Solitons, polarons, and phonons in the infinite polyyne chain

Abstract

The infinite polyyne chain, ( C?C ${)}_{\mathrm{\infty }}$, or polyyne, is interpreted as a Peierls distorted one-dimensional metal with strong intrinsic electron-phonon coupling at the half-filled band level. Because there are two degenerate π-electron bands in polyyne the effective internal degeneracy (N) of the electrons is 4, rather than 2 as in the model of polyacetylene. This leads to a rich variety of kink-soliton and polaron states and, in the limit of a continuum description, to the interesting result that polyyne is an approximate physical realization of an N=4 Gross-Neveu model relativistic field theory. The low-lying electronic excitations of the polymer are kink-solitons with charges 0, ±e, and ±2e. The lowest-lying ionization states are a polaron, a bipolaron, and a tripolaron, with charges ±e, ±2e, and ±3e, respectively. Photoexcitation of the polymer leads to a neutral polaron consisting of an electron and a hole bound by lattice distortion (‘‘polarexciton’’). Both the soliton and the polarons involve the appearance of localized intragap levels that are not present in the ground state. Moreover, a localized excited state exists for the polaron, while photoexcitation of the bipolaron and the tripolaron result in soliton-antisoliton pair production. Photoinduced absorption measurements on long finite polyynes in solution should be able to confirm the photogeneration of the polarexciton. Formation of the polaron states can be expected if doping with strong electron withdrawing species is possible. An ?dd?membered polyyne is predicted to contain a soliton in its ground-state configuration, the doubly ionized closed-shell chain being particularly stable. Soliton- or polaron-bearing acetylenic chains might be of relevance in astrophysics. The ground-state acoustic and optical branches of the phonon spectrum of the discrete chain are also calculated and an expression derived for the reduction of the speed of sound due to the electron-phonon coupling.