Phase-slip Processes Research Articles

Energy transfer and phase slip by quantum vortex motion in superfluid4He

The purpose of the present article is to emphasize the usefulness of the ideas of E. R. Huggins in thinking about vortex motion and phase slip in superfluid4He, and is primarily pedagogical. Several explicit illustrations of vortex motion and phase-slip processes are considered. In addition, it is shown that Huggins's results lead to a generalization and a more complete understanding of the familiar expression E+vs · p for the energy in the rest system of an excitation in the flowing superfluid, as applied to vortex excitations. Here, E is the energy and p is the momentum of the excitation in the moving system, and vs is the superfluid velocity.

Charge-density-wave phase slip in NbSe3

We have studied the phase-slip process by which charge-density-wave (CDW) current is converted to single-particle current at electrical contacts. Transport and X-ray scattering measurements indicate that an excess voltage V ps dropped between current contacts induces a large static deformation of the CDW phase. The measured V ps - and temperature-dependent phase-slip rates are consistent with a model in which CDW dislocation loops are thermally nucleatod in the presence of these deformations. The effects of impurities and contact perturbations on the phase slip process are also discussed

Phase Dynamics and Localized Solutions to the Ginzburg-Landau Type Amplitude Equations

We study different types of long wavelength phase modulation and localized modes in the dissipative media described by the Ginzburg-Landau type amplitude equations. We derive nonlinear phase equations for the phase instabilities and investigate their behaviors. When the phase description breaks down, phase slip process occurs and topologically different states come out. In a certain parameter range localized solutions or solitonlike solutions appear as stable solutions to the amplitude equations.

Phase Dynamics and Localized Solutions to the Ginzburg-Landau Type Amplitude Equations

We study different types of long wavelength phase modulation and localized modes in the dissipative media described by the Ginzburg·Landau type amplitude equations. We derive nonlinear phase equations for the phase instabilities and investigate their behaviors. When the phase descrip­ tion breaks down, phase slip process occurs and topologically different states come out. In a certain parameter range localized solutions or solitonlike solutions appear as stable solutions to the ampli­ tude equations. § 1. Dissipative structures and amplitude equations In thermodynamic equilibrium a given system usually rests in a homogeneous and stationary state. When the system is driven far from equilibrium by changing an external parameter such as temperature gradient, the homogeneous and stationary state becomes unstable and a new state called dissipative structure emerges_I) At the instability point some of the spatio-temporal symmetry properties inherent in the system are broken, and the new state generally has lower symmetry than in the thermodynamic branch. One of the useful theoretical approaches to treat spatially extended dissipative systems is the reductive perturbation method.I)-3). The real part of the eigenv·alues of the critical modes become zero at the bifurcation point so that the motion of the critical modes is slow near the bifurcation point. In the reductive perturbation method we eliminate the degrees of freedom that vary rapidly in space and time and derive a partial differential equation for the amplitude of the critical modes_ The amplitude equation describes slow evolution of the dissipative structure near the bifurcation point. There are several types of amplitude equations depending on the type of the instabilities and also on the symmetries of the system. 1.1. The Newell- Whitehead equation If the critical mode has a nonvanishing wavenumber Q,and at the same time if the eigenvalue of the critical mode is real and changes its sign at the bifurcation point, then a spatially periodic pattern with the wavenumber Qc will appear as a dissipative structure_ The corresponding amplitude equation for a one-dimensional system is the Ginzburg-Landau equation:

Charge-density-wave phase slip and current conversion inNbSe3

We report measurements of the phase-slip process by which charge-density-wave (CDW) current is converted to single-particle current at electrical contacts. An excess voltage ${\mathit{V}}_{\mathrm{ps}}$ produces a large static deformation of the CDW phase, which drives formation of dislocation loops. Measurements of the phase-slip rate as a function of the applied stress ${\mathit{V}}_{\mathrm{ps}}$ for both CDWs in ${\mathrm{NbSe}}_{3}$ reveal a diodelike relation, analogous to that for phase slip in superfluids. Our results are generally consistent with the predictions of Ramakrishna et al., and may have significant implications for study of CDW dynamics of temperatures well below the Peierls transition.

