in the frequency of the amplitude mode with increasing tensile strain along thea-axis (which drives the lattice intoa > c, withaandcthe lattice constants), and similar behavior for tensile strain alongc(c > a). This suggests that both strains stabilize the corresponding CDW order and further support the near equivalence of the CDW phases oriented ina- andc-axis, in spite of the orthorhombic space group. The results were analyzed within the time-dependent Ginzburg-Landau framework, which agrees well with the reflectivity dynamics. Our study presents an ultrafast approach to assess the stability of phases and order parameter dynamics in strained 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.

Quantized magnetic flux in a two-band superconducting condensate with a type-Kagome pinning center lattice

In this work we studied the vortex-configuration in a mesoscopic superconducting square in presence of an external magnetic field H applied parallel to its surface vector. We study the magnetization curves in a complete loop, the magnretic induction and the superconducting-electron density for the sample considering Neumann boundary conditions for the order parameter, via length Gennes extrapolation . The sample presents a pinnin center as a Kagome-type laticce at different critical temperature. We solve the generalized time-dependent Ginzburg-Landau equations for a two-condensate system using the Link-variable method considering a Field-Cooling process. Our results show that the vortices are always located at the pinning centers in non-conventional configurations, due to cuopling used.

Electric-field-induced crystallization of Hf0.5Zr0.5O2 thin film based on phase-field modeling

Ferroelectricity in crystalline hafnium oxide has attracted considerable attention because of its potential application for memory devices. A recent breakthrough involves electric-field-induced crystallization, allowing HfO2-based materials to avoid high-temperature crystallization, which is unexpected in the back-end-of-line process. However, due to the lack of clarity in understanding the mechanisms during the crystallization process, we aim to employ theoretical methods for simulation, to guide experimental endeavors. In this work, we extended our phase-field model by coupling the crystallization model and time-dependent Ginzburg-Landau equation to analyze the crystalline properties and the polarization evolution of Hf0.5Zr0.5O2 thin film under applying an electric field periodic pulse. Through this approach, we found a wake-up effect during the process of crystallization and a transformation from orthorhombic nano-domains to the stripe domain. Furthermore, we have proposed an innovative artificial neural synapse concept based on the continuous polarization variation under applied electric field pulses. Our research lays the theoretical groundwork for the advancement of electric-field-induced crystallization in the hafnium oxide system.

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.

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.

Roundabout-like defect as a guide of phase-slip lines in a superconducting thin film at low temperature

AbstractIn this work, we examined the kinematic vortex state in a low-temperature, mesoscopic superconducting thin film in presence of an external applied current $$\varvec{J}$$ J , at zero magnetic field. We analyzed the voltage-current ($$\varvec{V-I}$$ V - I ), resistivity-current ($$\varvec{R-I}$$ R - I ) curves, as well as the vortex-anti-vortex velocity $$\varvec{V_m}$$ V m and the superconducting-electron density (norm of the superconduting order parameter $$\varvec{\psi }$$ ψ ) as an applied current function. Additionally, we have calculated the voltage as a function of characteristic time ($$\varvec{V-t}$$ V - t ). The sample presents a roundabout shaped pinning center fabricated with a lower low-temperature superconducting material, which allows for control over the vortex dynamics within the sample. To study this system, we have solved the generalized time-dependent Ginzburg-Landau equations for a single-condensate system. Our results demonstrate that the kinematic vortices enter the sample through regions where the superconductivity is depleted, revealing an intriguing and novel behavior of the phase-slip lines in the defect. We found that when a higher $$\varvec{J}$$ J is applied and the defect is not centered, the point where the vortex anti-vortex pairs enter the film moves away from the defect and are located in a point tangent to the outer circle of the defect. Besides, our results show a way to control the dynamics of the vortices, critical currents, and points of annihilation or creation of the cinematic vortices by including defects in the sample, important in the design and development of devices applied in industry and engineering.

A phase-field simulation of easily switchable vortex structure for multilevel low-power ferroelectric memory

Ferroelectric materials with multi-directional polarization orders can form a variety of special domain structures, which have a wide range of applications. In this work, lead-free potassium sodium niobate ferroelectric thin films were simulated by solving the Time-Dependent-Landau-Ginzburg (TDLG) equation. Based on vortex topological structure characteristic of perovskite-type ferroelectric, domain types are simplified from 26 to 9 through virtual polarization vectors. By temperature selection, we accomplished a large easily switchable vortex structure with 20% side length. Based on this, as low as 0.04V/nm electric-field pulse was applied to explore vortex domain structures change. Under different low external electric-field pulses, conductance states change in vortex have been calculated and discussed systematically. Free energy computation results reveal that the domain wall (DW) conductance states primarily originate from the competition between electrostatic energy, gradient energy, and elastic energy. Finally, we propose the multilevel data ferroelectric memory through easily switchable vortex topological structures for the first time. Under electric-field pulses, diverse storage states were presented through 0/1 measurement of 8 positions. By achieving an easy-to-distinguish and robust-to-switch data map at the vortex structure, this work might provide a significant idea of vortex structure on low-power ferroelectric memory applications.

Ac Hall Effect and Photon Drag of Superconducting Condensates.

We suggest a theoretical description of the photogalvanic phenomena arising in superconducting condensates in the field of electromagnetic wave. The ac Hall effect and photon drag are shown to originate from the second-order nonlinear response of superconducting carriers caused by the suppression of their concentration due to the combined influence of the electron-hole asymmetry and charge imbalance generated by the incident electromagnetic wave. Starting from the time-dependent Ginzburg-Landau theory with the complex relaxation constant, we develop a phenomenological description of these phenomena and investigate the resulting behavior of the dc supercurrent and second harmonic induced by microwave radiation incident on a superconductor surface.

Steering of Vortices by Magnetic Field Tilting in Open Superconductor Nanotubes.

In planar superconductor thin films, the places of nucleation and arrangements of moving vortices are determined by structural defects. However, various applications of superconductors require reconfigurable steering of fluxons, which is hard to realize with geometrically predefined vortex pinning landscapes. Here, on the basis of the time-dependent Ginzburg-Landau equation, we present an approach for the steering of vortex chains and vortex jets in superconductor nanotubes containing a slit. The idea is based on the tilting of the magnetic field B at an angle α in the plane perpendicular to the axis of a nanotube carrying an azimuthal transport current. Namely, while at α=0∘, vortices move paraxially in opposite directions within each half-tube; an increase in α displaces the areas with the close-to-maximum normal component |Bn| to the close(opposite)-to-slit regions, giving rise to descending (ascending) branches in the induced-voltage frequency spectrum fU(α). At lower B values, upon reaching the critical angle αc, the close-to-slit vortex chains disappear, yielding fU of the nf1 type (n≥1: an integer; f1: the vortex nucleation frequency). At higher B values, fU is largely blurry because of multifurcations of vortex trajectories, leading to the coexistence of a vortex jet with two vortex chains at α=90∘. In addition to prospects for the tuning of GHz-frequency spectra and the steering of vortices as information bits, our findings lay the foundation for on-demand tuning of vortex arrangements in 3D superconductor membranes in tilted magnetic fields.

A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations

A generalized scalar auxiliary variable method for the time-dependent Ginzburg-Landau equations

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.