Geodesic
Microscopic theory of superconductivity in $\text{MgB}_2$-type systems
Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 1, pp. 113-128 Cet article a éte moissonné depuis la source Math-Net.Ru

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We calculate the upper critical magnetic field $H_{\mathrm{c} 2}$ in the framework of a microscopic superconductivity theory with two energy bands of different dimensions on the Fermi surface with the cavity topology typical of the compound $\mathrm{MgB}_2$ taken into account (an anisotropic system). We assume an external magnetic field parallel to the crystallographic $z$ axis. We obtain analytic formulas in the low-temperature range $(T/T_{\mathrm{c}}\ll1)$ and also near the critical temperature $\bigl((T-T_{\mathrm{c}})/T_{\mathrm{c}}\ll1\bigr)$. We compare the temperature dependence of $H_{\mathrm{c} 2}$ for a two-band anisotropic system with that of $H_{\mathrm{c} 2}^0$ corresponding to a two-band isotropic system (with Fermi-surface cavities of the same topology). We determine the role of the band-structure anisotropy, the positive curvature of the upper critical field near the critical temperature, and the important role of the ratio $v_1/v_2$ of the velocities on the Fermi surface in determining $H_{\mathrm{c} 2}$. We also obtain the values of the parameters $\Delta_1$ and $\Delta_2$ along the line of the critical magnetic field.
Keywords: two-band superconductivity, upper critical field, anisotropy. 
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V. A. Moskalenko; M. E. Palistrant; V. A. Ursu. Microscopic theory of superconductivity in $\text{MgB}_2$-type systems. Teoretičeskaâ i matematičeskaâ fizika, Tome 154 (2008) no. 1, pp. 113-128. http://geodesic.mathdoc.fr/item/TMF_2008_154_1_a7/

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