Electron-Phonon Umklapp Scattering Processes in the Low-Temperature Ultrasonic Attenuation and Electrical Resistivity of Potassium

The theoretical treatment by Rice and Sham of the electron-phonon contribution to the attenuation of ultrasound in the local limit and the ideal (phonon-limited) electrical resistivity of potassium is extended to include a careful evaluation of the role of umklapp scattering processes at low temperatures. The results have been explicitly separated into normal and umklapp scattering components and the rapid decrease of the umklapp components, and hence the total, at very low temperatures, is emphasized for both the attenuation and resistivity. The results obtained from a realistic phonon model are compared in one case with those from an isotropic Debye-like model with a quadratic dispersion relationship and purely longitudinal and transverse polarization vectors.