Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

Korznikova, Elena A.; Shcherbinin, S. A.; Ryabov, Denis; Chechin, G. M.; Екомасов, Е. Г.; Barani, Elham; Zhou, Kun; Dmitriev, Sergey V.

doi:10.1002/pssb.201800061

Cited by 37 publications

(12 citation statements)

References 78 publications

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“…Our results contribute to a deeper understanding of nonlinear dynamics of graphene lattice by analyzing stability and other properties of four exact nonlinear solutions in the form of delocalized nonlinear vibrational modes. Investigation of stability of two-component modes in graphene [40] can be a natural continuation of this study.…”

Section: Discussionmentioning

confidence: 83%

“…The interaction of carbon atoms is described by the potentials developed by Savin [41], taking into account the energy associated with deformation of valence bonds, valence angles, and dihedral angles. This potential has been successfully tested to solve a number of problems for sp2-carbon structures [14,19,21,24,[40][41][42].…”

Section: Simulation Detailsmentioning

confidence: 99%

“…Excitation of a DNVM with large amplitude alters elastic properties of hexagonal lattice with cubic anharmonicity [39]. Twocomponent DNVM in graphene generate second harmonic and some of them, counterintuitevily, result in negative pressure [40].…”

Section: Introductionmentioning

confidence: 99%

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Stability of delocalized nonlinear vibrational modes in graphene lattice

et al. 2019

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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.

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Section: Discussionmentioning

confidence: 83%

Section: Simulation Detailsmentioning

confidence: 99%

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Stability of delocalized nonlinear vibrational modes in graphene lattice

et al. 2019

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“…This direction of activity is connected with the idea put forward by Dmitriev, who suggests to construct a new type of discrete breathers in crystals by applying to the vibrational bushes some "localizing functions". A series of joint works of the Ufa and Rostov research groups in the field of nonlinear dynamics was published using this idea [37,38].…”

Section: Bushes Of Vibrational Modes and Discrete Breathersmentioning

confidence: 99%

Introduction to the theory of bushes of nonlinear normal modes for studying large-amplitude atomic vibrations in systems with discrete symmetry

Chechin

Ryabov

2020

Lett. Mater.

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The research group from the Rostov State University has been developing the theory of bushes of nonlinear normal modes (NNMs) in Hamiltonian systems with discrete symmetry since the late 90s of the last century. Group-theoretical methods for studying large-amplitude atomic vibrations in molecular and crystal structures were developed. Each bush represents a certain collection of vibrational modes, which do not change in time despite the time evolution of these modes, and the energy of the initial excitation remains trapped in the bush. Any bush is characterized by its symmetry group, which is a subgroup of the system's symmetry group. The modes contained in the given bush are determined by symmetry-related methods and do not depend on the interatomic interactions in the considered system. The irreducible representations of the point and space groups are essentially used in the theory of the bushes of NNMs, and this theory can be considered as a generalization of the well-known Wigner classification of the small-amplitude vibrations in molecules and crystals for the case of largeamplitudes vibrations. Since using of the irreducible representations of the symmetry groups can be an obstacle to an initial familiarization with the bush theory, in the present review, we explain the basic concepts of this theory only with the aid of the ordinary normal modes, which is well known from the standard textbooks considering the theory of small atomic vibrations in mechanical systems. Our description is based on the example of plane nonlinear atomic vibrations of a simple square molecule.

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“…Например, было показано, что возбуждение однокомпонентных ДНКМ в гексагональной решетке с кубической нелинейностью изменяет их константы упругости [6]. Некоторые из двумерных ДНКМ могут породить в графене отрицательное давление и привести к генерации второй гармоники с частотами заметно выше верхнего края спектра малоамплитудных фононных колебаний [7].…”

Section: Introductionunclassified

Динамика Трехкомпонентной Делокализованной Нелинейной Колебательной Моды В Графене

Щербинин¹,

Семенова²,

Семенов³

et al. 2019

Физика Твердого Тела

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The dynamics of a three-component nonlinear delocalized vibrational mode in graphene is studied with molecular dynamics. This mode, being a superposition of a root and two one-component modes, is an exact and symmetrically determined solution of nonlinear equations of motion of carbon atoms. The dependences of a frequency, energy per atom, and average stresses over a period that appeared in graphene are calculated as a function of amplitude of a root mode. We showed that the vibrations become periodic with certain amplitudes of three component modes, and the vibrations of one-component modes are close to periodic one and have a frequency twice the frequency of a root mode, which is noticeably higher than the upper boundary of a spectrum of low-amplitude vibrations of a graphene lattice. The data obtained expand our understanding of nonlinear vibrations of graphene lattice.

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Delocalized Nonlinear Vibrational Modes in Graphene: Second Harmonic Generation and Negative Pressure

Cited by 37 publications

References 78 publications

Stability of delocalized nonlinear vibrational modes in graphene lattice

Stability of delocalized nonlinear vibrational modes in graphene lattice

Introduction to the theory of bushes of nonlinear normal modes for studying large-amplitude atomic vibrations in systems with discrete symmetry

Динамика Трехкомпонентной Делокализованной Нелинейной Колебательной Моды В Графене

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