Time-dependent Ginzburg-Landau Formalism Research Articles

Driven responses of periodically patterned superconducting films

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 ${J}_{\mathrm{c}}$, 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.

Sensitivity of SQUID-on-tip (SOT) to a magnetic nano-particle

Within the state-of-the-art 3D Ginzburg–Landau (GL) formalism, we investigate the static features of the most sensitive SQUID-on-tip (SOT) device placed on the top of a nano-particle. The SOT sensor’s free energy, Cooper pair density, and screening current density in the loop are investigated for the nano-particle’s various placements and sizes. The dynamic aspects of the device, such as its voltage–current characteristics, are evaluated in the presence of transport current using the two-dimensional (2D) time-dependent GL formalism. The sensitivity of the SOT is examined using quantum oscillations of the device’s depairing current as a function of the nano-particle’s size and location. The location of the nano-particle at the device’s center and closer to the device’s loop is required for optimal SOT sensitivity.

(Invited) Theoretical Understanding of Nanoscale Ferroelectric Field-Effect-Transistor Having a Poly-Domain Structure

The emergence of ferroelectricity in doped HfO2 and (Hf,Zr)O2 (HZO) thin film with a typical thickness ~10 nm brings back the great interest in ferroelectric (FE) memories including the conventional ferroelectric random access memory, ferroelectric field-effect transistors (FEFET), and more recent negative capacitance field-effect transistors, in not only academia but also memory industry. In the industry, one of the most important issues concerning a FEFET is whether FEFET based NAND (FE-NAND) memory can be a next-generation device with superior performance to a conventional CTF-based NAND memory. For this purpose, it must have the multi-level capability and lower interference between adjacent memory cells. Because of sufficiently large ferroelectric polarization (10~15 uC/cm2 for typical HZO thin film), the multi-level capacity of FE-NAND would be higher than that of CTF-based NAND. However, an experimental result of FE-NAND devices shows that only a tenth of the expected memory window for the reading operation was achieved. At the same time, ten times larger erasing/writing voltages are required.In this work, we presented the comprehensive FEFET model to describe the writing process and reading process in FEFET from the fundamental viewpoint of metal-oxide-semiconductor (MOS) FET device physics in conjunction with the FE switching phenomenon. To capture the multi-domain nature of the ferroelectric thin film, we adopted the time-dependent Ginzburg-Landau (TDGL) formalism as a core physics of the switching kinetics. Furthermore, the FEFET model has been extended to a 3-Dimensional FE-NAND simulation. These models showed that the multi-domain nature of the ferroelectric film, which is shared by serial gates in the FE NAND device, not only degrades gate controllability on a target memory cell but also decreases a magnitude of surface potential. The extensive simulation results provided a critical view to understand the degraded memory window of FEFET and a possible strategy for the improvement.

Multiple reversals of vortex ratchet effects in a superconducting strip with inclined dynamic pinning landscape* *Project supported by the National Natural Science Foundation of China (Grant Nos. 11702034, 11972298, and 11702218), the China Postdoctoral Science Foundation (Grant No. 2019M663812), the Fundamental Research Funds for the Central Universities, China (Grant Nos. 300102129104, 3102018zy013, and 3102017jc01003), and the Young Talent Fund of

Using time-dependent Ginzburg–Landau formalism, we investigate the multiple reversals of ratchet effects in an unpatterned superconducting strip by the tilted dynamic pinning potential. In the case of collinear sliding potential and Lorentz force, vortices are always confined in the channels induced by sliding potential. However, due to the inclination angle of sliding pinning potential with respect to the Lorentz force, vortices could be driven out of the channels, and unexpected results with multiple reversals of vortex rectifications are observed. The mechanism of multiple reversals of vortex rectifications is explored by analyzing different vortex motion scenarios with increasing ac current amplitudes. The multiple reversals of transverse and longitudinal ratchet effects can be highly controlled by ac amplitude and dynamic pinning velocity. What’s more, at certain large current the ratchet effect reaches strongest within a wide range of pinning sliding velocity.

