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, T c , and the isotope exponent, β , are derived. Numerical calculations with the expressions newly reproduce near-experimental T c ( = 38.50 K ) and β ( = 0.38 ) . The influences of the interband attractive electron–acoustic ( λ π σ ) and electron–optical ( k π σ ) phonons as well as repulsive Coulomb pseudopotential ( μ π σ ∗ ) on T c and β are sketched. It is concluded that λ π σ and k π σ have near-identical elevating effects on T c and β but μ π σ ∗ has reverse effects, similar to the effect of interband impurity scattering.