Singularities of phonon spectra of superconductors observed with point contacts: A theory for dirty S-N contacts

Abstract

Nonlinearities in the conductance of point contacts between a superconductor and a normal metal are considered for applied voltages larger than the energy gap Δ. The voltage dependence of the conductance and the second derivative of the current-voltage characteristic, resulting from the local electron-phonon interaction in the contact region, are obtained for the case where electrons move diffusively through the contact, their mean free path being much shorter than the contact dimensiond. The conductance nonlinear structure corresponding to peaks of the Eliashberg function is calculated for simple model examples. These results are valid when the inequalityλd2Δ/ħD<1 holds, whereλ is the electron-phonon coupling constant andD is the electron diffusion coefficient. The second derivative,d2I/dV2, is obtained for voltages near the values corresponding to Van Hove singularities of the phonon density of states.