Nonlinear vibrational modes in graphene: group-theoretical results

Chechin, G. M.; Ryabov, Denis; Shcherbinin, S. A.

doi:10.22226/2410-3535-2016-1-9-15

Cited by 30 publications

(18 citation statements)

References 26 publications

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“…In [20] we found that in graphene monolayer, whose symmetry group in equilibrium state is G 0 = P6mm, only 4 one-dimensional, 14 two-dimensional, 1 three-dimensional and 6 four-dimensional vibrational bushes, corresponding to the points of high symmetry in the Brillouin zone, can be excited.…”

Section: Bushes Of Vibrational Nonlinear Normal Modesmentioning

confidence: 95%

“…A brief review of the group-theoretical methods for construction of bushes of nonlinear normal modes was presented in the previous paper [20], while full description of these methods can be found in [7,21].…”

Section: Bushes Of Vibrational Nonlinear Normal Modesmentioning

confidence: 99%

“…Some group-theoretical results on small-dimensional vibrational bushes in graphene were published in our previous paper [20], which was devoted to geometrical aspects of bushes of NNMs. We discussed their structure, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…Section 2 is devoted to some group-theoretical results which were not presented in the previous publication [20]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

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

Chechin¹,

Ryabov²,

Shcherbinin³

2017

LoM

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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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Section: Bushes Of Vibrational Nonlinear Normal Modesmentioning

confidence: 95%

Section: Bushes Of Vibrational Nonlinear Normal Modesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…Section 2 is devoted to some group-theoretical results which were not presented in the previous publication [20]. In Sec.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Chechin¹,

Ryabov²,

Shcherbinin³

2017

LoM

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“…Next step in the development of DB excitation methods was the investigation of delocalized nonlinear modes [18]. Application of localization function to those modes turned out to be a universal way to excitation of DBs of different types of symmetry in various crystals including graphene [15], Morse crystals [19 -20] and metals [21].…”

Section: Introductionmentioning

confidence: 99%

Hard-type anharmonicity gap discrete breather in 2D biatomic crystal

Семенов¹,

Fomin²,

Soboleva³

et al. 2017

LoM

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Spatially localized nonlinear oscillations in the form of a discrete breather (DB) is a recently discovered phenomenon widely investigated in different physical systems due to its potential impact on the structure and dynamics of those systems. Our molecular dynamics research is focused on the variety of DB in crystals. Depending on the type of the crystal and corresponding phonon spectrum one can get a gap DB or a DB with the frequency above the phonon spectrum. Most of gap DBs previously addressed in the literature were characterized by a soft nonlinearity type with frequencies splitting off from the upper edge of the phonon spectrum gap. In this work we managed to excite a hard nonlinearity type DB with a frequency within the band gap. In order to achieve this goal we have excited four types of delocalized vibrational modes in biatomic crystal with atomic mass difference m 1 / m 2 = 10 providing the existence of sufficiently wide phonon band gap. Analysis of amplitude-frequency dependences of two of those modes obtained in molecular dynamics simulations revealed the hard nonlinearity type with the frequency within the spectrum. The fourth mode with moving heavy atoms had the frequency within the band gap growing with the amplitude. Application of localization function with radial symmetry to this delocalized vibrational mode allowed us to obtain a DB with hard nonlinearity type in the band gap within the considered model of the crystal. Properties of the DB were analyzed.Keywords: nonlinear dynamics, 2D lattice, phonon band, discrete breather. Пространственно локализованные нелинейные колебания в форме дискретных бризеров были открыты около трех десятилетий назад и в настоящее время являются объектом для интенсивного изучения в различных физических системах ввиду возможности их значительного влияния на структуру и динамику этих систем. Наша работа по-священа молекулярно-динамическому исследованию возможного многообразия конфигураций и типов дискретных бризеров в кристаллах. В зависимости от типа кристалла и его фононного спектра могут быть реализованы дискрет-ные бризеры с частотой выше фононного спектра либо в его щели. Большинство описанных в литературе бризеров с частотой в щели фононного спектра характеризовались мягким типом нелинейности амплитудно-частотная зави-симость которых отщеплялась от верхней границы щели. В данной работе нам удалось возбудить бризер с жестким типом нелинейности частота которого отщепляется от нижней границы спектра и сконцентрирована на тяжелых 328 Semenov et al. / Letters on materials 7 (3), 2017 pp. 327-331 атомах биатомной решетки. Для этого в двумерном модельном кристалле стехиометрии A3B с разницей масс тяже-лых и легких атомов m 1 / m 2 = 10 были возбуждены несколько коротковолновых фононных мод с волновым вектором на границе первой зоны Бриллюэна. Анализ полученной посредством моделирования амплитудно-частотной зави-симости мод локализованных на легких атомах решетки выявил жесткий тип нелинейности и частоту в пределах фононного спектра. Для случая локализации моды на тя...

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Auxeticity from nonlinear vibrational modes

Korznikova

Bokij²,

Zhou

2016

Physica Status Solidi (b)

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Abstractauthoren It is demonstrated that the large‐amplitude, short‐wavelength vibrational modes excited in the lattice can change its elastic properties due to physical and/or geometric nonlinearity of the lattice bonds. Depending on the symmetry of the vibrational mode the symmetry of the elastic properties of the lattice can also change. Using as an example the two‐dimensional honeycomb structure with normalβ‐FPU pairwise interparticle interactions, we demonstrate that the excitation of a large‐amplitude vibrational mode in combination with equiaxial tensile strain can change the sign of the Poisson's ratio from positive to negative, thus leading to the auxetic property of the lattice. It is shown that the considered lattice supports discrete breathers, i.e., spatially localized nonlinear vibrational modes. The excitation of the discrete breathers as a result of the modulational instability of the extended short‐wavelength modes is analyzed. Our results contribute to the understanding of the relation between the elastic properties and nonlinear dynamics of the lattices of interacting particles. Extended vibrational modes in the 2D honeycomb lattice presented by the stroboscopic pictures of the particle motion. Excitation of such modes with sufficiently large amplitude in combination with equiaxial tension changes the sign of the Poisson's ratio of the lattice from positive to negative.

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Nonlinear vibrational modes in graphene: group-theoretical results

Cited by 30 publications

References 26 publications

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

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

Hard-type anharmonicity gap discrete breather in 2D biatomic crystal

Auxeticity from nonlinear vibrational modes

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