Features of the propagation of phonons in graphene nanostructures. Fast high-frequency phonons in a quasi-flexural mode

Abstract

The character of propagation in graphene nanostructures of quasi-flexural phonons, whose dispersion law differs from that of sound, is analyzed. Based on the calculation of the frequency dependences of the group velocities and the values of the path of quasiparticles for one period of oscillation, the frequency intervals are established at which: i) phonons propagate freely along all directions of reciprocal space—the propagon zone; ii) phonon propagation along some directions is impossible—diffuse zone; iii) phonons are localized at the nodes of the honeycomb lattice—the locon zone. A comparison is made with a similar classification of phonons in a three-dimensional crystal of cubic symmetry.