Breakdown of LO-TO polar splitting in nanowires*

The need for an accurate description of the vibrational properties of 1D materials is strongly motivated by the growing interest in low-dimensionality systems - semiconductor nanowires in particular - with vibrational spectroscopies probing accurately their properties.
In 3D polar materials, long-wavelength phonons (exactly those probed by IR and Raman spectroscopies) undergo a frequency splitting in their longitudinal and transverse optical modes which depends on the Born effective charges and the dielectric response. This splitting is driven by the need to build up an electrostatic energy density for longitudinal optical phonons. In 2D the splitting has been shown to depend upon the phonon wavevector and to vanish at small momenta [1]; here, we show that it also vanishes in 1D, but with a different asymptotic behavior. We develop an analytical model to describe the relevant physics, and compare it with first-principles simulations in realistic systems as a function of the nanowire diameter. The present work not only provides useful insight into the vibrational physics of nanowires but also a ready-to-use tool for the experimental community to encourage further studies.

[1] T. Sohier, M. Gibertini, M. Calandra, F. Mauri, and N. Marzari, Nano Lett. 17, 3758 (2017).