Electron-Phonon Umklapp-Scattering Processes in the Low-Temperature Thermal Resistivity of Potassium

Using the variational method, the electronic contribution to the low-temperature thermal conductivity of potassium is calculated for a number of different pseudopotentials and a realistic phonon spectrum. A detailed evaluation of electron-phonon umklapp-scattering effects is presented. In particular, umklapp processes have a negligible effect on the thermal resistivity and Wiedemann-Franz ratio below {~} 2^∘{}K, but significantly enhance both at temperatures above this. Higher-order corrections to the variational calculation are evaluated and it is found that these are significantly larger for the umklapp component of the thermal resistivity than for the normal component. The lattice contribution to the low-temperature thermal conductivity is calculated and compared with the results for the electronic component.