Interaction of longitudinal phonons with discrete breather in strained graphene

Abstract

We numerically analyze the interaction of small-amplitude phonon waves with standing gap discrete breather (DB) in strained graphene. To make the system support gap DB, strain is applied to create a gap in the phonon spectrum. We only focus on the in-plane phonons and DB, so the issue is investigated under a quasi-one-dimensional setup. It is found that, for the longitudinal sound waves having frequencies below 6 THz, DB is transparent and thus no radiation of energy from DB takes place; whereas for those sound waves with higher frequencies within the acoustic (optical) phonon band, phonon is mainly transmitted (reflected) by DB, and concomitantly, DB radiates its energy when interacting with phonons. The latter case is supported by the fact that, the sum of the transmitted and reflected phonon energy densities is noticeably higher than that of the incident wave. Our results here may provide insight into energy transport in graphene when the spatially localized nonlinear vibration modes are presented.

Phonons Scattering Off Discrete Asymmetric Solitons in the Absence of a Peierls-Nabarro Potential

“…To make these results more quantitative we use the energy density in Eq. ( 21) to define initial, reflected and transmitted energies as [18]…”

“…For future investigations, it would be particularly interesting to consider the scattering of large amplitude waves from a symmetric or asymmetric soliton. Several new interesting phenomena, such as soliton acceleration, the creation of multiple soliton and anti-soliton pairs, and resonant energy pumping, could eventually be observed [18,30]. where ∆ 2 ϕ n = 1 h 2 (ϕ n−1 − 2ϕ n + ϕ n+1 ).…”

Equilibration of sinusoidal modulation of temperature in linear and nonlinear chains

“…The Fourier law of thermal conductivity states that for macroscopic bodies, the heat flux is proportional to the temperature gradient with a proportionality coefficient κ, referred to as thermal conductivity. In a number of theoretical works [19][20][21][22][23][24][25][26][27][28][29][30][31], it was shown that in one-dimensional structures, Fourier's law does not work, in the sense that κ depends not only on the material, but also on the dimensions of the conductor, in particular, on its length L according to the power law κ ∼ L α , where the exponent is in the range 0 ≤ α ≤ 1. The case α = 1 corresponds to ballistic thermal conductivity, and for α = 0 we have normal, diffusive thermal conductivity obeying the Fourier law.…”

Wavelet imaging of transient energy localization in nonlinear systems at thermal equilibrium: The case study of NaI crystals at high temperature

“…Hamiltonian many-body systems with nonlinear interactions admit quite generally a special class of periodic orbits, whose amplitude-dependent frequency does not resonate by construction with any of the linear (normal) modes (NM) and whose oscillation pattern is typically exponentially localized in space. These modes, termed discrete breathers (DB) 1-3 or intrinsic localized modes (ILM), 4 have been shown theoretically to exist at zero temperature in a wide range of systems, including model lattices of beads and springs, such as the celebrated Fermi-Pasta-Ulam (FPU) chain, 5 real 2D and 3D crystals, 6 both in the gap 7 and above the phonon spectrum, 8 including cuprate high T c superconductors, 9 boron nitride, 10 graphene [11][12][13] and diamond, 14 disordered media [15][16][17] and biomolecules, 18 including proteins. 19,20 Nonlinear modes of this kind are surmised to play a subtle role in many condensed-matter systems.…”