Calculation of Tc and the ratio 2Δ(0)/kBTc of MgB2 within a two-band model of superconductivity

Superconductivity in the MgB₂ superconductor is described within the framework of a two-band Eliashberg formalism. Different gaps are assumed to open on the different parts of the Fermi surface of this compound. Separation of the order parameter (OP) into two components is achieved by taking the Fourier transform of the OP using the momentum states of the σ- and π-bands of MgB₂. Expressions for the T_c and the ratio 2Δ_σ(0)/k_BT_c for this superconductor are obtained. Numerical values for these two properties are obtained for a range of values of the cut-off frequency of the phonons responsible for the superconductivity and for a range of values of the ratio between the two energy gaps. This was done for various values of the normalized partial densities of states on the σ-sheet of the Fermi surface.