Intersoliton hopping transport of electrons in molecular crystals

Quarter-filled-band quasi-one-dimensional compounds which exhibit large Coulomb repulsion between two electrons on the same site ("large $U$") can support the formation of fractionally charged solitons. Electron hopping between solitons may contribute substantially to transport in these materials. We calculate the intersoliton electron hopping rate for transitions mediated by intramolecular phonons and by acoustic phonons. Acoustic phonons are found to be much less effective and are expected to contribute significantly only when intramolecular phonons are not excited or cannot satisfy conservation of energy. For the case of intramolecular phonons, we consider both hopping of an electron from a soliton pinned by an impurity to a second soliton which then becomes pinned, and hopping between a pair of solitons, one of which remains free to move. [Owing to the large on-chain dielectric constant (∼ 100-1000) in these materials, the solitons are probably not bound except at low temperatures.] The transition rates are used to find the hopping mobility for electrons in the soliton levels. Evaluation of the mobility due to the different hopping mechanisms for ${\mathrm{}(\mathrm{N}-\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{u}\mathrm{m})\mathrm{}}_{0.54}$ ${\mathrm{}\left(\mathrm{phenazine}\right)\mathrm{}}_{0.46}$ tetracyanoquinodimethane [${\mathrm{}\left(\mathrm{NMP}\right)\mathrm{}}_{0.54}$ ${\mathrm{}\left(\mathrm{Phen}\right)\mathrm{}}_{0.46}$-(TCNQ)] at a temperature of 100 K suggests that, unlike the polyacetylene case, the predominant process at temperatures $\gtrsim 100$ K is on-chain hopping, due to the large interchain distances involved. We find a mobility at 100 K of 0.06-1.03 ${\mathrm{cm}}^2$/V sec due to on-chain hopping, mediated by intramolecular phonons, between pinned and free solitons. This mobility should increase at higher temperatures. The thermoelectric power due to the various electron hopping processes is calculated as well. We find that for hopping processes involving transitions between pinned and free solitons there is a term in the thermopower involving the soliton pinning energy, in addition to the usual term involving electronic energy levels.