The microscopic theory of the upper critical field Hc2 in two-band   systems in the magnetic field directed parallel and perpendicular to the   plane (ab). Application to MgB2
  The microscopic superconductivity theory in MgB2 systems in the magnetic fields directed parallel and perpendicular to the plane (ab) is built. The two energy bands of different dimensions overlapping on the Fermi surface (two-dimensional sigma- band and three-dimensional pi-band) are taken into account. The theory is built taking into account the weak dispersion of the electron energy of sigma -band in z direction. The systems of equations for the superconductive transition temperature Tc and the upper critical field Hc2(ab) are obtained. The analytic solutions of the equations for Hc2^0(ab) are found in the two temperature areas: nearby the zero temperature T<<Tc^0 and in the vicinity of the superconductive transition temperature Tc^0-T<<Tc^0. The temperature dependencies of the upper critical fields Hc2(ab) and Hc2(c) on the temperature are built, and the anisotropy coefficient gammaH=Hc2^0(ab)/Hc2^0(c) is determined. It is shown that the value of Hc2(ab) exceeds greatly the value of Hc2(c) due to the system anisotropy (to small values of the average velocity of electrons in the crystallographic axis direction). 
M.E.Palistrant, I.D. Cebotari, V.A. Ursu