Infrared-active phonons in one-dimensional materials and their spectroscopic signatures

Dimensionality provides a clear fingerprint on the dispersion of infrared-active, polar-optical phonons. For these phonons, the local dipoles parametrized by the Born effective charges drive the LO-TO splitting of bulk materials; this splitting actually breaks down in two-dimensional materials. Here, we develop the theory for one-dimensional (1D) systems—nanowires, nanotubes, and atomic and polymeric chains. Combining an analytical model with the implementation of density-functional perturbation theory in 1D boundary conditions, we show that the dielectric splitting in the dispersion relations collapses as x2log(x)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${x}^{2}\log (x)$$\end{document} at the zone center. The dielectric properties and the radius of the 1D materials are linked by the present work to these red shifts, opening infrared and Raman characterization avenues.