Effects of an anisotropic relaxation time on the electron-electron scattering resistivity in K and Cu

Abstract

The contribution of normal electron-electron scattering to the electrical resistivity of K and Cuin the presence of an anisotropic relaxation time is calculated using the relaxation time approximation (RTA) and also, for the first time, using the formally exact variational method. As sources of anisotropic scattering we consider (i) electron-dislocation scattering according to a model of Kaveh and Wiser for potassium, and (ii) a high longitudinal magnetic field B applied to a copper single crystal. It is found that, as compared with the variational method, the RTA overestimates the increase of the electron-electron scattering resistivity pee = A , , p with anisotropy. The calculated enhancement ofA,, in copper by a magnetic field depends sensitively on the crystallographic orientation. Comparison with the experimental coefficients A,, for B I/ (111) yields an Umklapp fraction of A = 0.04-0.06 for electronelectron scattering in Cu, which is smaller than A = 0.28 as previously calculated by Black. The dislocation model cannot account quantitatively for the large variation in the experimental A,, in potassium.