Computer simulations of quantum phase slippage in superfluid 3He

Quantum-dynamic processes of phase slippage in3He are demonstrated to be associated with superfluid vortex nucleation, thus confirming Anderson's scenario for phase slippage through vortex generation and motion in superfluids. We also encounter more complex phase-slip processes, involving phase-slip centers (PSC), phase-slip lines (PSL), and various combinations thereof (PSC + PSL, PSC + PSC, etc.) for the coupled multi-component order-parameter amplitudes. The total order parameter does not vanish - phase slippage in superfluid 3He is inherently a nonlocal process in space-time. Time-dependent Ginzburg-Landau (TDGL) theory is used to compute the current-phase relation for superfluid 3He flow driven by a chemical-potential difference; this serves to provide results that are useful to the experimentalists for an interpretation of their data. Our simulations reveal a tendency for avalanches of vortices to appear simultaneously in long channels, during the period of a single Josephson oscillation. We also simulate dynamics of vortex interactions, such as vortex recombination and an intrinsic “vortex mill”, in which a vortex bifurcates into two vortices of the same circulation plus one of the opposite circulation.

Dynamics of voltage-driven Josephson junction arrays

The authors discuss the dynamics of voltage-driven Josephson junction arrays with negligible capacitances. The array dynamics shows a sensitive dependence on initial phases, leading to current-spike structures in the time-averaged I-V relations. They demonstrate this effect explicitly for the simple system of a two-junction chain, which they also use to illustrate the main features of current response to external driving voltages. They then show that a class of simplified ansatz solutions of two-dimensional voltage-driven Josephson junction arrays under a perpendicular magnetic field can be reduced to two-junction dynamics. In both cases, they find that coherent phase-slip processes can lead to subharmonic lockings with an external RF field.

Dynamics of vortex nucleation in 3He-A flow.

Quantum phase slippage in superfluid $^{3}\mathrm{He}$ flow is simulated numerically in rectangular slab geometries. Assuming that the flow is confined to a channel having horizontal surfaces close to each other, the spatial problem reduces to the two transverse dimensions; we report time-dependent computer simulations of superfluid $^{3}\mathrm{He}$ flow in 2+1 dimensions using the time-dependent Ginzburg-Landau equations. The quantum-dynamic processes of phase slippage in $^{3}\mathrm{He}$ are demonstrated to be associated with superfluid vortex nucleation; we thus confirm Anderson's assumption for phase slippage through vortex motion in superfluids. We also find several other phase-slip scenarios involving vortices, phase-slip lines, and combinations thereof for the coupled multicomponent order-parameter amplitudes. We consider both diffuse and specular boundary conditions at the side walls and demonstrate that our results are essentially independent of the boundaries. We compute the critical current for vortex nucleation as a function of the channel width, and compare it with existing theories of vortex nucleation; we also discuss our calculations in connection with experiments on phase slippage in $^{3}\mathrm{He}$ flow. One of our most important results is that the superfluid order parameter for the vortices generated in the computer simulations does not vanish anywhere; i.e., the vortices possess superfluid core structures; hence the processes of phase slip for superfluid $^{3}\mathrm{He}$ are nonlocal in space-time.

Magnetic field effect on phase-slip processes in superconducting microbridges

Abstract We have observed the resistive regular steps in current-voltage characteristics of an indium variable-thickness microbridge in the presence of a magnetic field H near the critical temperature. From the differential resistance of steps, we obtained the H dependence of size of dissipative region, and compared it with the phase-slip model with the modified pair-breaking time and quasiparticle-diffusion length.

Flux dynamics and the growth of the superconducting phase.

We present a detailed investigation of the growth of the superconducting phase in a magnetic field. For type-I superconductors, the planar normal-superconductor interface is dynamically unstable. In the nucleation regime this feature leads to interface motion similar to that found in the solid-liquid transition. In the spinodal regime the spinodal growth proceeds by a sequence of phase-slip processes, unique to a system with a complex order parameter. In type-II superconductors, vortex absorption stabilizes a planar interface, despite the negative surface tension.

Phase slip and the origin of broad-band noise in NbSe 3

We have investigated the phase slip process which occurs between regions with different time-averaged charge density wave velocities. Longitudinal phase slip at electrical contacts is temperature activated and requires a minimum voltage V ps o . We evaluate the characteristic parameters and their dependence on the CDW order parameter Δ(T). Transverse phase slip, or velocity shear, occurs as a finite size effect associated with irregular crystal cross sections, and is the dominant source of broad band noise in NbSe 3.

Phase-slip critical fluctuations and the order-disorder transition of the CDW in o-TaS 3

A narrow peak of noise caused by spontaneous resistance fluctuations is observed in o-TaS 3 samples of few Kelvins below the CDW transition, but exactly at the temperature where metastability disappears. The fluctuations are supposed to be the result of the development, in the region where metastability is absent, of the phase-slip process which is responsible for the relaxation of metastable states. The widths of both the noise peak and the resistance anomaly are approximately the same, and are consistent with the energy of thermal activation of phase slip. This suggests the destruction of long-range order in the CDW as a result of its melting through the thermal activation of phase slip.

