Multichannel Landauer formula for thermoelectric transport with application to thermopower near the mobility edge

Various thermoelectric linear transport coefficients are defined and calculated for two reservoirs connected with ideal multichannel leads and a segment of an arbitrary disordered system. The reservoirs have different temperatures and chemical potentials. All of the inelastic scattering (and, thus, the dissipation) is assumed to occur only in the reservoirs. The definitions of the chemical potentials and temperature differences across the sample itself (mostly due to elastic scattering) are presented. Subtleties of the thermoelectric effects across the sample are discussed. The associated transport coefficients display deviations from the Onsager relations and from the Cutler-Mott formula for the thermopower (although the deviations vanish for a large number of channels and/or high resistance). The expression obtained is used to predict the critical behavior of the electronic thermopower near the mobility edge. It is shown to satisfy a scaling form in the temperature and separation from the mobility edge.