Transverse intrinsic localized modes in monatomic chain and in graphene

Hizhnyakov, V.; Klopov, M.; Shelkan, A.

doi:10.1016/j.physleta.2016.01.011

Cited by 30 publications

(37 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…substitution t by −t. At the same time, analysis of formula (24) and results of numerical simulations suggest that thermal processes in infinite harmonic crystals are irreversible.…”

Section: Exact Formula For the Temperature Matrixmentioning

confidence: 98%

“…In contrast, approximate formula (24) does not have this artifact. According to formula (24), temperature matrix of the unit cell x at time t depends on initial temperature matrices of unit cells which are not farther from cell x than max k,j |v j g |t .…”

Section: Exact Formula For the Temperature Matrixmentioning

confidence: 99%

“…In this section, we apply general solution (24) to several particular initial temperature profiles. The results are valid for all lattices described by equations of motion (4).…”

Section: Specific Profiles Of Initial Temperaturementioning

confidence: 99%

See 2 more Smart Citations

Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell

Kuzkin

2019

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

We study thermal processes in infinite harmonic crystals having a unit cell with arbitrary number of particles. Initially particles have zero displacements and random velocities, corresponding to some initial temperature profile. Our main goal is to calculate spatial distribution of kinetic temperatures, corresponding to degrees of freedom of the unit cell, at any moment in time. An approximate expression for the temperatures is derived from solution of lattice dynamics equations. It is shown that the temperatures are represented as a sum of two terms. The first term describes high-frequency oscillations of the temperatures caused by local transition to thermal equilibrium at short times. The second term describes slow changes of the temperature profile caused by ballistic heat transport. It is shown, in particular, that local values of temperatures, corresponding to degrees of freedom of the unit cell, are generally different even if their initial values are equal. Analytical findings are supported by results of numerical solution of lattice dynamics equations for diatomic chain and graphene lattice. Presented theory may serve for description of unsteady ballistic heat transport in real crystals with low concentration of defects. In particular, solution of the problem with sinusoidal temperature profile can be used for proper interpretation of experimental data obtained by the transient thermal grating technique.

show abstract

“…substitution t by −t. At the same time, analysis of formula (24) and results of numerical simulations suggest that thermal processes in infinite harmonic crystals are irreversible.…”

Section: Exact Formula For the Temperature Matrixmentioning

confidence: 98%

Section: Exact Formula For the Temperature Matrixmentioning

confidence: 99%

See 1 more Smart Citation

Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell

Kuzkin

2019

Continuum Mech. Thermodyn.

View full text Add to dashboard Cite

show abstract

“…This TDB does not decay, as it should according to the theory presented above. An account of the compression mentioned in the theory, allowing one to explain the values ε ≈ 0.113 and ω 0 ≈ 0.1883 found in simulations, is given in [21] in Appendix. Note that if to use these values of ε and ω 0 in Eq.…”

Section: Numerical Study Of Transverse Discrete Breathes In the Chainmentioning

confidence: 99%

“…in graphene), due the lack of atoms in transverse direction the odd anarmonicities for the shifts are absent. Therefore for these systems there may exist localized anharmonic transverse modes with the frequencies above the spectrum of corresponding phonons [21]. Although these frequencies are in resonance with the longitudinal (chain) or in-plane (graphene) phonons, the modes can decay only due to weak anharmonic processes and therefore can have very long life time.…”

Section: Introductionmentioning

confidence: 99%

Discrete breathers above phonon spectrum

Hizhnyakov¹,

Shelkan²,

Haas³

et al. 2016

LoM

Self Cite

View full text Add to dashboard Cite

It is shown that in some metals (Ni, Nb, Fe, Cu) may exist discrete breathers with frequencies above the top of the phonon spectrum. These excitations are mobile: they may propagate along the crystallographic directions transferring energy of > 1 eV over large distances. The discrete breathers with the frequencies above the top of the phonon bands may also exist in covalent crystals (diamond, Si and Ge). It is also found that in monatomic chains and planes (e.g. in graphene), the transverse discrete breathers may be excited above the spectrum of corresponding phonons. Although these vibrations are in resonance with longitudinal (chain) or in-plane (graphene) phonons the lifetime of them may be very long.

show abstract

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

Korznikova

Shcherbinin

Ryabov

et al. 2018

Physica Status Solidi (b)

View full text Add to dashboard Cite

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.

show abstract

Transverse intrinsic localized modes in monatomic chain and in graphene

Cited by 30 publications

References 25 publications

Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell

Unsteady ballistic heat transport in harmonic crystals with polyatomic unit cell

Discrete breathers above phonon spectrum

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

Contact Info

Product

Resources

About