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Results for “Time-dependent Ginzburg-Landau”

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

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).

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Universal time-dependent Ginzburg-Landau theory

We study the hydrodynamics of superconductors within the framework of Schwinger-Keldysh effective field theory (EFT). We show that in the vicinity of the superconducting phase transition the most general leading-order EFT satisfying the local Kubo-Martin-Schwinger condition is described by a version of the time-dependent Ginzburg-Landau (TDGL) equations augmented with stochastic terms. This version of TDGL is applicable in the gapless regime independent of any microscopic details. Within this approach, it is possible to include systematically the effects of nonuniform temperature and heat conductivity, as well as explicit or spontaneous breaking of time reversal. Here, we also introduce a thermal version of the Josephson relation and use it to construct an exotic hydrodynamics describing a phase of matter where heat can flow without dissipation.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗
DOE OSTI2025

Coarsening dynamics of Ising-nematic order in a frustrated Heisenberg antiferromagnet

We study the phase ordering dynamics of the classical antiferromagnetic 𝐽 1 −𝐽 2 (nearest-neighbor and next-nearest-neighbor couplings) Heisenberg model on the square lattice in the strong frustration regime (𝐽 2 /𝐽 1 > 1/2). While thermal fluctuations preclude any long-range magnetic order at finite temperatures, the system exhibits a long-range spin-driven nematic phase at low temperatures. The transition into the nematic phase is further shown to belong to the two-dimensional Ising universality class based on the critical exponents near the phase transition. Our large-scale stochastic Landau-Lifshitz-Gilbert simulations find a two-stage phase ordering when the system is quenched from a high-temperature paramagnetic state into the nematic phase. In the early stage, collinear alignments of spins lead to a locally saturated Ising-nematic order. Once domains of well-defined Ising order are developed, the late-stage relaxation is dominated by curvature-driven domain coarsening, as described by the Allen-Cahn equation. The characteristic size of Ising-nematic domains scales as the square root of time, similar to the kinetic Ising model described by the time-dependent Ginzburg-Landau theory. Our results confirm that the late-stage ordering kinetics of the spin-driven nematic, which is a vestigial order of the frustrated Heisenberg model, belongs to the dynamical universality class of a nonconserved Ising order. Interestingly, the system shows no violation of the superuniversality hypothesis under weak bond disorder. The dynamic scaling invariance is preserved in the presence of weak bond disorder. Here, we also discuss possible applications of our results to materials for which vestigial Ising-nematic order is realized.

Antiferromagnets↗
DOE OSTI2022

Driven responses of periodically patterned superconducting films

Here, we simulate the motion of a commensurate vortex lattice in a periodic lattice of artificial circular pinning sites having different diameters, pinning strengths, and spacings using the time-dependent Ginzburg-Landau formalism. Above some critical DC current density J c , the vortices depin, and the resulting steady-state motion then induces an oscillatory electric field E (t) with a defect "hopping" frequency f 0 , which depends on the applied current density and the pinning landscape characteristics. The frequency generated can be locked to an applied AC current density over some range of frequencies, which depends on the amplitude of the DC as well as the AC current densities. Both synchronous and asynchronous collective hopping behaviors are studied as a function of the supercell size of the simulated system and the (asymptotic) synchronization threshold current densities determined.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Vortex dynamics induced by scanning SQUID susceptometry

In this work, we measured the local magnetic response of a niobium thin film by applying a millitesla-scale AC magnetic field using a micron-scale field coil and detecting the response with a micron-scale pickup loop in a scanning superconducting quantum interference device (SQUID) susceptometry measurement. Near the film's critical temperature, we observed a steplike nonlinear and dissipative magnetic response due to the dynamics of a small number of vortex-antivortex pairs induced in the film by the local applied AC field. We modeled the dynamics of the measurement using a combined two-dimensional London-Maxwell and time-dependent Ginzburg-Landau approach, allowing us to construct a detailed real-space picture of the vortex motion causing the observed dissipative response. This work pushes scanning SQUID susceptometry of two-dimensional superconductors beyond the regime of linear response and lays the foundation for microscopic studies of vortex dynamics and pinning in superconducting devices and more exotic materials systems.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

