Vortex lattice structure in ad-wave superconductor with orthorhombic distortion
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The vortex lattice structure in an orthorhombic d-wave superconductor under a magnetic field parallel to the c axis is studied near the upper critical field using the phenomenological ${D}_{2h}$ symmetric Ginzburg-Landau free-energy density. The equilibrium vortex lattices are commonly body-centered rectangular lattice with no rotation relative to the underlying crystal. At certain temperature which depends on the parameters describing the $a\ensuremath{-}b$ anisotropy, the flux lattice undergoes a second-order phase transition with the direction of the elongation of the rectangular lattice rotated by $90\ifmmode^\circ\else\textdegree\fi{}$ (e.g., from the b-axis direction to the a-axis direction). The phase transition temperature is estimated within two microscopic models.Keywords:
Orthorhombic crystal system
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Anisotropy of Critical Fields in MgB 2 : Two–Band Ginzburg–Landau Theory for Layered Superconductors
The temperature dependence of the anisotropy parameter of upper critical field γHc2 (T) = H⊥c2 (T)/H⊥c2 (T) and London penetration depth γλ(T) = λ⊥(T)/λ⊥ (T) are calculated using two-band Ginzburg–Landau theory for layered superconductors. It is shown that, with decreasing temperature the anisotropy parameter γHc2 (T) is increased, while the London penetration depth anisotropy γλ(T) reveals an opposite behavior. Results of our calculations are in agreement with experimental data for single crystal MgB2 and with other calculations. Results of an analysis of magnetic field Hc1 in a single vortex between superconducting layers are also presented.
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Type-II superconductor
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The Ginzburg-Landau theory has been formulated in a proper form to include the magnetization effect due to penetration of the magnetic field within the superconductor. Modified Ginzburg-Landau equations were obtained and solved for the case of thin films and filaments in vacuo or imbedded in normal material. The resulting expressions describe the behavior of the critical field of thin films and filaments as functions of thickness and temperature. They reduce to Clogston's critical field in the limit of vanishing thickness. They also provide a simple criterion for distinguishing between different types of the superconducting-normal transitions.
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The upper critical field for coupled layered superconductors with local pairs is analyzed within the mean-field approach for the anisotropic negative-U Hubbard model. Effects of reduced dimensionality are investigated by solving the Ginzburg-Landau equations to obtain critical fields for different anisotropy ratios. The Harper's-type system of equations is solved analytically for some special field values. Limitations of Peierls substitution are also discussed.
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In this paper, we report our extensive investigations of layered superconductors within a continuous Ginzburg-Landau model. The calculated results suggest that the parallel upper critical field generally increases with the transition temperature and may be correlated with the behaviours of the order parameters. The calculated upper critical fields of MgB2 are in reasonably good agreement with experiment. The obtained order parameters of MgB2, YBCO and Hg1223 respectively demonstrate a three-dimensional, quasi-three-dimensional and two-dimensional behaviour, as expected.
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We investigate the upper critical field in a dirty two-band superconductor within quasiclassical Usadel equations. The regime of very high anisotropy in the quasi-2D band, relevant for ${\mathrm{MgB}}_{2},$ is considered. We show that strong disparities in pairing interactions and diffusion constant anisotropies for two bands influence the in-plane ${H}_{c2}$ in a different way at high and low temperatures. This causes temperature-dependent ${H}_{c2}$ anisotropy, in accordance with recent experimental data in ${\mathrm{MgB}}_{2}.$ The three-dimensional band most strongly influences the in-plane ${H}_{c2}$ near ${T}_{c},$ in the Ginzburg-Landau (GL) region. However, due to a very large difference between the c-axis coherence lengths in the two bands, the GL theory is applicable only in an extremely narrow temperature range near ${T}_{c}.$ The angular dependence of ${H}_{c2}$ deviates from a simple effective-mass law even near ${T}_{c}.$
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Solid-state physics
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