We study the peculiarities of coherency in the superconductivity of two-orbital system. The superconducting phase transition is caused here by the on-site intra-orbital attractions (negative-U Hubbard model) and interorbital pair-transfer interaction. The dependencies of critical and non-critical correlation lengths on interaction channels and band llings are analyzed.

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A two-band model of MgB2 superconductivity is developed. It exploits repulsive σ-π interband coupling besides the σ-intraband electron-phonon attraction and Coulomb interaction. With an adjustable set of parameters the observed dependences of the gaps, specific heat and second critical magnetic field on temperature, furthermore Tc vs. Al-doping, and the Tc isotope effect exponent are reproduced without further fittings. The unconventional MgB2 superconductivity can be ascribed to the specific band structure and the role of electron interactions.

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