Lower critical field and magnetization of strong-coupling, type II superconductors in the dirty limit

Rammer, J.

doi:10.1007/bf00116866

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…For superconductors with arbitrary purity the FLL was computed from microscopic theory in the quasiclassical formulation by Eilenberger (1968), which expresses the free energy in terms of energy-integrated Green functions; see also Usadel (1970) for the limit of impure superconductors (with numerical solutions by Watts-Tobin et al 1974 andRammer 1988) and the carefull discussion of this quasiclassical approximation by Serene and Rainer (1983). The computations by , Kramer and Pesch (1974), Watts-Tobin et al (1974), Rammer et al (1987), and Rammer (1988) used a circular cell method, which approximates the hexagonal Wigner-Seitz cell of the triangular FLL by a circle, and the periodic solutions by rotationally symmetric ones with zero slope at the circular boundary (Ihle 1971). Improved computations account for the periodicity of the FLL (Klein 1987, Rammer 1991a, see also the calculation of the density of states near B c2 by Pesch (1975) and recent work by Golubov and Hartmann (1994).…”

Section: Ideal Flux-line Lattice From Microscopic Bcs Theorymentioning

confidence: 99%

The flux-line lattice in superconductors

1995

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Magnetic flux can penetrate a type-II superconductor in form of Abrikosov vortices (also called flux lines, flux tubes, or fluxons) each carrying a quantum of magnetic flux φ 0 = h/2e. These tiny vortices of supercurrent tend to arrange in a triangular flux-line lattice (FLL) which is more or less perturbed by material inhomogeneities that pin the flux lines, and in high-T c superconductors (HTSC's) also by thermal fluctuations. Many properties of the FLL are well described by the phenomenological Ginzburg-Landau theory or by the electromagnetic London theory, which treats the vortex core as a singularity. In Nb alloys and HTSC's the FLL is very soft mainly because of the large magnetic penetration depth λ: The shear modulus of the FLL is c 66 ∼ 1/λ 2 , and the tilt modulus c 44 (k) ∼ (1 + k 2 λ 2 ) −1 is dispersive and becomes very small for short distortion wavelength 2π/k ≪ λ. This softness is enhanced further by the pronounced anisotropy and layered structure of HTSC's, which strongly increases the penetration depth for currents along the c-axis of these (nearly uniaxial) crystals and may even cause a decoupling of two-dimensional vortex lattices in the Cu-O layers. Thermal fluctuations and softening may "melt" the FLL and cause thermally activated depinning of the flux lines or of the two-dimensional "pancake vortices" in the layers. Various phase transitions are predicted for the FLL in layered HTSC's. Although large pinning forces and high critical currents have been achieved, the small depinning energy so far prevents the application of HTSC's as conductors at high temperatures except in cases when the applied current and the surrounding magnetic field are small.

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Section: Ideal Flux-line Lattice From Microscopic Bcs Theorymentioning

confidence: 99%

The flux-line lattice in superconductors

1995

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“…In Refs. [9][10][11][12][13], the GL equations and the equations of the microscopic theory of superconductivity were solved numerically in the framework of circular cell approaches and it was shown that this approximation not only yields good results at low induction but also at H ∼ H c2 . A similar approach was used in Ref.…”

Section: Introductionmentioning

confidence: 99%

Approximate Ginzburg-Landau solution for the regular flux-line lattice: Circular cell method

et al. 2001

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A variational model is proposed to describe the magnetic properties of type-II superconductors in the entire field range between Hc1 and Hc2 for any values of the Ginzburg-Landau parameter κ > 1/ √ 2. The hexagonal unit cell of the triangular flux-line lattice is replaced by a circle of the same area, and the periodic solutions to the Ginzburg-Landau equations within this cell are approximated by rotationally symmetric solutions. The Ginzburg-Landau equations are solved by a trial function for the order parameter. The calculated spatial distributions of the order parameter and the magnetic field are compared with the corresponding distributions obtained by numerical solution of the Ginzburg-Landau equations. The comparison reveals good agreement with an accuracy of a few percent for all κ values exceeding κ ≈ 1. The model can be extended to anisotropic superconductors when the vortices are directed along one of the principal axes. The reversible magnetization curve is calculated and an analytical formula for the magnetization is proposed. At low fields, the theory reduces to the London approach at κ ≫ 1, provided that the exact value of Hc1 is used. At high fields, our model reproduces the main features of the well-known Abrikosov theory. The magnetic field dependences of the reversible magnetization found numerically and by our variational method practically coincide. The model also refines the limits of some approximations which have been widely used. The calculated magnetization curves are in a good agreement with experimental data on high-Tc superconductors.

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“…To describe the vortex structure at arbitrary fields we employ the circular cell approximation [19][20][21][22]. Within this approach the unit cell of the hexagonal vortex lattice hosting a single vortex is replaced by a circular cell with the centre at the point of superconducting phase singularity.…”

Section: Modelmentioning

confidence: 99%

“…The approach presented in Sec. II reduces to the single-band model, if λ 12 = λ 21 = 0 and D 1,2 = D. For λ 11 > λ 22 , it corresponds to the description of the independent stronger-superconductivity band. Fig.…”

Section: A Single-band Limitmentioning

confidence: 99%

Field dependence of the vortex-core size in dirty two-band superconductors

Vargunin

Силаев

2019

Phys. Rev. B

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We study the structure of Abrikosov vortices in two-band superconductors for different external magnetic fields and different parameters of the bands. The vortex core size determined by the coherence lengths are found to have qualitatively different behaviour from that determined by the quasiparticle density of states spatial variation. These different vortex core length scales coincide near the upper critical field, while the discrepancy between them becomes quite significant at lower fields. Within the diffusive approximation we demonstrate several generic regimes in the field dependence of the vortex core sizes determined by the disparity of diffusion constants in the two bands.

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Lower critical field and magnetization of strong-coupling, type II superconductors in the dirty limit

Cited by 10 publications

References 26 publications

The flux-line lattice in superconductors

The flux-line lattice in superconductors

Approximate Ginzburg-Landau solution for the regular flux-line lattice: Circular cell method

Field dependence of the vortex-core size in dirty two-band superconductors

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