Superconductivity in two-band systems with a variable carrier density:: The case of MgB2

A theory of the thermodynamic properties of a two-band superconductor with a low carrier density is developed; it is based on a phonon superconductivity mechanism with a strong electron-phonon coupling. This theory can describe the variation of the critical temperature T-c, the energy gaps Delta(1) and Delta(2), and the relative electronic specific heat jump (C-S - C-N)/C-N at T = T-c with the carrier density in the compound MgB2 when substitutional impurities of various valences are introduced into this system. The values of T-c, Delta(1), and Delta(2) are shown to decrease as this compound is doped by electrons and to remain constant (or almost constant) as it is doped by holes. This behavior follows from the mechanism of filling the sigma and pi energy bands, which overlap at the Fermi surface. The theory agrees qualitatively with experimental data. This agreement is found to be better when intra-and interband electron scattering by an impurity potential is taken into account.