Theory of the low-temperature Seebeck coefficient in dilute alloys

The Seebeck coefficient in dilute alloys at low temperatures is investigated in a simple model in which free electrons are scattered by a random array of fixed impurities and interact with longitudinal Debye phonons through a Fr\"ohlich Hamiltonian. As has been shown by Vilenkin, the wave-number dependence of the Fourier-transformed impurity potential removes the near cancellation of several contributions due to the electron-phonon renormalizations discussed by Vilenkin and Taylor. The net electron-phonon enhancement of the Seebeck coefficient is found to be close to the usual mass-enhancement ratio in the case of a screened Coulomb potential.