Instability of vibrational modes in hexagonal lattice

The phenomenon of modulational instability is investigated for all four delocalized short-wave vibrational modes recently found for the two-dimensional hexagonal lattice with the help of a group-theoretic approach. The polynomial pair potential with hard-type quartic nonlinearity (β-FPU potential with β > 0) is used to describe interactions between atoms. As expected for the hard-type anharmonic interactions, for all four modes the frequency is found to increase with the amplitude. Frequency of the modes I and III bifurcates from the upper edge of the phonon spectrum, while that of the modes II and IV increases from inside the spectrum. It is also shown that the considered model supports spatially localized vibrational mode called discrete breather (DB) or intrinsic localized mode. DB frequency increases with the amplitude above the phonon spectrum. Two different scenarios of the mode decay were revealed. In the first scenario (for modes I and III), development of the modulational instability leads to a formation of long-lived DBs that radiate their energy slowly until thermal equilibrium is reached. In the second scenario (for modes II and IV) a transition to thermal oscillations of atoms is observed with no formation of DBs.