Phenomenological Theory of Vortex Motion in Type-II Superconductors

Mathieu, P.; Simon, Y.

doi:10.1209/0295-5075/5/1/012

Cited by 49 publications

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“…Here we need to recall the main outlines of the MS phenomenological theory [11,14]. The mixed state is regarded as a continuum on the scale of the vortex spacing a, and the vortex array is described locally by the vector G>=«v?ov, where v is a unit vector along VL.…”

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“…The local mean density of the free energy F is expressed as a function of a reduced set of macroscopic variables, in particular the electromagnetic field E, B, the supercurrent Jj (or the superfluid velocity V^), and cw. The equations for thermodynamic equilibrium are obtained by minimizing the magnetic free enthalpy of the sample, and a complete set of transport equations is derived [11]. MS use the same rigorous standard method as that used by Bekarevitch and Khalatnikov in their theory of vortex motion in rotating Hell [15].…”

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“…From Eqs. (l) and (2) and from Maxwell equations, it is easily seen that such a distortion of the vortex array takes place, and associated J^ flow, only over a small depth d--X{\ -i-co/jiQe) ~*^^ from the surface, while J5-0 and (o -B in the bulk [11]. For instance, if a slab is inclined to the applied field [ Fig.…”

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“…As shown in Fig. 1(b), this new boundary condition allows a net transport supercurrent to flow near the surface [11,16]. Thus connecting Ic with s(co,T) and sinOc^S 1, we are able to account for the order of magnitude of critical currents in soft samples, as well as for their field and temperature dependence [16].…”

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“…So it is convenient to separate J into two parts as Ji + J2, where Ji = -curie is the nondissipative part of the current [11]. Ji is defined, at any point and time, as the supercurrent (including diamagnetic currents) that would come into equilibrium with the vortex array in its instantaneous configuration.…”

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Critical-current fluctuations and flux-flow noise in type-II superconductors

Plaçais¹,

Mathieu²,

Simon³

1993

Phys. Rev. Lett.

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By relying on a recent theory of transport in the mixed state and a related model of pinning in soft materials, the instantaneous critical current is introduced as a well-defined part I\ of the total constant current. This nondissipative and time-dependent I\ is assumed to be randomly distributed near the sample surface, and is described as a 2D turbulent homogeneous flow. Auto-and cross-correlation functions of both voltage and magnetic field noises are predicted and are in full agreement with experiments.PACS numbers: 74.60.Ge, 74.60Jg Flux-flow noise has been extensively studied, particularly during the 1960's and 1970's [1-6]. The spectrum and amplitude of the noise voltage dV(t), typically 10 ~^-10 "'' V/(Hz) ^/^ in the 0-10 kHz bandwidth, were regarded as significant parameters revealing the more or less irregular motion of vortex lines (VL) in the presence of pinning. The reader is referred to the excellent critical review by Clem [7]. In view of the experimental difficulties and the increasing intricacy of interpretations, this scope has been practically discarded since about 1980.It should be noted that soft samples were used, classically shaped as foils or strips perpendicular to the applied magnetic field. Low to moderate critical currents /^ are required to avoid spurious sources of noise due to excessive dissipation, such as flicker noise [7]. Therefore, at working temperatures (4.2 K [1,2,5] or close to the X point [6]), the authors had to operate at the onset of the /-K curve; in this region, where flux flow is essentially inhomogeneous along the sample [8], measurements yield unreliable results.Recently [9], we have reconsidered the problem of noise, both theoretically and experimentally. We have performed a series of experiments in superfluid helium in order to widely explore the flux-flow regime. Voltage noise, magnetic field noise around the sample, and thermal Joule noise [10] were investigated, as well as their cross correlations. By relying on a phenomenological theory of vortex motion, recently published by two of us, Mathieu and Simon (MS) [11], we were able to work out a consistent theory of noise, the principle of which is brought forward in this Letter.Roughly speaking, two mechanisms have been advanced to account for the voltage noise quantitatively. In their pioneering work, van Ooijen and van Gurp [1] assumed that flux bundles nucleated randomly at one edge and moved rigidly across the sample with constant velocity VL. This process gives rise to a time sequence of statistically independent pulses, the cutoff' frequency of the noise spectrum being related to the time of flight of bundles. This analogy with the electronic "shot noise" was attractive, but more and more adjustable parameters were introduced to fit the data; besides the flux bundle size ipb, others include the fraction of pinned vortices [2], or a distribution of subpulse times [6]. Somewhat artificially, ipb is found to be a rapidly decreasing function of current, falling off* below the flux quantum <^o [2,6]. Moreov...