Nonlinear conductivity of quasi-one-dimensional TaS3 at low temperatures

The nonlinear conductivity in orthorhombic and monoclinic TaS3 has been measured as a function of temperature from the Peierls transition temperature down to 4.2 K in the electric field range 10-2-500 V cm-1. At liquid-helium temperature a sharp increase in conductivity is measured in a very limited variation range of voltages. A general description based on phase-slip processes is given to explain these nonlinear properties in the whole temperature range.

Topology of superfluid phase slippage for 'he flow in a channel

The momentum-space topology of phase slippage in superfluid 3 He flowing through a narrow channel is discussed, on the basis of numerical integration of the time-dependent Ginzburg-Landau equations. Here the phase-slip processes are associated with superfluid-core phase-slip centers — delocalized in space-time.

Superfluid phase slippage in 3He flow through a narrow channel.

An investigation of phase slippage in flowing superfluid $^{3}\mathrm{He}$ is presented, based on the numerical integration of time-dependent Ginzburg-Landau equations. The quantum-dynamical phase-slip processes in $^{3}\mathrm{He}$ are found to be associated with superfluid-core phase-slip centers---in contrast with the resistive state for superconductors where phase-slip centers have normal cores.

Inverse AC-Josephson effect in superconducting in and Pb-whiskers

HF-radiation has been applied to In and Pb-whiskers by surrounding the sample by a superconducting loop. In both cases the voltage-current characteristics show steps of zero slope related to the frequency of the HF-field by the Josephson-relation, indicating the existence of phase-slip processes at Josephson frequency.

Transport Properties of Charge-Density Waves

The remarkable electrical behaviour of NbSe3 and a few other quasi low-dimensional metals arises from the presence, at low enough temperatures, of charge-density waves (CDWs) which can be set into motion by an applied electric field. This entails a co-opearative motion of the electrons, essentially as suggested by Frohlich (1954), and leads to non-linearity, non-locality and freqancy-dependence in the conduction, the appearance of periodic components of current in a steady field, syncronization phenomena when alternating and direct fields are applied together, and a veriety of hysteresis and memory effects. Explanations of this behaviour have mostly been based on semi-classical phenomenological models, in which the CDW is regarded as an elastically deformalble object, pinned to the lattice by randomly distributed impurities. However, the experimental evidence leaves some doubt as to whether the important physical processes have been correctly identified, and progress at a microscopic level has been rather limited. In this survey of charge-density wave transport, the extent to which recent experimental work makes it necessary to abandon the conventional picture of the moving CDW "sliding" over impurities is considered. It is concluded that processes of phase-slip, involving local disruption of the CDW, are an essential part of the motion.

Thermally initiated phase-slip in the motion and relaxation of charge-density waves in niobium triselenide

The relation between two well known charge-density-wave (CDW) transport phenomena, namely the apparent increase in the threshold field ET for continuous Frohlich conduction in short specimens, and the memory effect seen when the direction of current flow is reversed, is investigated in experiments on NbSe3 at temperatures T between 59 and 114 K. The experiments show that the processes of phase-slip that occur near the current terminals during continuous Frohlich conduction are initiated thermally, probably by the creation of a vortex, and are responsible also for relaxing the metastable distortion of the CDW that remains after current ceases.

Evidence for thermally-initiated phase-slip in Charge-Density Waves in niobium triselenide

Experiments on niobium triselenide between 80K and 135K indicate that the processes of phase-slip which occur near the current terminals during charge-density wave (CDW) conduction are initiated thermally. The same processes appear responsible for relaxing the metastable states of the CDW, by which memory of the direction of current flow is retained. The rate of phase-slip is consistent with the processes commencing by the thermal creation of phase vortices in the strained CDW near the terminals.

Microwave-induced resistive state in ultrathin superconducting aluminium films

We have performed resistance and tunneling measurements on very thin super-conducting Al films, irradiated with 45 GHz microwave radiation. For microwave powers above a critical value we observed a transition to an inhomogeneous resistive state. The orderparameter in the superconducting regions of the inhomogenous state is slightly lower than the value at zero microwave power. The experimental results cannot be explained with theoretical models based on a nonequilibrium distribution function of the quasiparticles. An alternative model is proposed, based on phase-slip processes induced by the microwave current, which is in qualitative agreement with the observations.