Switchable reversal of vortex ratchet with dynamic pinning landscape

Vortex rectifications are well known as drifting vortices along an “easy” direction when asymmetric potential is introduced to break the inversion symmetry for the vortex motion. Using the time-dependent Ginzburg–Landau formalism, we show an approach to switch the reversal of vortex ratchets by a dynamic pinning landscape, which is highly tuned by varying the sliding velocity of the dynamic pinning potential and its characteristic sizes and densities. Besides the anticipated positive rectified voltage with an easy vortex motion along the sliding direction of dynamic pinning sites, contrary to intuition, we also observe a negative dc voltage with vortices moving preferentially uphill, i.e., against the sliding direction. The mechanism of such reversal of vortex ratchets is different from previous work, which is revealed based on the dragging effect on the vortex motion by the sliding pinning sites.

Modeling of Negative Capacitance in Ferroelectric Thin Films.

The negative capacitance (NC) effect in ferroelectric thin films has attracted a great deal of attention from the material and semiconductor device communities because it could be a possible solution to the impending problems related to field-effect transistor power consumption and dynamic random-access memory charge loss. A short discussion on the fundamental premise of the NC effect is presented. A phase-field model based on the time-dependent Ginzburg-Landau (TDGL) formalism in conjunction with the Chensky-Tarasenko (C-T) formalism for multidomain configuration is then developed to reveal the subtle correlation between the domain wall motion and NC effect for different thicknesses of ferroelectric and dielectric films. When a ferroelectric film becomes thin enough, a stripe domain structure can be achieved through competition between the electrostatic energy and domain wall energy. This stripe domain structure is quite resilient to transition to a homogeneous polarization state, making it very useful for (quasi-)static NC operation. Finally, the physical implications of the numerical results are explored with analytical modeling. It is identified that the domain wall motion in the stripe domain structure remains dominated by the external field, even when the entire film is in the (quasi-)static NC state.

Velocimetry of superconducting vortices based on stroboscopic resonances.

An experimental determination of the mean vortex velocity in superconductors mostly relies on the measurement of flux-flow resistance with magnetic field, temperature, or driving current. In the present work we introduce a method combining conventional transport measurements and a frequency-tuned flashing pinning potential to obtain reliable estimates of the vortex velocity. The proposed device is characterized using the time-dependent Ginzburg-Landau formalism, where the velocimetry method exploits the resonances in mean vortex dissipation when temporal commensuration occurs between the vortex crossings and the flashing potential. We discuss the sensitivity of the proposed technique on applied current, temperature and heat diffusion, as well as the vortex core deformations during fast motion.

Phase-field model coupling cracks and dislocations at finite strain

A new 3D continuum model is developed to simultaneously describe cracks and dislocations in materials undergoing finite strain deformations. Significant advances are made to account for fracturing in a cubic symmetrical system and to correctly model the microscopic dislocation properties into a Time-Dependent Ginzburg–Landau formalism. In addition, the interaction between dislocations and free borders (crack lips, surfaces…) is naturally described. As an example, the model is used to investigate the effects of plasticity on the delamination and buckling of thin films deposited on substrates. It may also be helpful in any other situation where cracks and dislocations take place and in which finite strain effects must be considered.

Vortex-antivortex dynamics in mesoscopic symmetric and asymmetric superconducting loops with an applied ac current

In the framework of the time-dependent Ginzburg-Landau formalism, we study the dynamics of vortex-antivortex (V-Av) pairs in mesoscopic symmetric and asymmetric superconducting loops under an applied ac current. In contrast to the case of a constant biasing dc current, the process of the V-Av collision and annihilation is strongly affected by the time-periodic ac signal. As the direction of the applied ac current is reversed, the existed V-Av pair moves backward and then collides with a new created Av-V pair in a symmetric loop. In the presence of an appropriate external magnetic field, a novel sinusoidal-like oscillatory mode of the magnetization curve is observed, and the periodic dynamical process of the V-Av annihilation occurs in both branches of the sample. Moreover, for the asymmetric sample with an off-centered hole the creation point of the V-Av pair shifts away from the center of the sample, and the creation and annihilation dynamics of V-Av pairs turns out to be very different from the symmetric case.