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Critical-current fluctuations and flux-flow noise in type-II superconductors

Plaçais¹,

Mathieu²,

Simon³

1993

Phys. Rev. Lett.

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Identification of pinning centres in high T _c superconducting thin films by AC susceptibility

Crété

Bernard

Pommereau

et al. 2004

phys. stat. sol. (c)

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We compare vortex pinning properties of high temperature superconductors (HTS) thin films and correlate these to microstructure to identify pinning centres. We have grown YBa 2 Cu 3 O 7-δ (YBCO), YBCO/PrBa 2 Cu 2.8 Ga 0.2 O 7-δ (YBCO/PBCGO), NdBa 2 Cu 3 O 7-δ (NBCO) thin films and superlattices on (100) SrTiO 3 . We show that pinning by intersections of twin boundaries usually dominates except for strained superlattices [1] and for the NBCO thin films presenting only one [1, 1, 0] twin variant (the [11 0] being completely eliminated), thereby drastically reducing the density of twin boundary intersections (TBI). As expected, AC susceptibility measurements show low pinning properties of these samples. Using High Resolution AC susceptibility, we have discriminated several mechanisms contributing to vortex pinning in a given sample. Indeed, when we eliminated TBI pinning in NBCO thin films, several peaks were observed in χ(T) curve, each one presumably associated with a specific pinning mechanism. A large variety of defects can pin vortices: vacancies, foreign atoms in interstitial or substitutional position, dislocations, stacking faults, grain and twin boundaries, large inclusions, surface roughness... Oxygen vacancies in CuO 2 planes could depress the superconducting order parameter if they are clustered. However, this hypothesis is controversial because it is difficult to characterise the distribution of this kind of defect. Inclusions of non-superconducting parasitic phase play a similar role when their size is of the order of a few nanometres [5]. According to the literature [6], the surface roughness of the films is also at the origin of vortex pinning because of the thickness modulation. Larger inclusions can pin several vortices. Outgrowths, nucleated in the bulk of the films, can be large non-superconducting zones in the volume of the superconductor and are prone to pin vortices. Meanwhile, their pinning efficiency depends on the potential profile at the interface, which is not well defined.Linear defects, because of the shape similitude with vortices, can have a strong pinning energy if their transversal extension is of the order of the coherence length ξ. Such are dislocations [7], appearing during island coalescence or during strain relaxation [8], and amorphous tracks created by heavy ion irradiation [9]. Grain boundaries (in cuprates thin films) and twin planes (in monocristals and films, in particu-

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Vortex Dynamics in Superfluids and Superconductors

Sonin

Krusius

1994

The Vortex State

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Phenomenological Theory of Vortex Motion in Type-II Superconductors

Abstract: Based on the analogy of the Bekarevich-Khalatnikov theory of He 11, a continuum description of vortex motion in the mixed state is presented. The possibility of critical surface currents and associated surface Joule effects is inferred, in agreement with experiment.

Cited by 49 publications

References 9 publications

Critical-current fluctuations and flux-flow noise in type-II superconductors

Critical-current fluctuations and flux-flow noise in type-II superconductors

Identification of pinning centres in high T _c superconducting thin films by AC susceptibility

Vortex Dynamics in Superfluids and Superconductors

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Phenomenological Theory of Vortex Motion in Type-II Superconductors

Abstract: Based on the analogy of the Bekarevich-Khalatnikov theory of He 11, a continuum description of vortex motion in the mixed state is presented. The possibility of critical surface currents and associated surface Joule effects is inferred, in agreement with experiment.

Cited by 49 publications

References 9 publications

Critical-current fluctuations and flux-flow noise in type-II superconductors

Critical-current fluctuations and flux-flow noise in type-II superconductors

Identification of pinning centres in high T c superconducting thin films by AC susceptibility

Vortex Dynamics in Superfluids and Superconductors

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Identification of pinning centres in high T _c superconducting thin films by AC susceptibility