Current-voltage characteristic of narrow superconducting wires: Bifurcation phenomena

Баранов, В. В.; Balanov, A. G.; Kabanov, V. V.

doi:10.1103/physrevb.84.094527

Cited by 20 publications

(26 citation statements)

References 23 publications

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“…However, our work focuses on analytical methods for the inhomogeneous system, which as stated previously makes the steady state and linearization to much more difficult to handle. We show that a simplified system can be obtained through weakly nonlinear analysis and that this system contains the normal form obtained in [27] as the size of the weak link shrinks to zero. We also demonstrate that in addition to the infinite period bifurcation for small u, a hysteresis exists in our system for large u values, similar to that in Ref.…”

Section: Introductionmentioning

confidence: 92%

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Phase slips in superconducting weak links

2017

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Superconducting vortices and phase slips are primary mechanisms of dissipation in superconducting, superfluid, and cold atom systems. While the dynamics of vortices is fairly well described, phase slips occurring in quasi-one dimensional superconducting wires still elude understanding. The main reason is that phase slips are strongly non-linear time-dependent phenomena that cannot be cast in terms of small perturbations of the superconducting state. Here we study phase slips occurring in superconducting weak links. Thanks to partial suppression of superconductivity in weak links, we employ a weakly nonlinear approximation for dynamic phase slips. This approximation is not valid for homogeneous superconducting wires and slabs. Using the numerical solution of the timedependent Ginzburg-Landau equation and bifurcation analysis of stationary solutions, we show that the onset of phase slips occurs via an infinite period bifurcation, which is manifested in a specific voltage-current dependence. Our analytical results are in good agreement with simulations.

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Section: Introductionmentioning

confidence: 92%

“…The phase slip state of homogenous systems have recently been analyzed in much greater detail 27 . Using bifurcation analysis, Baranov et.…”

Section: Introductionmentioning

confidence: 99%

Phase slips in superconducting weak links

2017

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“…1 Their dynamics is still poorly understood and at the moment is of a great research interest. [12][13][14][15][16] Previously it was found out that the parameter u = τ ψ /τ θ , where τ ψ is the relaxation time of the amplitude of the order parameter (OP) and τ θ is the relaxation time of the phase of the OP, governs the dynamics of PSCs in a narrow superconducting ring. 12,13 With this, the superconducting channel can demonstrate two dynamical regimes.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of resistive state in thin superconducting channels

2013

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We theoretically study how the dynamics of the resistive state in narrow superconducting channels shunted by an external resistor depends on channel's length L, the applied current j, and parameter u characterizing the penetration depth of the electric field in the nonequilibrium superconductors. We show that changing u dramatically affects both the behaviour of the current-voltage characteristics of the superconducting channels and the dynamics of their order parameter. Previously, it was demonstrated that when u is less than the critical value uc1, which does not depend on L, the phase slip centers appear simultaneously at different spots of the channel. Herewith, for u > uc1 these centres arise consecutively at the same place. In our work we demonstrate that there is another critical value for u. Actually, if u does not exceed a certain value uc2, which depends on L, the current-voltage characteristic exhibits the step-like behaviour. However, for u > uc2 it becomes hysteretic. In this case, with increase of j the steady state, which corresponds to the time independent distribution of the order parameter along the channel, losses its stability at switching current value jsw, and time periodic oscillations of both the order parameter and electric filed occur in the channel. As j sweeps down, the periodic dynamics ceases at certain retrapping current value jr < jsw. Shunting the channel by a resistor increases the value of jr, while jsw remains unchanged. Thus, for some high enough conductivity of the shunt jr and jsw eventually coincide, and the hysteretic loop disappears. We reveal dynamical regimes involved in the hysteresis, and discuss the bifurcation transitions between them.

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“…[20][21][22][23]25,26 In the deterministic dynamics studied here phase slips occur when the local amplitude of the current is greater than an energy barrier determined by the local magnitude of the order parameter. (Note that the random initial conditions mean that this magnitude will be different on different sites and that the random currents implied by the random phases will lead to different order parameter magnitudes at intermediate times even if the initial condition is a space independent order parameter magnitude).…”

Section: Quench Dynamicsmentioning

confidence: 99%

Electromagnetic response during quench dynamics to the superconducting state: Time-dependent Ginzburg-Landau analysis

Kennes

Millis

2017

Phys. Rev. B

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We use a numerical solution of the deterministic TDGL equations to determine the response induced by a probe field in a material quenched into a superconducting state. We characterize differences in response according to whether the probe is applied before, during, or after the phase stiffness has built up to its final steady state value. We put an emphasis on the extend to which superfluid response requires a non-negligible phase stiffness, which for the considered quench has to build up dynamically. A key finding is that the time dependent phase stiffness controls the likelihood of phase slips as well as the magnitude of the electromagnetic response. Additionally, we address the electromagnetic response expected if the probe itself is strong enough to activate phase slip processes. If the probe is applied before phase stiffness is sufficiently build up we find that phase slips occur so that the vector potential is compensated and no long term supercurrent is induced, while if applied at sufficient phase stiffness a weak probe pulse will induce a state with a long-lived supercurrent. If the probe is strong enough to activate the phase slip process the supercurrent state will only be metastable with a lifetime that scales logarithmically with the amplitude of fluctuations in the magnitude of the order parameter. Finally, we study the response to experimentally motivated probe fields (electric field that integrates to zero). Interestingly, depending on the relative time difference of the probe field to the build up of superconductivity, long-lived supercurrents can be induced even though the net change in vector potential is zero.

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Current-voltage characteristic of narrow superconducting wires: Bifurcation phenomena

Cited by 20 publications

References 23 publications

Phase slips in superconducting weak links

Phase slips in superconducting weak links

Dynamics of resistive state in thin superconducting channels

Electromagnetic response during quench dynamics to the superconducting state: Time-dependent Ginzburg-Landau analysis

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