Breakdown of LO-TO polar splitting in 1D materials and its application to nanowires and nanotubes*

Accurate models and simulations of the vibrational properties of 1D materials are crucial for the analysis and prediction of transport and spectroscopic properties. In the long-wavelength limit, longitudinal polar-optical phonons (those probed by IR and Raman spectroscopies) are known to undergo a frequency shift which depends strongly on dimensionality. In 3D, this leads to a roughly constant separation between the optical modes across the Brillouin zone, termed LO-TO splitting. At variance with this, in 2D the dielectric shift has been shown to depend upon the phonon wavevector and to linearly vanish at small momenta¹. Using  analytical models and density-functional perturbation theory in a newly-implemented one-dimensional framework, we show that it also vanishes in 1D, but with a logarithmic asymptotic behavior. We demonstrate the relevance of our work by studying a portfolio of realistic systems: BN atomic-chain, BN armchair nanotubes and GaAs nanowires of varying size. We then discuss the polar and mechanical nature of the phonon energy shift and its dependency on dimensionality. This work not only provides useful insight into the vibrational physics of a wide class of 1D  materials,  but also a ready-to-use tool for the experimental community to encourage further studies.