Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state

Kogan, V. G.; Clem, John R.; Deang, Jennifer; Gunzburger, Max

doi:10.1103/physrevb.65.094514

Cited by 22 publications

(13 citation statements)

References 25 publications

(8 reference statements)

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“…These early theo-ries were extended to investigate signatures of surface superconductivity fluctuations on transport coefficients [35,36] and thermodynamic properties [37] at the onset of nucleation, and further to analyze critical field in the superconducting films focusing specifically on the boundary and finite thickness effects [38,39]. The effect of anisotropy on H c3 was considered within GL theory [40]. The critical field was also analyzed for the case of unconventional pairing [41,42], and for the case of multiband superconductor in the context of MgB 2 assuming disordered dominated regimes that were treated with the help of semiclassical Usadel equations [43].…”

Section: Introductionmentioning

confidence: 99%

Onset of surface superconductivity beyond the Saint-James–de Gennes limit

et al. 2017

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We revisit the problem of the surface superconductivity nucleation focusing on the detailed study of the critical field H c3 as a function of temperature and disorder. Using the semiclassical Eilenberger formalism we find that away from the Ginzburg-Landau region the ratio between the nucleation critical field H c3 and the upper critical field H c2 deviates strongly from the Saint-James-de Gennes limit. In particular, the H c3 /H c2 is found to be a nonmonotonic function of temperature, which reaches the maximum for a set of parameters corresponding to a crossover region from ballistic to diffusive scattering, when the mean-free path in a bulk of a superconductor is of the same order as zero-temperature superconducting coherence length. We also analyze the robustness of the nucleated phases with respect to diffusive scattering off the sample boundary by solving exactly corresponding eigenvalue problem of an integral equation for the critical field. The implications of these results for the transport in superconductors of various geometries near H c3 are briefly discussed. In particular, we present results for the mechanism of magnetoconductivity oscillations due to surface superconductivity effects.

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Section: Introductionmentioning

confidence: 99%

Onset of surface superconductivity beyond the Saint-James–de Gennes limit

et al. 2017

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“…Kogan et al [24] solved the linearized anisotropic GL equations to study the nucleation of superconductivity in anisotropic superconductors having an arbitrary orientation of the sample surface relative to the crystal principal axes. The surface critical field H c3 is found to be less than 1.695H c2 unless the field is situated along one of the principal crystal planes.…”

Section: Introductionmentioning

confidence: 99%

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Kim¹,

Gunzburger²,

Peterson³

et al. 2009

CiCP

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A computational study of superconducting states near the superconductingnormal phase boundary in mesoscopic finite cylinders is presented. The computational approach uses a finite element method to find numerical solutions of the linearized Ginzburg-Landau equation for samples with various sizes, aspect ratios, and crosssectional shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The vector potential is determined using a finite element method with two penalty terms to enforce the gauge conditions that the vector potential is solenoidal and its normal component vanishes at the surface(s) of the sample. The eigenvalue problem for the linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions is solved and used to construct the superconducting-normal phase boundary for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately reflect the discrete symmetry of each sample boundary were found through the computational approach. These V-AV configurations are realized just within the phase boundary in the magnetic field-temperature phase diagram. Comparisons are made between the results obtained for the different sample shapes.

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“…For distances exceeding ζ(T ) the order parameter approaches zero rapidly. The dependence of the ratio H c3 /H c2 on the material properties [3,4,5], sample geometry and topology [6,7,8], and temperature [9,10,11] has become a subject of intensive investigations.…”

mentioning

confidence: 99%

“…The method described above can be generalized for an arbitrary direction of crystallographic axes with respect to the surface of a superconductor. For strongly anisotropic superconductors, surface superconductivity might disappear if the surface does not coincide with crystallographic planes [8].…”

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confidence: 99%

Surface Superconductivity of Dirty Two-Band Superconductors: Applications toMgB2

Gorokhov

2005

Phys. Rev. Lett.

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The minimal magnetic field H(c2) destroying superconductivity in the bulk of a superconductor is smaller than the magnetic field H(c3) needed to destroy surface superconductivity if the surface of a superconductor coincides with one of the crystallographic planes and is parallel to the external magnetic field. While for a dirty single-band superconductor the ratio of H(c3) to H(c2) is a universal temperature-independent constant 1.6946, for dirty two-band superconductors this is not the case. I show that in the latter case the interaction of the two bands leads to a novel scenario with the ratio H(c3)/H(c2) varying with temperature and taking values larger and smaller than 1.6946. The results are applied to MgB(2) and compared with recent experiments (A. Rydh, cond-mat/0307445).

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Nucleation of superconductivity in finite anisotropic superconductors and the evolution of surface superconductivity toward the bulk mixed state

Cited by 22 publications

References 25 publications

Onset of surface superconductivity beyond the Saint-James–de Gennes limit

Onset of surface superconductivity beyond the Saint-James–de Gennes limit

Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors

Surface Superconductivity of Dirty Two-Band Superconductors: Applications toMgB2

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