Thermal noise and drift mobility of randomly moving electrons in homogeneous materials with highly degenerate electron gas

An application of free electron theory in terms of Fermi statistics is discussed. The main attention is drawn to interpretation of conductivity of metals, superconductors in the normal state, and semiconductors under conditions of high degeneracy of electron gas. The general expressions, based on the Fermi-Dirac distribution of electrons, and the Kubo formula for conductivity contain the effective density of randomly moving free electrons and are valid for degenerate/non-degenerate electron gas. The expressions for the diffusion coefficient, drift mobility, and electrical conductivity will be discussed together with useful approximations for materials with non-degenerate electron gas and materials with any degree of degeneracy.