Eliashberg Functionα2(E)F(E)and the Strong-Coupling Behavior of a Disordered Superconductor

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Abstract
The electron-phonon interaction in a disordered superconductor is calculated. One finds additional electron-phonon processes which do not conserve the lattice momentum and a reduction of the normal and the umklapp processes. The additional electron-phonon processes contribute particularly to processes with low energy transfer, so that the Eliashberg function depends linearly on the energy in the low-energy region. This is in agreement with recent tunneling experiments. The linear part of the Eliashberg function causes the strong-coupling behavior of disordered superconductors. Therefore, the anomalous properties of a disordered superconductor can be explained by the change in the electron-phonon interaction.