Metal-insulator transition in trans-polyacetylene.

Abstract

We have calculated the band structure for a chain of doped trans-polyacetylene using the electronic part of the Su-Schrieffer-Heeger Hamiltonian plus the Coulomb potential arising from ions and charged solitons surrounding the chain. The lattice structure used was that determined by x rays for Na-doped polyacetylene. To agree with a number of experimental observations the donated electrons were taken to be in soliton states at all dopant concentrations. In obtaining the potential of a point charge on a chain in the metallic state, the confinement of the free electrons to a chain was taken into account. Because screening depends on the calculated energy levels, specifically on the density of states at the Fermi energy, \ensuremath{\eta}(${E}_{F}$), in the metallic state, which, in turn, depend on the potential used to obtain them, self-consistency was required in the calculations.The energy-level structure was found to depend strongly on the ion spacing, conveniently measured in terms of the average spacing a of C-H's along the chain. For ion spacing 5a, characteristic of the Na-ion-rich regions up to an average dopant concentration of \ensuremath{\sim}6%, the chain remained semiconducting. For ion spacing 4a, which appears to characterize the next phase for Na doping, metallic behavior was found for a doped chain length of \ensuremath{\sim}100 sites or more. Self-consistency was fulfilled with \ensuremath{\eta}(${E}_{F}$) equal to the value obtained from the saturation spin susceptibility in the metallic state. In addition to sufficiently long chains that the level spacing is comparable to kT, the metal-insulator transition is found to require considerable overlap of electron wave functions on adjacent solitons and a fairly deep potential well. The transition is best described as a Mott transition. Our model predicts that a sample in the metallic state at room temperature becomes semiconducting at lower temperature. Evidence for this is found in the temperature variation of the spin susceptibility and of ESR linewidth.It is argued that the energy-level distribution in the metallic state is similar for other dopants. We show also that our model is consistent with the optical absorption observed for doped polyacetylene.