The Upper Critical Field Hc2 in Advanced Superconductors with Anisotropic Energy Spectrum

A brief review of works on the microscopic theory of determining the upper critical field in two-band isotropic and anisotropic superconductors is given. The research is based on a set of the Ginzburg–Landau equations for the order parameters in a magnetic field that are studied in terms of the classical approach to a superconducting system in a magnetic field. Two inequivalent energy bands with different topology of Fermi surface cavities overlapping on the Fermi surface are discussed. The cases of the direction of the external magnetic field \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{H}//$\end{document} the (ab) plane and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\vec{H}//$\end{document} the crystallographic c axis are studied. The equations for determining Hc2(ab) and Hc2(c) for a pure superconductor and a superconductor doped with electrons and holes are derived. The analytical solutions to these equations in the vicinity of the superconducting transition temperature (Tc−T≪Tc) and in the vicinity of zero (T≪Tc) are found. The temperature and impurity dependences of the upper critical fields Hc2(ab) and Hc2(c), as well as the anisotropy coefficient γH, are studied. The resulting theory is applied to determine the dependences of the above magnetic characteristics of intermetallic compound MgB2. The theory agrees qualitatively with experimental data.