Two-band-type superconducting instability in MgB2

Using the bight-binding method for the pi -bands in MgB2, the Hubbard on-si te Coulomb interaction on two inequivalent boron p(z)-orbitals is transform ed into expressions in terms of rr-band operators. For scattering processes relevant to the problem in which a wave vector q is parallel to (z) over c ap, it is found to take a relatively simple form consisting of intra-band C oulomb, scattering, interband pair scattering etc. with large constant coup ling constants. This allows to get a simple expression for tile amplitude o f interband pair scattering,between two pi -bands, which diverges if the in terband polarization function in it becomes large enough. The latter was ap proximately evaluated and found to be largely enhanced in tile band structu re in MgB2 These results lead to a divergent interband pair scattering, mea ning two-band-type superconducting instability with enhanced T-c. Adding a subsidiary BCS attractive interaction in each band into consideration, a se mi-quantitative gap equation is given, and T-c. and isotope exponent. alpha are derived. The present instability is asserted to be the origin of high T-c in MgB2.