Beyond Eliashberg Superconductivity in MgB2 : Anharmonicity, Two-Phonon Scattering, and Multiple Gaps

Density-functional calculations of the phonon spectrum and electron-phonon coupling in MgB2 are presented. The E2g phonons, which involve in-plane Bdisplacements, couple strongly to the px,y electronic bands. The isotropic electron-phonon coupling constant is calculated to be about 0.8. Allowing for different order parameters in different bands, the superconducting λ in the clean limit is calculated to be significantly larger. The E2g phonons are strongly anharmonic, and the nonlinear contribution to the coupling between the E2g modes and the px,y bands is significant