Large-amplitude in-plane atomic vibrations in strained graphene monolayer: bushes of nonlinear normal modes

Аннотация на русском языке

In this paper, we study some low-dimensional bushes of nonlinear normal modes in graphene using ab initio calculations based on the density functional theory. The amplitude-frequency dependencies of one-dimensional bushes are found. The excitation transfer between nonlinear vibrational modes of different symmetry that belong to the same bush is investigated.Conventional normal modes are independent of each other in the framework of harmonic approximation. When small anharmonic terms in the Hamiltonian are taken into account, these dynamical objects are only approximate and one can speak about their interactions. In our previous works, the theory of bushes of nonlinear normal modes has been developed for dynamical systems with discrete symmetry groups. With the aid of this theory it is possible to find some exact solutions beyond the harmonic approximation. Each bush is an invariant manifold corresponding to a collection of m nonlinear normal modes, where m is the bush dimension. During the evolution of a given bush, this collection conserves, but amplitudes of the modes, entering the bush, change in time. Previously, we proved with the aid of group-theoretical methods, that in graphene under uniform strain (space symmetry group P6mm) there can exist 4 bushes with m = 1, 14 bushes with m = 2, 1 bush with m = 3, 6 bushes with m = 4, and etc. In this paper, we study some low-dimensional bushes in graphene using ab initio calculations based on the density functional theory. The amplitude-frequency dependencies of one-dimensional bushes are found. The excitation transfer between nonlinear vibrational modes of different symmetry that belong to the same bush is investigated.

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