Superheating fields of superconductors: Asymptotic analysis and numerical results

Dolgert, Andrew J.; Bartolo, S. John Di; Dorsey, Alan T.

doi:10.1103/physrevb.53.5650

Cited by 39 publications

(47 citation statements)

References 9 publications

(18 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…(2) gives B v close to the superheating field B s = 0.745B c , above which the Meissner state in extreme type-II superconductors with κ = λ/ξ ≫ 1 becomes absolutely unstable with respect to weak periodic perturbations of the order parameter 39,40,41,42,43,44 as the Meissner current density at the surface B v /µ 0 λ exceeds the local depairing current density J d . For B 0 > B v , a vortex moves in and out the superconductor under the action of the rf field.…”

Section: Penetration Of a Vortex Over The Oscillating Surface Barmentioning

confidence: 98%

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

2008

View full text Add to dashboard Cite

We consider nonlinear dynamics of a single vortex in a superconductor in a strong rf magnetic field B0 sin ωt. Using the London theory, we calculate the dissipated power Q(B0, ω), and the transient time scales of vortex motion for the linear Bardeen-Stephen viscous drag force, which results in unphysically high vortex velocities during vortex penetration through the oscillating surface barrier. It is shown that penetration of a single vortex through the ac surface barrier always involves penetration of an antivortex and the subsequent annihilation of the vortex antivortex pairs. Using the nonlinear Larkin-Ovchinnikov (LO) viscous drag force at higher vortex velocities v(t) results in a jump-wise vortex penetration through the surface barrier and a significant increase of the dissipated power. We calculate the effect of dissipation on nonlinear vortex viscosity η(v) and the rf vortex dynamics and show that it can also result in the LO-type behavior, instabilities, and thermal localization of penetrating vortex channels. We propose a thermal feedback model of η(v), which not only results in the LO dependence of η(v) for a steady-state motion, but also takes into account retardation of temperature field around rapidly accelerating vortex, and a long-range interaction with the surface. We also address the effect of pinning on the nonlinear rf vortex dynamics and the effect of trapped magnetic flux on the surface resistance Rs calculated as a function or rf frequency and field. It is shown that trapped flux can result in a temperature-independent residual resistance Ri at low T , and a hysteretic low-field dependence of Ri(B0), which can decrease as B0 is increased, reaching a minimum at B0 much smaller than the thermodynamic critical field Bc. We propose that cycling of rf field can reduce Ri due to rf annealing of magnetic flux which is pumped out by rf field from the thin surface layer of the order of the London penetration depth.

show abstract

Section: Penetration Of a Vortex Over The Oscillating Surface Barmentioning

confidence: 98%

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

2008

View full text Add to dashboard Cite

show abstract

“…The threshold is defined by the condition that the external field at the sample edges, H /(1 − n), exceeds the field of first penetration into an infinite sample H p (1/2 1/4 κ 1/2 )(1 + 5.44κ/1 + 4.78κH c ) (ref. 14), which gives the superheating field H sh = (1 − n)H p for the lower bound of field penetration into a finite superconducting sample.…”

