Instability of vibrational modes in hexagonal lattice

Korznikova, Elena A.; Bachurin, D.V.; Fomin, S Yu; Chetverikov, A. P.; Dmitriev, Sergey V.

doi:10.1140/epjb/e2016-70595-2

Cited by 62 publications

(19 citation statements)

References 42 publications

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“…This fact allows an attempt of excitation of a DB based on the latter mode. One should mention that realization of those modes in the crystal can result in elastic properties modification [22] and modulation instability being a reason for excitation of random DBs [23].…”

Section: Simulation Detailsmentioning

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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Section: Simulation Detailsmentioning

confidence: 99%

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

Семенов¹,

Fomin²,

Soboleva³

et al. 2017

LoM

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“…ДНКМ при достаточно больших амплитудах часто оказываются модуляционно неустойчивыми. Интересно, что развитие модуляционной неустойчивости ДНКМ может приводить к локализации энергии на дискретных бризерах [15], что еще раз указывает на тесную взаимосвязь между делокализованными и локализованными нелинейными колебаниями решетки. Отметим, что распад модуляционно-неустойчивой колебательной π-моды с образованием дискретных бризеров впервые наблюдался в работе [16] и позднее в нелинейных решетках различной размерности [12,17,18].…”

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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“…This approach has been used successfully for excitation of new types of discrete breathers in graphene and in two‐dimensional Morse lattices . Second, DNVM at sufficiently large amplitudes demonstrate modulational instability which can result in spontaneous formation of discrete breathers . Third, it was shown that excitation of DNVM affects elastic properties of the lattice and, in combination with homogeneous tension, can result in appearance of auxeticity of the hexagonal lattice (negativity of its Poisson's ratio) …”

Section: Introductionmentioning

confidence: 99%

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

Korznikova

Shcherbinin

Ryabov

et al. 2018

Physica Status Solidi (b)

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With the help of molecular dynamics simulations, delocalized nonlinear vibrational modes (DNVM) in graphene are analyzed. Such modes are dictated by the lattice symmetry, they are exact solutions to the atomic equations of motion, regardless the employed interatomic potential and for any mode amplitude (though for large amplitudes they are typically unstable). In this study, only one-and two-component DNVM are analyzed, they are reducible to the dynamical systems with one and two degrees of freedom, respectively. There exist 4 one-component and 12 two-component DNVM with in-plane atomic displacements. Any two-component mode includes one of the one-component modes. If the amplitudes of the modes constituting a two-component mode are properly chosen, periodic in time vibrations are observed for the two degrees of freedom at frequencies ω and 2ω, that is, second harmonic generation takes place. For particular DNVM, the higher harmonic can have frequency nearly two times larger than the maximal frequency of the phonon spectrum of graphene. Excitation of some of DNVM results in the appearance of negative in-plane pressure in graphene. This counterintuitive result is explained by the rotational motion of carbon hexagons. Our results contribute to the understanding of nonlinear dynamics of the graphene lattice.

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Instability of vibrational modes in hexagonal lattice

Cited by 62 publications

References 42 publications

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

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

Динамика Трехкомпонентной Делокализованной Нелинейной Колебательной Моды В Графене

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

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