Regular Article

Stability of delocalized nonlinear vibrational modes in graphene lattice

¹ Bashkir State University, 32 Zaki Validy Str., Ufa 450076, Russia
² Mirny Polytechnic Institute (branch) of North-Eastern Federal University, 5/1 Tikhonov Str., Mirny 678170, Sakha (Yakutia), Russia
³ Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the RAS, 71 October Avenue, Ufa 450054, Russia
⁴ Ufa State Aviation Technical University, 12 Marx str., Ufa 450008, Russia
⁵ National Research Tomsk State University, 36 Lenin Avenue, Tomsk 634050, Russia

^a e-mail: elena.a.korznikova@gmail.com

Received: 9 September 2019
Published online: 11 November 2019

Abstract

Crystal lattices support delocalized nonlinear vibrational modes (DNVMs), which are determined solely by the lattice point symmetry, and are exact solutions of the equations of atomic motion for any interatomic potential. DNVMs are interesting for a number of reasons. In particular, DNVM instability can result in the formation of localized vibrational modes concentrating a significant part of the lattice energy. In some cases, localized vibrational modes can be obtained by imposing localizing functions upon DNVM. In this regard, stability of DNVMs is an important issue. In this paper, molecular dynamics is employed to address stability of all four delocalized modes in a graphene lattice in the presence of small perturbations both in the plane and normal to the plane of the lattice. When DNVM amplitude is above the stability threshold, atom trajectories deviate from the mode pattern exponentially in time. Critical exponents are calculated for the in- and out-of-plane displacements. Stability threshold amplitudes are established. Interestingly, in three of the studied DNVMs the in-plane displacements diverge faster, but in one of them the instability develops through the out-of-plane displacements. This result can be explained by the difference in atomic vibration patterns of DNVMs. Reported results refine our understanding of the nonlinear dynamics of graphene lattice and can be useful in the design of electro-mechanical resonators and sensors.