Nontrivial behavior of the thermoelectric power: Electron-electron versus electron-phonon scattering

The thermoelectric power nontrivial temperature behavior, observed in metals and other structures can be due either to electron-electron or electron-phonon scattering as long as:approximations do not drastically hide the behavior. The case of electron-electron scattering was treated by:Hildebrand et al. [Phys. Rev. B 56, R4317 (1997)]. The case of the electron-phonon scattering is reconsidered here in the framework of the variational method, but also in the relaxation-time approximation. Physical-approximations, e.g., on the degeneracy of the the charge carriers, on elastic or inelastic scattering contributions,:and on standard cutoffs, are discussed. Dimensionality effects of the phonon and/or electron spectrum are stressed in view of comparing systems for which the electrical resistivity is known. Asymptotic expressions are compared. It is also shown that a direct correspondence between final formulas within different:formalisms; is hardly available.