Solitons in the Peierls condensate: Phase solitons

The electron-phonon system in one dimension is studied within the adiabatic (Hartree) and Hartree-Fock approximations. The equations of motion for the Pierls order parameter at zero temperature are derived from a microscopic Hamiltonian and an effective Lagrangian is constructed. Charged phase solitons describe systems whose electron density is at or near M-fold commensurability with M3. For M=2, the order parameter is real in the adiabatic approximation, but becomes complex when both acoustic and optical phonons are coupled, or for a nonadiabatic theory. The latter is studied with a Coulomb exchange force and phase solitons are derived. The soliton charge is 2M for all M2. When M=4, the pinning potential can be anomalously low, in agreement with data on TaS3 and similar compounds.