Theory of Point Contact Spectroscopy in Normal Metals.

Using the pseudopotential theory and a Monte-Carlo technique, we have calculated the point contact spectral functions of Kulik, Omelynchuk and Shekhter, and of van Gelder as well as (alpha)('2)F((omega)) for realistic models of sodium and potassium. We have compared these functions with the experimental point contact data of Jansen et al. Although there is qualitative agreement between all of the calculated functions and experiment for the case of sodium, there are quantitative discrepancies which we can attribute to the martensitic transformation not taken into account in the present calculation. For potassium there is good agreement between the calculated point contact spectral functions and experiment except at very low energies. For both sodium and potassium, the main longitudinal peak is broader for experiment than for any of the calculated functions. We suggest that this broadening may be due to impurity scattering of electrons. The theories of Kulik et al. and of van Gelder, which consider the electron-phonon interaction as the only electron scattering mechanism, cannot explain the occurence of the very low energy peak in the measured characteristic of potassium. We have introduced the scattering of electrons from phasons, the excitations associated with the phase fluctuations of a charge-density wave, in the above theories and calculated its contribution to the point contact spectral function of potassium. From the good agreement between our calculated phason contribution and the experimental data we infer that the low energy peak in the measured characteristic of potassium could very well be due to the interaction of electrons with phasons. This result can be interpreted as the possible direct evidence of the existence of phasons in potassium. To understand the causes of the background in the experimental point contact spectra, we have extended the theory of Kulik et al. to include the impurity scattering in the relaxation-time approximation and applied it to a simple model of a spherical Fermi surface with Debye phonons. We have found that for this model, the inclusion of the electron-impurity scattering results in a broadening of the phonon peak. However, this model of impurity scattering does not produce any background.