Phase-slip Lines Research Articles

Critical currents, phase slip centers, and phase slip lines in superconducting films in the absence of external magnetic field

The temperature dependence of the current–voltage characteristics of high-quality thin films of tin from 7 to 50 μm thick is investigated in the absence of external magnetic field. For the first time on the same samples phase slip centers are observed near Tc, where the films are narrow channels, and phase slip lines are observed at lower temperatures, where the films become wide. The critical current exhibits temperature crossover, which affects its absolute value, but in a certain temperature interval a temperature dependence of the form (1−T/Tc)3/2 is maintained. When the temperature is decreased further, the critical current at which vortices due to the self-field of the current can enter the sample depends linearly on temperature and corresponds to the Aslamazov–Lempitsky theory. The temperature at the start of crossover with decreasing temperature coincides with the temperature at which the film width is equal to four times the penetration depth of a weak magnetic field perpendicular to the film plane. On one side of this equality the films are narrow, and on the other side they are wide. The current at which the first phase slip center forms is the Ginzburg–Landau critical current for pair-breaking, distributed uniformly over the width of the film. The current of formation of the first phase slip line is the current of vortex-state instability predicted by Aslamazov and Lempitsky, which is distributed over the width of the film in a specific way.

Dynamics of the superconducting condensate in the presence of a magnetic field. Channelling of vortices in superconducting strips at high currents

On the basis of the time-dependent Ginzburg–Landau equation we studied the dynamics of the superconducting condensate in a wide two-dimensional sample in the presence of a perpendicular magnetic field and applied current. We could identify two critical currents: the current at which the pure superconducting state becomes unstable ( J c2 1 Everywhere in the paper we define the current by J=I/d=∫ 0 Wj(x) dx . 1 ) and the current at which the system transits from the resistive state to the superconducting state ( J c1< J c2). The current J c2 decreases monotonically with external magnetic field, while J c1 exhibits a maximum at H ∗ . For sufficient large magnetic fields the hysteresis disappears and J c1= J c2= J c. In this high magnetic field region and for currents close to J c the voltage appears as a result of the motion of separate vortices. With increasing current the moving vortices form `channels' with suppressed order parameter along which the vortices can move very fast. This leads to a sharp increase of the voltage. These `channels' resemble in some respect the phase slip lines which occur at zero magnetic field.

Josephson behavior of phase-slip lines in wide superconducting strips.

Phase-slip lines can be viewed as dynamically created Josephson junctions in a homogeneous superconducting film. In contrast to phase-slip centers, phase-slip lines occur in wide superconducting strips, where the order parameter may vary in two dimensions. We investigated phase-slip lines in two different materials using several methods. We observed Shapiro steps under microwave radiation, which shows that the frequency of the order parameter oscillation is equal to Josephson frequency. A periodic oscillation of a critical current versus the applied magnetic field was found in strips with a hole in the middle. The latter effect provides a clear evidence of macroscopic quantum interference across a phase-slip line. We have used low temperature scanning laser microscopy to visualize the phase-slip lines and to distinguish them from possible local inhomogeneities in the films.

Phase-Slip Lines and Superconductivity Enhancement by Microwave Irradiation in Thin-Film Type-II Superconductors

Phase-Slip Lines and Superconductivity Enhancement by Microwave Irradiation in Thin-Film Type-II Superconductors

Mesoscopic multiterminal Josephson structures. I. Effects of nonlocal weak coupling

We investigate nonlocal coherent transport in ballistic four-terminal Josephson structures (in which bulk superconductors (terminals) are connected through a clean normal layer, e.g., a two-dimensional electron gas). Coherent anisotropic superposition of macroscopic wave functions of the superconductors in the normal region produces phase slip lines (2D analogs to phase-slip centers) and time-reversal symmetry breaking 2D vortex states in it, as well as such effects as phase dragging and magnetic flux transfer. The tunneling density of local Andreev states in the normal layer is shown to contain peaks at the positions controlled by the phase differences between the terminals. We obtain the general dependence of these effects on the controlling supercurrent/phase differences between the terminals of the ballistic mesoscopic four-terminal SQUID.

Observation of enhancement of superconductivity by an external electromagnetic field and of rf phase-slip lines in wide tin films

The enhancement of superconductivity by an external electromagnetic field and rf phase-slip lines are observed in wide tin films. The temperature, frequency, and power dependences of the critical current are investigated and demonstrate the phenomena observed. It is shown that this class of nonequilibrium effects is common to both narrow and wide films.

