Statistics of solitons in quarter-filled-band, large-Uquasi-one-dimensional crystals

There is evidence that solitons are created by doping in certain of the quarter-filled-band semiconducting molecular crystals having large Coulomb repulsion for two electrons on the same site (‘‘large U ’’). Since, as has been shown for polyacetylene, soliton concentrations depend on the concentrations of band carriers, it is necessary to know the chemical potentials of the solitons to find the electronic Fermi energy. We derive in this work the relations between soliton chemical potentials and the Fermi energy for quarter-filled-band, large-U semiconductors and use them to find concentrations of solitons, electrons, and holes as a function of temperature and chemical doping. Numerical results are presented for parameters appropriate to (N-methylphenazinium${)}_{\mathrm{x}}$(phenazine${)}_{1\mathrm{-}\mathrm{x}}$tetra- cyanoquinodimethanide [(NMP${)}_{\mathrm{x}}$(Phen${)}_{1\mathrm{-}\mathrm{x}}$TCNQ] for x=0.50 (exactly quarter-filled band) and x=0.54 (4% donor doping). The Fermi energy is found to be twice the chemical potential of the negatively charged solitons. For doped systems, the Fermi energy decreases approximately linearly with temperature at low temperatures, with a slope depending on the level of doping. At low temperatures we find also that the number of solitons will be less than twice the number of dopant molecules (their number at T=0 K) due to promotion of electrons from soliton levels to the conduction band and subsequent soliton recombination.