Thermoelectric Power in the Nearly-Free-Electron Model

Abstract

The thermoelectric power in the nearly-free-electron model is re-examined with specific reference to the especially long-standing theoretical problem posed by occurrences among pure monovalent metals of a negative Hall coefficient but a positive electron-diffusion thermopower. The physical picture is clarified by referring steady-state excitations of the electron gas to the current-free equilibrium distribution, and a summary is given of the evidence which shows Fermi-surface anisotropy to be unimportant for an explanation of the "reversed sign" thermopowers. It is pointed out that the scattering of an electron by the pseudopotential of a single ion generally exhibits Coulomb-core interference which is the analog of the Coulomb-nuclear interference in nuclear physics, and that this can yield the required energy dependence of the transport mean free path. This is illustrated by a model calculation which allows analytic evaluation of all results and which contains only the simplest ingredients: free electrons, a relaxation time, an isotropic elastic-continuum structure factor for acoustic phonons, and a point-ion pseudopotential. The model can accommodate a rather wide range of thermopower coefficients of either sign, and allows a sharp reversal of sign for modest changes of the parameters. Although no quantitative comparison is attempted, estimates of the parameter values appropriate to real systems indicate that Coulomb-core interference effects discriminate between real metals rather satisfactorily and are, in fact, strong enough to produce positive thermopowers with little, if any, additional help.