Interband interactions and three-square-well potentials on the superconductivity of MgB2

Superconductivity in magnesium diboride, MgB2, is described within the framework of Bogoliubov-Valatin two-band and two-gap formalism, employing a three-square-well potential model. The expressions for the superconducting transition temperature, Tc, and the isotope exponent, β, are derived. Numerical calculations with the expressions newly reproduce near-experimental Tc(=38.50K) and β(=0.38). The influences of the interband attractive electron-acoustic (λπσ) and electron-optical (kπσ) phonons as well as repulsive Coulomb pseudopotential (μπσ∗) on Tc and β are sketched. It is concluded that λπσ and kπσ have near-identical elevating effects on Tc and β but μπσ∗ has reverse effects, similar to the effect of interband impurity scattering.