Translationally invariant polarons in conjugated conducting polymers

A simple effective Hamiltonian for the electron-phonon coupling in the conjugated polymers is derived from the Su-Schrieffer-Heeger model with quantized lattice motions. Phonons correspond to lattice quantum fluctuations around the dimerized positions. Both acoustic and optical modes are considered. The energy-momentum relation for the polaron is calculated variationally, with the aid of Lee-Low-Pines transformation. The discrete translational invariance of an ideal conjugated polymer is. explicitly enforced. Analytical expression for the polaron effective mass m* is obtained. m* turns out to be, in general, much larger than the conduction-band effective mass.