An efficient iterative method for dynamical Ginzburg-Landau equations

Here we propose a new finite element approach to solving the time-dependent Ginzburg-Landau equations for superconductivity under the temporal gauge and design an efficient preconditioner for the Newton iteration of the resulting discrete system. It solves the vector magnetic potential in $H$(curl) space by the lowest order of the second kind N´ed´elec element. This approach offers a simple way to deal with the boundary conditions, leading to a stable and reliable performance for superconductor geomtry with reentrant corners. The bench-marking in numerical simulations verifies the efficiency of the proposed preconditioner, which can be employed to significantly speed up in large-scale computations.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2022

Superfluid transition temperature and fluctuation theory of spin-orbit- and Rabi-coupled fermions with tunable interactions

Here, we obtain the superfluid transition temperature of equal Rashba-Dresselhaus spin-orbit- and Rabi-coupled Fermi superfluids, from the Bardeen-Cooper-Schrieffer (BCS) to Bose-Einstein condensate (BEC) regimes in three dimensions for tunable s-wave interactions. In the presence of Rabi coupling, we find that spin-orbit coupling enhances (reduces) the critical temperature in the BEC (BCS) limit. For fixed interactions, we show that spin-orbit coupling can convert a first-order (discontinuous) phase transition into a second-order (continuous) phase transition, as a function of Rabi coupling. We derive the Ginzburg-Landau free energy to sixth power in the superfluid order parameter to describe both continuous and discontinuous phase transitions as a function of spin-orbit and Rabi couplings. Lastly, we develop a time-dependent Ginzburg-Landau fluctuation theory for an arbitrary mixture of Rashba and Dresselhaus spin-orbit couplings at any interaction strength.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2021

Nonequilibrium charge-density-wave order beyond the thermal limit

The interaction of many-body systems with intense light pulses may lead to novel emergent phenomena far from equilibrium. Recent discoveries, such as the optical enhancement of the critical temperature in certain superconductors and the photo-stabilization of hidden phases, have turned this field into an important research frontier. Here, we demonstrate nonthermal charge-density-wave (CDW) order at electronic temperatures far greater than the thermodynamic transition temperature. Using time- and angle-resolved photoemission spectroscopy and time-resolved X-ray diffraction, we investigate the electronic and structural order parameters of an ultrafast photoinduced CDW-to-metal transition. Tracking the dynamical CDW recovery as a function of electronic temperature reveals a behaviour markedly different from equilibrium, which we attribute to the suppression of lattice fluctuations in the transient nonthermal phonon distribution. A complete description of the system’s coherent and incoherent order-parameter dynamics is given by a time-dependent Ginzburg-Landau framework, providing access to the transient potential energy surfaces.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Dynamical criticality of spin-shear coupling in van der Waals antiferromagnets

Abstract The interplay between a multitude of electronic, spin, and lattice degrees of freedom underlies the complex phase diagrams of quantum materials. Layer stacking in van der Waals (vdW) heterostructures is responsible for exotic electronic and magnetic properties, which inspires stacking control of two-dimensional magnetism. Beyond the interplay between stacking order and interlayer magnetism, we discover a spin-shear coupling mechanism in which a subtle shear of the atomic layers can have a profound effect on the intralayer magnetic order in a family of vdW antiferromagnets. Using time-resolved X-ray diffraction and optical linear dichroism measurements, interlayer shear is identified as the primary structural degree of freedom that couples with magnetic order. The recovery times of both shear and magnetic order upon optical excitation diverge at the magnetic ordering temperature with the same critical exponent. The time-dependent Ginzburg-Landau theory shows that this concurrent critical slowing down arises from a linear coupling of the interlayer shear to the magnetic order, which is dictated by the broken mirror symmetry intrinsic to the monoclinic stacking. Our results highlight the importance of interlayer shear in ultrafast control of magnetic order via spin-mechanical coupling.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bidirectional Ultrafast Control of Charge Density Waves via Phase Competition

The intricate competition between coexisting charge density waves (CDWs) can lead to rich phenomena, offering unique opportunities for phase manipulation through electromagnetic stimuli. Here, leveraging time-resolved x-ray diffraction, we demonstrate ultrafast control of a CDW in EuTe 4 upon optical excitation. At low excitation intensities, the amplitude of one of the coexisting CDW orders increases at the expense of the competing CDW, whereas at high intensities, it exhibits a nonmonotonic temporal evolution characterized by both enhancement and reduction. This transient bidirectional controllability, tunable by adjusting photoexcitation intensity, arises from the interplay between optical quenching and phase-competition-induced enhancement. Our findings, supported by phenomenological time-dependent Ginzburg-Landau theory simulations, not only clarify the relationship between the two CDWs in EuTe 4 , but also highlight the versatility of optical control over order parameters enabled by phase competition.