Fluctuation effects on the transport properties of unitary Fermi gases

In this Rapid Communication we investigate the fluctuation effects on the transport properties of unitary Fermi gases in the vicinity of the superfluid transition temperature ${T}_{\mathrm{c}}$. Based on the time-dependent Ginzburg-Landau formalism of the Bose-Einstein condensate--BCS crossover, we investigate both the residual resistivity below ${T}_{\mathrm{c}}$ induced by phase slips and the paraconductivity above ${T}_{\mathrm{c}}$ due to pair fluctuations. These two effects have been well studied in the weak-coupling BCS superconductor and here we generalize them to the unitary regime of ultracold Fermi gases. We find that while the residual resistivity below ${T}_{\mathrm{c}}$ increases as one approaches the unitary limit, consistent with recent experiments, the paraconductivity exhibits nonmonotonic behavior. Our results can be verified with the recently developed transport apparatus using mesoscopic channels.

Numerical solution of the time dependent Ginzburg-Landau equations for mixed (d + s)-wave superconductors

The time-dependent Ginzburg-Landau formalism for (d + s)-wave superconductors and their representation using auxiliary fields is investigated. By using the link variable method, we then develop suitable discretization of these equations. Numerical simulations are carried out for a mesoscopic superconductor in a homogeneous perpendicular magnetic field which revealed peculiar vortex states.

Synchronized dynamics of Josephson vortices in artificial stacks of SNS Josephson junctions under both dc and ac bias currents

Nonlinear dynamics of Josephson vortices (fluxons) in artificial stacks of superconducting-normal-superconducting Josephson junctions under simultaneously applied time-periodic ac and constant biasing dc currents is studied using the time dependent Ginzburg-Landau formalism with a Lawrence-Doniach extension. At zero external magnetic field and dc biasing current the resistive state of the system is characterized by periodic nucleation and annihilation of fluxon-antifluxon pairs, relative positions of which are determined by the state of neighboring junctions. Due to the mutual repulsive interaction, fluxons in different junctions move out of phase. Their collective motion can be synchronized by adding a small ac component to the biasing dc current. Coherent motion of fluxons is observed for a broad frequency range of the applied drive. In the coherent state the maximal output voltage, which is proportional to the number of junctions in the stack, is observed near the characteristic frequency of the system determined by the crossing of the fluxons across the sample. However, in this frequency range the dynamically synchronized state has an alternative---a less ordered state with smaller amplitude of the output voltage. Collective behavior of the junctions is strongly affected by the sloped sidewalls of the stack. Synchronization is observed only for weakly trapezoidal cross sections, whereas irregular motion of fluxons is observed for larger slopes of the sample edge.

Non-conventional vortex configurations in a mesoscopic flat disk

The influence of superficial defects on the vortex configurations of a thin superconducting disk is investigated within the time dependent Ginzburg–Landau formalism. The free energy, magnetization, vorticity, and the Cooper pair density are calculated for both metastable and stable vortex configurations and different number of defects on its surface in the presence of an external magnetic field applied perpendicular to the disk area. We show that the competition between the confinement geometry and the geometric position of the defects leads to non-conventional vortex configurations which are not compatible with the symmetry of the sample geometry.

Stable ‘antiferromagnetic’ vortex lattice imprinted into a type-II superconductor

In type-II superconductors, where vortices and antivortices tend to annihilate, only a ‘ferromagnetic’ vortex lattice, with the same orientation of vortex magnetic moments, is usually formed in a homogeneous external magnetic field. Using the time-dependent Ginzburg–Landau formalism, we demonstrate that a checkerboard vortex–antivortex lattice (‘antiferromagnetic vortex lattice’), imprinted onto a superconducting film by a periodic array of underlying clockwise and counterclockwise microcoils generating spatially periodic positive and negative magnetic field pulses and then trapped by an array of artificial pinning centers, remains stable even after the imprinting magnetic field pulse is switched off.

