17. We have calculated the tunneling density of states of MgB₂ for different tunneling directions by directly solving the two-band Eliashberg equations in the real-axis formulation. This procedure reveals the fine structures of the density of states due to the optical phonons. Then we show that the numeric inversion of the standard single-band Eliashberg equations (the only available method), when applied to the two-band density of states of MgB₂, may lead to wrong estimates of the strength of certain phonon branches (e.g. the E_2g) in the extracted electron-phonon spectral function a²F(w). The fine structures produced by the two-band interaction at energies between 20 and 100 meV turn out to be clearly observable only for tunneling along the ab planes, when the extracted a²F(w) contains the combination a²F_ss(w) +a²F_sp(w), together with a minor a²F_pp(w) +a²F_ps(w)component (related figure). Only in this case it is possible to extract information on the s-band contribution to the spectral functions. For any other tunneling direction, the p-band contribution (which does not determine the superconducting properties of MgB₂) is dominant and almost coincides with the whole a²F(w) for tunneling along the c axis. Our results are compared with recent experimental tunneling and point-contact data.

O.V. Dolgov, R.S. Gonnelli, G.A. Ummarino, A.A. Golubov, S.V. Shulga, J. Kortus
"Extraction of the electron-phonon interaction from tunneling data in the multigap superconductor MgB₂", Phys. Rev. B, 68, 132503, (2003).