Effect of solitons on Peierls gap in highly correlated quarter-filled-band crystals

It has recently been proposed by Rice and Mele [Phys. Rev. B 25, 1339 (1982)] that fractionally charged solitons can exist in quarter-filled-band, quasi-one-dimensional crystals that are highly correlated, i.e., crystals in which the Coulomb repulsion $U$ for a second electron on the same site is much larger than the bandwidth $4t$. In the limit $\frac{U}{4t}\to \infty$, the electronic states of the system are singly occupiable and solitons with charges $\pm \frac{\mathrm{}\left|e\right|\mathrm{}}{2}$ can be created. We have calculated the equilibrium soliton populations in such crystals, taking into account solitons generated both thermally and chemically (by doping). Thermally generated soliton populations are much larger than those expected in polyacetylene, for example, because of smaller Peierls gaps in the usual quarter-filled-band large-$U$ crystals. We find also that the presence of solitons reduces both the zero-temperature value of the Peierls gap and the semiconductor-metal transition temperature. Comparison is made with recent conductivity data of Epstein et al. [Phys. Rev. Lett. 49, 1037 (1982)] for ${(\mathrm{N}-\mathrm{m}\mathrm{e}\mathrm{t}\mathrm{h}\mathrm{y}\mathrm{l}\mathrm{p}\mathrm{h}\mathrm{e}\mathrm{n}\mathrm{a}\mathrm{z}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{u}\mathrm{m})}_x{\left(\mathrm{phenazine}\right)}_{1-x}\mathrm{tetracyanoquinodimethane}$ [${\left(\mathrm{NMP}\right)}_x{\left(\mathrm{Phen}\right)}_{1-x}\mathrm{TCNQ}$] for $0.50<x<\mathrm{}0.54\mathrm{}$. Disappearance of the Peierls gap is predicted in the region where the experimental activation energy goes to zero.