mentioning

confidence: 99%

Rayleigh instability of confined vortex droplets in critical superconductors

et al. 2014

View full text Add to dashboard Cite

Depending on the Ginzburg-Landau parameter κ, superconductors can either be fully diamagnetic if κ < 1/ √ 2 (type I superconductors) or allow magnetic flux to penetrate through Abrikosov vortices if κ> 1/ √ 2 (type II superconductors; refs 1,2). At the Bogomolny critical point, κ = κ c = 1/ √ 2, a state that is infinitely degenerate with respect to vortex spatial configurations arises 3,4 . Despite in-depth investigations of conventional type I and type II superconductors, a thorough understanding of the magnetic behaviour in the near-Bogomolny critical regime at κ ∼ κ c remains lacking. Here we report that in confined systems the critical regime expands over a finite interval of κ forming a critical superconducting state. We show that in this state, in a sample with dimensions comparable to the vortex core size, vortices merge into a multi-quanta droplet, which undergoes Rayleigh instability 5 on increasing κ and decays by emitting single vortices. Superconducting vortices realize Nielsen-Olesen singular solutions of the Abelian Higgs model, which is pervasive in phenomena ranging from quantum electrodynamics to cosmology 6-9 . Our study of the transient dynamics of Abrikosov-Nielsen-Olesen vortices in systems with boundaries promises access to non-trivial e ects in quantum field theory by means of bench-top laboratory experiments.The evolution of magnetic properties of an infinite superconductor when crossing κ c is shown in Fig. 1. Type I superconductors with κ < κ c expel magnetic field H until it reaches a critical field H c beyond which superconductivity is destroyed (Fig. 1b,e). In type II superconductors with κ > κ c , superconductivity extends into a wider region, H c1 < H < H c2 , where magnetic field penetrates the sample in the form of Abrikosov vortices, tiny filaments of the normal phase surrounded by encircling supercurrents (Fig. 1a,d (ref. 10), where ξ is the coherence length and D is the sample thickness. The intermediate state forms in the interval (1 − n)H c < H < H c (n < 1 is the shape-dependent demagnetization factor) triggered by the local magnetic field near the edges of the sample exceeding the critical value H c and locally destroying superconductivity (Fig. 1c,f). In type II superconductors, nucleation of superconductivity occurs first near the sample boundary at a specific surface critical field H c3 > H c2 . In type I superconductors H c3 can exceed H c if κ κ c , as shown in Fig. 1b,e. Near κ-induced criticality, with domains containing only a few flux quanta, the intermediate state is unstable towards breaking into an Abrikosov lattice and transient effects become important. To analyse transient behaviour, we consider a sample with κ κ c containing a single domain or droplet of the normal phase, that is, a sample with the lateral size L comparable to the period d of the domain structure. This droplet is nothing but a giant vortex with a normal core comprising several flux quanta 11 . Its critical fission occurs by splitting an N -quanta droplet (Nq-droplet) into a (N − 1)q-drople...

show abstract

“…This framework requires a combination of a shooting approach (introduced rigorously in [17]) with a semi-implicit method (which is A-stable) for the numerical computation of solutions, as well as Hermite-element approximations in the stage of the stability study. The efficiency of this framework is distinguished by the fact that small values of the initial datum f 0 = f (0) can be considered here, contrary to an approach using the method of matched asymptotic expansions as in [20], where the formal pair, from which the expansion of h sh (κ) is determined, cannot be an approximate solution of (1)-(3) for such an initial value. The robustness of the present framework is noticed since it also allows us to study the stability of solutions between the two regimes of κ.…”

Section: Introductionmentioning

confidence: 90%

“…In contrast with the approach of [20], we are here concerned with a numerical framework that leads us both to a determination of the superheating field and to a study of the stability of solutions in each regime of κ. This framework requires a combination of a shooting approach (introduced rigorously in [17]) with a semi-implicit method (which is A-stable) for the numerical computation of solutions, as well as Hermite-element approximations in the stage of the stability study.…”

Section: Introductionmentioning

confidence: 99%

“…Based on a formal approach, namely the method of matched asymptotic expansions, Dolgert et al [20] introduce in the weak-κ regime an expansion of h sh (κ) in powers of κ 1 2 . It results from this paper that the numerical values of h sh (κ), obtained from a computation of solutions by a Newton-type method, agree quite well with the formal values given by the introduced asymptotic expansion.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Numerical study of the stability of solutions for the half-space Ginzburg–Landau model

Castillo

Mefire

2010

J Eng Math

View full text Add to dashboard Cite

International audienceBased on a shooting alternative that allows us to numerically solve the one-dimensional system of Ginzburg-Landau in an unbounded domain, we perform here a numerical study of the stability of solutions of this system. This stability notion, from a physical point of view, means that each solution of the system is identified as stable when it minimizes the corresponding Ginzburg-Landau functional. As opposed to our previous paper, we are concerned here with a more general study since the weak and large regimes of the Ginzburg-Landau parameter are considered and the initial data are no longer subject to the de Gennes condition. We also numerically investigate certain conjectures regarding the superheating field

show abstract

Superheating fields of superconductors: Asymptotic analysis and numerical results

Cited by 39 publications

References 9 publications

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

Dynamics of vortex penetration, jumpwise instabilities, and nonlinear surface resistance of type-II superconductors in strong rf fields

Rayleigh instability of confined vortex droplets in critical superconductors

Numerical study of the stability of solutions for the half-space Ginzburg–Landau model

Contact Info

Product

Resources

About