Band transport in quasi-one-dimensional conductors in the phonon-scattering regime and application to tetrathiofulvalene-tetracyanoquinodimethane

Starting from a simple model for the lattice vibrations in a molecular crystal, I develop the transport theory for noninteracting electrons in a tight-binding band scattered by one- and two-phonon processes. The matrix elements for scattering by acoustic phonons, by librons, and by internal-mode phonons are obtained in the usual way from a simple Hamiltonian. For the one-phonon (1p) processes it is shown that a relaxation time exists and the Boltzmann equation is easily solved. With this solution formal expressions are obtained for conductivity $\ensuremath{\sigma}$ and thermopower $Q$. These are evaluated for the acoustic and libron cases for degenerate material in order to display the specific dependences on bandwidth, Fermi energy, phonon frequency, temperature, etc. Approximate expressions are also obtained for $\ensuremath{\sigma}$ and $Q$ for two-phonon (2p) processes. The formalism is then applied to calculate $\ensuremath{\sigma}$ and $Q$ numerically for tetrathiofulvalene-tetracyanoquinodimethane (TTF-TCNQ) for which the basic model should be reasonably valid in the temperature range $\ensuremath{\sim}100<T<300$ K. It is shown that the requirement that the Fermi level be the same for TTF and TCNQ, while the lattice constant and bandwidth change with temperature leads to the charge transfer's decreasing \ensuremath{\sim}20% from 60 to 300 K. The internal modes, for which the frequencies and coupling constants are fairly well known, are found to account for one-quarter of the resistivity at 300 K. The coupling constants for the other 1p processes required to match the observed resistivity versus $T$ are of the order of those deduced theoretically and experimentally for the LA mode, and therefore seem reasonable. The bandwidths that give good fits for $\ensuremath{\sigma}$ and $Q$, and are consistent with most other experiments, are 0.5 eV for TCNQ, half that for TTF. Similar fits are obtained by including some 2p processes, up to $\frac{1}{3}$ of the total scattering. Calculations are carried out also for tetraselenufulvalene-tetracyanoquinodimethane (TSeF-TCNQ). The large pressure dependence of $\ensuremath{\sigma}$ at 300 K for TSeF-TCNQ, \ensuremath{\sim} 18%/kbar, is well explained by the pressure-variation of the bandwidth and acoustic-mode frequencies, plus some smaller effects. The additional 10%/kbar observed for TTF-TCNQ may be largely due to greater changes for TTF due to its small bandwidth. In contrast to all of the above, the proponents of the "two-libron" theory of transport for TTF-TCNQ claim that 1p scattering is negligible in the range $\ensuremath{\sim}100<T<300$ K, 2p processes being predominant. These claims are examined and found quite unconvincing. Allowing for the uncertainty in the coupling to LA and TA phonons, I find that the contribution of 2p scattering must be less than 50% at room temperature and smaller, of course, below; it may be negligible at all temperatures.