Stability Limits of the Meissner State and the Mechanism of Spontaneous Vortex Nucleation in Superconductors

Kramer, Lorenz

doi:10.1103/physrev.170.475

Cited by 64 publications

(58 citation statements)

References 17 publications

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“…͑However, for smaller mesoscopic samples, the value of H p can be significantly larger than the Matricon-Saint-James result, enhancing the geometrical effect of the square sample, see Sec. IV.͒ For →0 our results agree with the known behavior of the superheating field in type-I supeconductors, H p ϳ1/ͱ [30][31][32]. For →ϱ we obtain that H p →H c in agreement with the result of Refs.…”

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confidence: 90%

Surface barrier in mesoscopic type-I and type-II superconductors

Hernandez

Domı́nguez

2002

Phys. Rev. B

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We study the surface barrier for magnetic-field penetration in mesoscopic samples of both type-I and type-II superconductors. Our results are obtained from numerical simulations of the time-dependent Ginzburg-Landau equations. We calculate the dependence of the first field for flux penetration (H p ) with the Ginzburg-Landau parameter () observing an increase of H p with decreasing for a superconductor-insulator boundary condition ͓("ϪiA)⌿͉ n ϭ0͔ while for a superconductor-normal boundary condition ͑approximated by the limiting case of ⌿͉ S ϭ0) H p has a smaller value independent of and proportional to H c . We study the magnetization curves and penetration fields at different sample sizes and for square and thin-film geometries. For small mesoscopic samples we study the peaks and discontinuous jumps found in the magnetization as a function of magnetic field. To interpret these jumps we consider that vortices located inside the sample induce a reinforcement of the surface barrier at fields greater than the first penetration field H p1 . This leads to multiple penetration fields H pi ϭH p1 ,H p2 ,H p3 , . . . for vortex entrance in mesoscopic samples. We study the dependence on sample size of the penetration fields H pi . We explain these multiple penetration fields, extending the usual Bean-Livingston analysis by considering the effect of vortices inside the superconductor and the finite size of the sample.

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confidence: 90%

Surface barrier in mesoscopic type-I and type-II superconductors

Hernandez

Domı́nguez

2002

Phys. Rev. B

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“…(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

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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.

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“…As shown in Ref. [18], we can restrict our attention to perturbations independent of z and write δf (x, y) = δf (x) cos ky, δq(x, y) = (δq x sin ky, δq y cos ky, 0),…”

Section: B Linear Stability Calculation Of the Superheating Fieldmentioning

confidence: 99%

Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: stability theory, disorder, and laminates

Liarte

Posen

Transtrum

et al. 2017

Supercond. Sci. Technol.

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Theoretical limits to the performance of superconductors in high magnetic fields parallel to their surfaces are of key relevance to current and future accelerating cavities, especially those made of new higher-Tc materials such as Nb3Sn, NbN, and MgB2. Indeed, beyond the so-called superheating field H sh , flux will spontaneously penetrate even a perfect superconducting surface and ruin the performance. We present intuitive arguments and simple estimates for H sh , and combine them with our previous rigorous calculations, which we summarize. We briefly discuss experimental measurements of the superheating field, comparing to our estimates. We explore the effects of materials anisotropy and the danger of disorder in nucleating vortex entry. Will we need to control surface orientation in the layered compound MgB2? Can we estimate theoretically whether dirt and defects make these new materials fundamentally more challenging to optimize than niobium?Finally, we discuss and analyze recent proposals to use thin superconducting layers or laminates to enhance the performance of superconducting cavities. Flux entering a laminate can lead to so-called pancake vortices; we consider the physics of the dislocation motion and potential re-annihilation or stabilization of these vortices after their entry.

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Stability Limits of the Meissner State and the Mechanism of Spontaneous Vortex Nucleation in Superconductors

Cited by 64 publications

References 17 publications

Surface barrier in mesoscopic type-I and type-II superconductors

Surface barrier in mesoscopic type-I and type-II superconductors

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

Theoretical estimates of maximum fields in superconducting resonant radio frequency cavities: stability theory, disorder, and laminates

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