Ab initio simulation of gap discrete breathers in strained graphene

The methods of the density functional theory were used for the first time for the simulation of discrete breathers in graphene. It is demonstrated that breathers can exist with frequencies lying in the gap of the phonon spectrum, induced by uniaxial tension of a monolayer graphene sheet in the “zigzag” direction (axis $X$), polarized in the “armchair” direction (axis $Y$). The found gap breathers are highly localized dynamic objects, the core of which is formed by two adjacent carbon atoms located on the $Y$ axis. The atoms surrounding the core vibrate at much lower amplitudes along both the axes ($X$ and $Y$). The dependence of the frequency of these breathers on amplitude is found, which shows a soft type of nonlinearity. No breathers of this type were detected in the gap induced by stretching along the $Y$ axis. It is shown that the breather vibrations may be approximated by the Morse oscillators, the parameters of which are determined from ab initio calculations. The results are of fundamental importance, as molecular dynamics calculations based on empirical potentials cannot serve as a reliable proof of the existence of breathers in crystals.