Small-polaron effects on the dc conductivity and thermoelectric power of the one-dimensional Mott semiconductor

The effects of intra (molecular) -site vibrations on the dc conductivity, thermoelectric power, and one-electron density of states are calculated and studied. The one-dimensional half-filled-band Hubbard model is coupled locally in space to phonons and the approximation used assumes that the electron bandwidth is small. The one-electron density of states is Gaussian broadened in energy, even for zero bandwidth and zero temperature. Consequently there is a finite density of states at the Fermi energy (in the Mott-Hubbard gap). As temperature increases, the separate peaks in the density of states become less discernible. The dc conductivity exhibits a rounded maximum as a function of temperature and falls off as $T^{\frac{-3\mathrm{}}{2}}$ at high temperature. At very low temperatures, below a region of thermally activated behavior, the conductivity begins to rise and diverges as $T^{-1\mathrm{}}$. This behavior is shown to be a consequence of both the electron-phonon coupling and the strong electron-electron interaction. The thermoelectric power is formulated for the strongly interacting model system and it is found that it vanishes—a result that appears to be a consequence of the particle-hole symmetry of the half-filled band.