Phonon Conductance of Potassium- and Sodium-Doped Transpolyacetylene Chain

A theoretical approach for the study of phonon dynamics and scattering properties of doped transpolyacetylene chain is presented. The coherent reflection and transmission scattering cross-sections for phonons incident on the doped unit cell boundary are calculated in accordance with the Landauer-Buttiker electron scattering description, using the matching procedure with the nearest and next nearest neighbor elastic force constants. This is done for two different dopants, namely, the potassium and sodium atoms. Our numerical results yield an understanding of the transpolyacetylene chain dynamical properties and the effects on phonon conductance due to phonon incident on the doped unit cell boundary. The coherent reflection and transmission coefficients show characteristic spectral features, depending on the cutoff frequencies for the propagating phonons and on the nature of the dopants. They illustrate the occurrence of Fano resonances in the scattering spectra that result from the interactions of propagating elastic waves of the undoped transpolyacetylene chain with the localized modes due to the breakdown of the translation symmetry in the x direction.