Interaction and disorder in charge density waves - application to polyacetylene

Charge density waves (CDW) in one dimensional conductors are studied with the following interactions: electron-phonon (e-p), electron-electron (e-e) and electron-disorder (e-d). The ordered system is studied with e-p interaction in the adiabatic limit and weak coupling e-e interactions with renormalization group methods. An exponent δ defines a renormalization of the effective electronic energy and gap. The effect depends on commensurability and whether the CDW is centered on sites or on bonds. The effect of weak e-d interaction introduces an exponent p. Analysis of Raman scattering, as done in polyacetylene yields a relation between phonon frequency and electronic gap. This analysis shows a different type of disorder in trans (CH)_X and in mixed trans-cis (CH)_X, i.e. different p values. An estimate of δ is also possible.