Discrete breathers in deformed graphene

The linear and nonlinear dynamics of elastically deformed graphene have been studied. The region of the stability of a planar graphene sheet has been represented in the space of the two-dimensional strain $(\varepsilon_{xx},\varepsilon_{yy})$ with the $x$ and $y$ axes oriented in the zigzag and armchair directions, respectively. It has been shown that the gap in the phonon spectrum appears in graphene under uniaxial deformation in the zigzag or armchair direction, while the gap is not formed under a hydrostatic load. It has been found that graphene deformed uniaxially in the zigzag direction supports the existence of spatially localized nonlinear modes in the form of discrete breathers, the frequency of which decreases with an increase in the amplitude. This indicates soft nonlinearity in the system. It is unusual that discrete breather has frequency within the phonon spectrum of graphene. This is explained by the fact that the oscillation of the discrete breather is polarized in the plane of the graphene sheet, while the phonon spectral band where the discrete breather frequency is located contains phonons oscillating out of plane. The stability of the discrete breather with respect to the small out-of-plane perturbation of the graphene sheet has been demonstrated.