charge density waves↗
DOE OSTI2024

Microscopic examination of rf-cavity-quality niobium films through local nonlinear microwave response

The performance of superconducting radio-frequency (SRF) cavities is sometimes limited by local defects. To investigate the rf properties of these local defects, especially those that nucleate rf magnetic vortices, a near-field magnetic microwave microscope is employed. Local third-harmonic response ( P 3 f ) and its temperature dependence and rf power dependence are measured for one Nb / Cu film grown by direct current magnetron sputtering (DCMS) and six Nb / Cu films grown by high-power impulse magnetron sputtering (HiPIMS) with systematic variation of deposition conditions. Five out of the six HiPIMS Nb / Cu films show a strong third-harmonic response that is likely coming from rf vortex nucleation due to a low- T c surface defect with a transition temperature between 6.3 and 6.8 K, suggesting that this defect is a generic feature of air-exposed HiPIMS Nb / Cu films. A phenomenological model of surface-defect grain boundaries hosting a low- T c impurity phase is introduced and studied with time-dependent Ginzburg-Landau (TDGL) simulations of probe-sample interaction to better understand the measured third-harmonic response. The simulation results show that the third-harmonic response of rf vortex nucleation caused by surface defects exhibits the same general features as the data, including peaks in third-harmonic response with temperature, and their shift and broadening with higher microwave amplitude. We find that the parameters of the phenomenological model (the density of surface defects that nucleate rf vortices and the depth an rf vortex travels through these surface defects) vary systematically with film deposition conditions. From the point of view of these two properties, the Nb / Cu film that is most effective at reducing the nucleation of rf vortices associated with surface defects can be identified. Published by the American Physical Society 2024

Wang, Chung-Yang (ORCID:0000000184299633)↗
DOE OSTI2022

Mechanisms of in-plane magnetic anisotropy in superconducting NbSe 2

Here we present a unifying picture of the magnetic in-plane anisotropies of two-dimensional superconductors based on transition metal dichalcogenides. The symmetry considerations are first applied to constrain the form of the conductivity tensor. We hence conclude that the twofold periodicity of transport distinct from the planar Hall-related contributions requires a tensor perturbation. At the same time, the sixfold periodic variation of the critical field results from the Rashba spin-orbit coupling on a hexagonal lattice. We have considered the effect of a weak tensor perturbation on the critical field, gap function, and magnetoconductivity. The latter is studied using the time-dependent Ginzburg-Landau phenomenology. The common origin of the π periodicity in transport and thermodynamics properties is identified. The scheme constructed here is applied to describe the existing theoretical scenarios from a unified point of view. This allows us to single out the differences and similarities between the suggested approaches.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Understanding resistance oscillation in the CsV 3 Sb 5 superconductor

A recent demonstration of the periodic oscillation of resistance in the thin film of the CsV 3 ⁢Sb 5 superconductor with a hole in the film suggests that charge-4⁢ e and charge-6⁢⁢ e Cooper pairs may have condensed in this compound. While exciting, such interpretation calls for a precise determination of the effective area for the passage of Cooper pairs from one end of the lead to the other. Unlike the traditional Little-Parks effect where the rim around the hole is thin, the effective hole area is not obviously defined for the “thick-rim geometry” adopted in the experiment. Here, we note that the experiment was conducted in a regime where the superconductivity is strongly fluctuating, which motivates an analysis based on the spacetime formulation of the time-dependent Ginzburg-Landau theory. Further, we argue that under appropriate conditions, the optimal semiclassical path is not the geometrically shortest one, but the one that moves along the edge of the hole and takes advantage of the reduced fluctuations at the boundary of the hole. The condition for the crossover from the geometrically shortest path to the path that sticks to the wall is clarified. In such a scenario, the geometric area of the hole indeed emerges as the effective area for the flux, providing a theoretical justification to the interpretation given by J. Ge et al. (arXiv:2201.10352). The conclusion of our analysis may have implications for similar experiments in other superconductors where the geometry of the device is not obviously that of the Little-Parks experiment employing the thin wall, but of the thick-rim type such as used in the experiment.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Microwave microscope studies of trapped vortex dynamics in superconductors