Negative-[formula omitted] regime in the ac magnetic response of superconductor nanoshells

The time-dependent Ginzburg–Landau formalism is applied to analyze the vortex states and vortex dynamics in superconducting spherical nanoshells, subjected to mutually perpendicular strong dc and weak ac magnetic fields. We demonstrate that nonuniformity of the shell thickness can dramatically affect the ac magnetic response of a 3D array of superconducting nanoshells. Remarkably, this response is strongly influenced not only by the relevant geometric and material parameters and the ac-field frequency but also by the magnitude of the applied dc field: by changing this field the real part of the effective ac magnetic permeability can be tuned from positive values significantly larger than one down to negative values.

Magneto-transport properties of curved mesoscopic superconducting strips

Transport properties of curved mesoscopic superconducting strips are investigated in theframework of the time-dependent Ginzburg–Landau formalism. The geometries of thesuperconducting strips considered here are either a section of a cylindrical shell ora full cylindrical shell in which the magnetic field is applied perpendicular tothe axis. The cylindrical section can exhibit considerably asymmetric transportproperties, making it potentially interesting as a sub-micrometer scale superconductingcurrent rectifier. The full cylindrical surface exhibits well developed dissipativebranches in the voltage–current curves, that can be accounted for by kinematicvortex–antivortex phase slip lines. Such kinds of phase slip lines cause voltage oscillationsin a frequency range higher than the one associated with the familiar flux flowregime.

A single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface

We investigate the behaviour of a single Abrikosov vortex trapped in a mesoscopic superconducting cylindrical surface with a magnetic field applied transverse to its axis. In the framework of the time-dependent Ginzburg–Landau formalism we show that, provided the transport current and the magnetic field are not large, the vortex behaves as an overdamped quasi-particle in a tilted washboard potential. The cylindrical thin strip with the trapped vortex exhibits E(J) curves and time-dependent electric fields very similar to the ones exhibited by a resistively shunted Josephson weak link.

Vortex Core Deformation and Stepper-Motor Ratchet Behavior in a Superconducting Aluminum Film Containing an Array of Holes

We investigated experimentally the frequency dependence of a superconducting vortex ratchet effect by means of electrical transport measurements and modeled it theoretically using the time-dependent Ginzburg-Landau formalism. We demonstrate that the high frequency vortex behavior can be described as a discrete motion of a particle in a periodic potential, i.e., the so-called stepper-motor behavior. Strikingly, in the more conventional low frequency response a transition takes place from an Abrikosov vortex rectifier to a phase slip line rectifier. This transition is characterized by a strong increase in the rectified voltage and the appearance of a pronounced hysteretic behavior.

Local probing of the vortex–antivortex dynamics in superconductor/ferromagnet hybridstructures

In-plane ferromagnetic bars, densely packed in a linear array underneath a superconductingbridge, create two types of vortex chains of opposite polarity inside the superconductor. Inthis work we investigate both experimentally and theoretically the dynamics of these vortexchains as a function of an external magnetic field for two different arrangements ofmagnetic moments, namely parallel and antiparallel. The theoretical approach,based on the time-dependent Ginzburg–Landau formalism, confirms previouslyproposed empirical models implemented to describe the basic properties of thesehybrid systems. In addition, local transport measurements allow us to probe thedynamics of individual vortex channels as a function of the applied magneticfield. These measurements evidence a drastic reduction of the dissipation in thechannel populated with vortices having opposite polarity to the applied field.

Dynamics of kinematic vortices in a mesoscopic superconducting loop

Using the time-dependent Ginzburg–Landau formalism, we study the dynamic properties of a submicron superconducting loop in applied current and in presence of a perpendicular magnetic field. The resistive state of the sample is caused by the motion of kinematic vortex–antivortex pairs. Vortices and antivortices move in opposite directions to each other, perpendicularly to the applied drive, and the periodic creation and annihilation of such pairs results in periodic oscillations of the voltage across the sample. The dynamics of these kinematic pairs is strongly influenced by the applied magnetic field, which for high fields leads to the flow of just vortices. Kinematic vortices can be temporarily pinned inside the loop with observable trace in the voltage vs. time characteristics.