New Insight into Electric Force in Metal and the Quadratic Electrical Resistivity Law of Metals at Low Temperatures

Considering that Einstein's relation between the diffusion coefficient and the drift mobility of free randomly moving charge carriers in homogeneous materials including metals is always valid, it is shown that the effective electric force acting on free electrons in metal depends on the ratio between the kinetic free electron energy at the Fermi surface to the classical particle energy 3 kT/2. The electrical resistivity of elemental metals dependence on very low temperatures has the quadratic term, which has been explained by electron-electron scattering. In this paper, it is shown that the quadratic term of the electrical resistivity at low temperatures is caused by scattering of the free randomly moving electrons by electronic defects due to linear effective free electron scattering cross-section dependence on temperature, but not by electron-electron scattering.