Trapped vortices in superconductors introduce residual resistance in superconducting radio-frequency (SRF) cavities and disrupt the operation of superconducting quantum and digital electronic circuits. Understanding the detailed dynamics of trapped vortices under oscillating magnetic fields is essential for advancing these technologies. We have developed a near-field magnetic microwave microscope to study the dynamics of a limited number of trapped vortices under the probe when stimulated by a localized rf magnetic field. By measuring the local second-harmonic response (𝑃 2⁢f ) at subfemto-Watt levels, we isolate signals exclusively arising from trapped vortices, excluding contributions from surface defects and Meissner screening currents. Toy models of niobium superconductor hosting vortex pinning sites are introduced and studied with time-dependent Ginzburg-Landau (TDGL) simulations of probe/sample interaction to better understand the measured second-harmonic response. The simulation results demonstrate that the second-harmonic response of trapped vortex motion under a localized rf magnetic field shares key features with the experimental data. Here, this measurement technique provides access to vortex dynamics at the micrometer scale, such as depinning events and spatially resolved pinning properties, as demonstrated in measurements on a niobium film with an antidot flux pinning array.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

Nonlinear inductive response of pinned superconducting vortices in artificial pinning sites

Using the time dependent Ginzburg-Landau equations, we simulate the inductive responses of a variety of thin-film systems containing patterned antidots with different sizes and shapes. The results for all shapes show that the kinetic inductance diverges as the applied current approaches a critical current that is below the BCS depairing current. In conclusion, exploiting the similarity of the observed current-voltage behavior to that of Josephson junctions, we obtain an empirical equation that well fits the inductivity curve as a function of the applied current.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2024

A-B Transition in Superfluid $^3$He and Cosmological Phase Transitions

First-order phase transitions in the very early universe are a prediction of many extensions of the Standard Model of particle physics and could provide the departure from equilibrium needed for a dynamical explanation of the baryon asymmetry of the Universe. They could also produce gravitational waves of a frequency observable by future space-based detectors such as the Laser Interferometer Space Antenna. All calculations of the gravitational wave power spectrum rely on a relativistic version of the classical nucleation theory of Cahn-Hilliard and Langer, due to Coleman and Linde. The high purity and precise control of pressure and temperature achievable in the laboratory made the first-order A to B transition of superfluid $^3$He ideal for test of classical nucleation theory. As Leggett and others have noted, the theory fails dramatically. The lifetime of the metastable A phase is measurable, typically of order minutes to hours, far faster than classical nucleation theory predicts. If the nucleation of B phase from the supercooled A phase is due to a new, rapid intrinsic mechanism that would have implications for first-order cosmological phase transitions as well as predictions for gravitational wave production in the early universe. Here we discuss studies of the A-B phase transition dynamics in $^3$He, both experimental and theoretical, and show how the computational technology for cosmological phase transition can be used to simulate the dynamics of the A-B transition, support the experimental investigations of the A-B transition in the QUEST-DMC collaboration with the goal of identifying and quantifying the mechanism(s) responsible for nucleation of stable phases in ultra-pure metastable quantum phases.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Role of Equilibrium Fluctuations in Light-Induced Order

Engineering novel states of matter with light is at the forefront of materials research. An intensely studied direction is to realize broken-symmetry phases that are “hidden” under equilibrium conditions but can be unleashed by an ultrashort laser pulse. Despite a plethora of experimental discoveries, the nature of these orders and how they transiently appear remain unclear. To this end, we investigate a nonequilibrium charge density wave (CDW) in rare-earth tritellurides, which is suppressed in equilibrium but emerges after photoexcitation. Using a pump-pump-probe protocol implemented in ultrafast electron diffraction, we demonstrate that the light-induced CDW consists solely of order parameter fluctuations, which bear striking similarities to critical fluctuations in equilibrium despite differences in the length scale. By calculating the dynamics of CDW fluctuations in a nonperturbative model, we further show that the strength of the light-induced order is governed by the amplitude of equilibrium fluctuations. Overall, these findings highlight photoinduced fluctuations as an important ingredient for the emergence of transient orders out of equilibrium. Our results further suggest that materials with strong fluctuations in equilibrium are promising platforms to host hidden orders after laser excitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