Phonon dispersion of a two-dimensional boron sheet on Ag(111)

Abstract

Two-dimensional (2D) atomically thin boron layers designated as borophene or boraphene, attract great interest as promising post-graphene 2D materials. The borophene layer phonon structure has not yet been clarified by experimentation in spite of its importance for application for possible superconduction and thermal technologies. For this work we measured, by experimentation, the phonon dispersion of an incommensurate three-domain ${\ensuremath{\chi}}_{3}$-borophene formed on Ag(111) using high-resolution electron energy loss spectroscopy. Measured phonons were analyzed using first-principles theoretical calculations. Because the phonon band of the substrate Ag(111) lies in a low-energy region, the borophene phonon is well separated from the substrate. For our calculations, a commensurate slab supercell model was adopted, the periodicity of which was Ag(111) $3\ifmmode\times\else\texttimes\fi{}3$. The lattice parameter of the model was determined using experimentally obtained phonon data. The highest frequency phonon of an isolated borophene layer was fitted to the data as a function of the electronic charge in it. The best fitted lattice parameter was used in the supercell model. The model well reproduced the experimentally observed phonon dispersion. No marked anomaly was found in the phonon structure.