Phonons in one-dimensional Peierls systems with internal degrees of freedom.

Abstract

An extension of the frozen-phonon approach is presented that permits us to calculate phonon dispersion curves for a one-dimensional system subject to Peierls distortion in the whole Brillouin zone. A number of systems with monomers possessing both lattice and internal degrees of freedom and with various filling ratios are investigated. The nature of the soft mode common for all the systems studied is discussed putting emphasis on its difference from the soft mode in the well-studied Peierls systems with one degree of freedom per monomer. It is found that the presence of internal degrees of freedom has considerable impact on the soft modes and phonon dispersions. The behavior of the phonon dispersion curves and the force constants resulting from the electron-phonon interaction are studied as a function of electron-phonon coupling constants. A model system with two types of monomers, one of which possesses an internal degree of freedom and with a filling ratio of 3/4, is used to explain experimental results on a recently synthesized quasi-one-dimensional compound ${\mathrm{Ca}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{3}$.