Electron-phonon spectral function and two-band model in tunneling measurement on MgB2

In the present work we calculate for the first time the density of states of MgB2 for different tunneling directions by directly solving the two-band Eliashberg equations in the real-axis formulation starting from the first-principle calculation of the interband and intraband electron-phonon spectral functions. This complicated numeric procedure allows preserving the fine structures of the DOS in the phonon energy range. We show that the numeric inversion of the standard single-band Eliashberg equations when applied to the densities of states obtained by the two-band model may lead to artifacts in the extracted electron-phonon spectral function α2 F(ω). We also suggest that the small DOS structures produced by the two-band inter-action at energies between 20 and 100 meV can be observed only at very low temperature in junctions in perfect clean limit.