On dynamic regime of phase-slip lines in wide superconducting films

Resistive current states in wide superconducting tin films with a dynamic phase slippage have been investigated experimentally. We studied simultaneously the processes of the phase-slip lines' evolution and the heat exchange between the sample and a surrounding medium. Steps on the voltage dependence of the thermal flow from the sample were observed. They demonstrate an instantaneous decrease of the thermal flow from the sample at voltages when a destruction of the stable phase-slip state occurs due to the thermal instability. This phenomenon was analyzed in view of the theory predicting the pulsed phonon fluxes from the active phase-slip regions. We explained the discovered peculiarities by a fast disappearance of the phase-slip lines' structure that operated as a source of phonons. The expression for the thermal energy drop was derived for our case. A comparison of the experimental and calculated dependencies demonstrated a qualitative coincidence.

Spatially resolved characterization of superconducting films and cryoelectronic devices by means of low temperature scanning laser microscope

The work describes the low temperature scanning laser microscopy technique used for spatially resolved characterization of superconducting films and film-based cryoelectronic circuits in the temperature range from 2 to 300 K. The determination of superconducting parameters for separate elements of a high T c Josephson junctions array and imaging of the resistive transition in a high T c superconducting polycrystalline film are demonstrated. The spatial evolution of the resistive state of a Sn thin film strip associated with the phase slip lines formation is visualized.

Spatially resolved study of transition to the phase-slip lines resistive state in wide superconducting strips

The voltage images of nonequilibrium resistive state associated with a phase-slip lines (PSLs) formation in a current-carrying superconducting Sn strip were obtained using low-temperature scanning laser microscopy (LTSLM). The transition to the PSLs started from dynamic-mixed state by single PSL nucleation. The number of PSLs increases rapidly while increasing the current density, the spatial rearrangement of the whole resistive structure being observed.

Tunnel junction with the thin-film electrodes in a resistive phase-slip state

Resistive current state of wide superconducting tin films with the phase-slip lines has been studied experimentally. We measured the current-voltage characteristics (CVCs) of the junction with the electrodes-wide films in the resistive phase-slip state. Features related to the formation and evolution of the phase-slip lines in wide films have been discovered on the CVCs of the tunnel junction.

Two row switching regimes in two-dimensional Nb-Pb Josephson-junction array

A crossover in the two-dimensional Nb-Pb Josephson-junction array from the coherent phase slip line regime to quasiparticle row switching regime has been observed as temperature decreased. The boundary between these regimes corresponds to the temperature when the fluxon mass vanishes (β c ≃ 35)

Kinematic vortices and phase slip lines in the dynamics of the resistive state of narrow superconductive thin film channels

The resistive state of a superconducting thin film channel (bridge) of intermediate width W(ξ⪡W⪡λeff, ξ is the coherence length and λeff is the effective magnetic penetration depth) - this case is relevant to the nanoscale high-Tc superconductor thin film bridges - is studied by simulations of two-dimensional time-dependent Ginzburg-Landau equations. It is found that in the uniform narrow channel at high dimensionless conductivity Σ the dynamical behavior is due to appearance of the phase slip lines, but at lower Σ vortices appear in the resistive state. In inhomogeneous channels vortices appear at any Σ. We call these vortices kinematic vortices because, unlike the Abrikosov vortices, they can not be treated as quasiparticles. They move with any velocity depending on the current distribution over the bridge (the bridge inhomogeneity). The more uniform the current distribution, the higher the vortex velocity. A kinematic vortex with infinite velocity is a phase slip line.

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 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 behaviour of the instability currents in resistive state of wide films

The resistive state properties of wide tin films in a transverse magnetic field have been described for a wide temperature region. The essential changes in the I–V curves and instability currents behaviour with decreasing temperature from critical value is observed experimentally. The phase-slip lines array can be represented as a weak links chain formed against the background of a dynamic vortex state.

Dissipative states in a current-carrying superconducting film

The system of the generalized time-dependent Ginzburg-Landau equations (GTDGLE) describing dirty superconductors nearTc is solved numerically for a thin quasi-two-dimensional, current-carrying layer. In a certain current range one has superconducting states with dissipation which should lead to a step structure in the current voltage characteristic as observed in experiments.1 Depending on the parameters one either has phase slip line (PSL) solutions, which are the two-dimensional analogs of the one-dimensional phase slips (PSCs) or vortex street (VS) solutions, where vortices which are nucleated spontaneously in pairs move perpendicular to the direction of the current. We discuss the range of stable existence of these states and transitions between different states.

Visualization of resistive states of superconducting films

A method is described for visualization of various resistive states in two-dimensional superconductors when scanning their surface with a laser beam. Experiments were made on Sn films to obtain a two-dimensional picture of a separate phase slip line, and a temperature field was plotted of a superconducting film under inhomogeneous heat transfer. The sample IV curve with nodal points of resistive states under study is given together with the block diagram of the experimental set-up.