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REVIEWS OF TOPICAL PROBLEMS
Ginzburg–Landau theory: the case of two-band superconductors
I. N. Askerzadeab a Institute of Physics, Azerbaijan National Academy of Sciences
b Department of Physics, Faculty of Sciences, Ankara University, Turkey
Abstract:
Recent studies of two-band superconductors using the Ginzburg–Landau (GL) theory are reviewed. The upper and lower critical fields [
$H_{c2}(T)$ and
$H_{c1}(T)$, respectively], thermodynamic magnetic field
$H_{cm}(T)$, critical current density
$j_c(T)$, magnetization
$M(T)$ near the upper critical field, and the upper critical field
$H^{\mathrm{film}}_{c2}(T)$ of thin films are examined from the viewpoint of their temperature dependence at a point
$T_c$ using the two-band GL theory. The results are shown to be in good agreement with the experimental data for the bulky samples of superconducting magnesium diboride,
$\mathrm{MgB}_2$, and nonmagnetic borocarbides
$\mathrm{LuNi}_2\mathrm{B}_2\mathrm{C}$ and
$\mathrm{YNi}_2\mathrm{B}_2\mathrm{C}$. The specific heat jump turns out to be smaller than that calculated by single-band GL theory. The upper critical field of thin films of two-band superconductors is calculated and the Little–Parks effect is analyzed. It is shown that magnetic flux quantization and the relationship between the surface critical magnetic field
$H_{c3}(T)$ and the upper critical field
$H_{c2}(T)$ are the same as in the single-band GL theory. Extension of the two-band GL theory to the case of layered anisotropy is presented. The anisotropy parameter of the upper critical field
$H_{c2}$ and the London penetration depth
$\lambda$, calculated for
$\mathrm{MgB}_2$ single crystals, are in good agreement with the experimental data and show opposite temperature behavior to that in single-band GL theory.
PACS:
74.20.De,
74.25.-q,
74.70.Ad Received: January 25, 2006
DOI:
10.3367/UFNr.0176.200610a.1025
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