Low-temperature resistivity from electron-dual-phonon processes for alkali metals.

Abstract

A calculation of the contribution from electron--dual-phonon scattering to the low-temperature electrical resistivity for alkali metals is carried out. It is found that the low-temperature resistivity from umklapp electron--dual-phonon scattering processes follows nearly the same exponential rule ${\mathrm{BT}}^{4}$ exp(-FTHETA'/T) as resulted from umklapp electron--single-phonon scattering, where FTHETA' is dependent on the minimum available wave vector of phonons and the coefficient B is proportional to (m/M${)}^{2}$, the square of the mass ratio of electron to ion. However, the constant FTHETA' we find from dual-phonon processes is only half of that from single-phonon processes. It is expected that this scattering mechanism has a significant effect on the low-temperature resistivity of some light alkali metals with high Debye temperature at very low temperatures. Our calculation shows that the resistivity of the lithium that resulted from dual-phonon processes will be larger than the one from single-phonon processes when the temperature is below 4 K.