Eliashberg Function<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>α</mml:mi></mml:mrow><mml:mrow><mml:mn>2</mml:mn></mml:mrow></mml:msup></mml:mrow><mml:mn/><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo><mml:mi>F</mml:mi><mml:mo>(</mml:mo><mml:mi>E</mml:mi><mml:mo>)</mml:mo><mml:mn/></mml:math>and the Strong-Coupling Behavior of a Disordered Superconductor

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.

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