Interaction of longitudinal phonons with discrete breather in strained graphene

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.     

Instability of vibrational modes in hexagonal lattice

The phenomenon of modulational instability is investigated for all four delocalized short-wave vibrational modes recently found for the two-dimensional hexagonal lattice with the help of a group-theoretic approach. The polynomial pair potential with hard-type quartic nonlinearity (β-FPU potential with β > 0) is used to describe interactions between atoms. As expected for the hard-type anharmonic interactions, for all four modes the frequency is found to increase with the amplitude. Frequency of the modes I and III bifurcates from the upper edge of the phonon spectrum, while that of the modes II and IV increases from inside the spectrum. It is also shown that the considered model supports spatially localized vibrational mode called discrete breather (DB) or intrinsic localized mode. DB frequency increases with the amplitude above the phonon spectrum. Two different scenarios of the mode decay were revealed. In the first scenario (for modes I and III), development of the modulational instability leads to a formation of long-lived DBs that radiate their energy slowly until thermal equilibrium is reached. In the second scenario (for modes II and IV) a transition to thermal oscillations of atoms is observed with no formation of DBs.     

Energy localization and transport in two-dimensional Fermi–Pasta–Ulam lattices

We investigate energy localization and transport in the form of discrete breathers and their movability in two-dimensional Fermi–Pasta–Ulam(FPU) lattices. We study the dynamics of the two-dimensional Fermi–Pasta–Ulam(FPU) lattice, incorporating the complicated effects of geometry, long-range interactions as well as nonlinear dispersion. We obtain several exact discrete breather(DB) solutions, such as the odd-parity and even-parity DBs, compact-like DBs and moving DBs for various geometries of the two-dimensional FPU chain. We show that DBs also exist in the same lattice in presence of next-nearest neighbour interaction. Large-amplitude exact subsonic travelling kink-soliton solutions are obtained in such a periodic chain in presence of long-range nonlinear dispersive interaction in the long-wavelength and weakly nonlinear limit. Such a two-dimensional FPU lattice admits finite amplitude nonlinear sinusoidal wave (NSW) solutions with short commensurate as well as incommensurate wavelengths for different geometries of the chain. The usefulness of these solutions for energy localization and transport in various physical systems are discussed.     

Discrete breathers in alpha-uranium

Uranium is an important radioactive material used in the field of nuclear energy and it is interesting from the scientific point of view because it possesses unique structure and properties. There exist several experimental reports on anomalies of physical properties of uranium that have not been yet explained. Manley et al. [Phys. Rev. Lett. 96, 125501 (2006); Phys. Rev. B 77, 214305 (2008)] speculate that the excitation of discrete breathers (DBs) could be the reason for anisotropy of thermal expansion and for the deviation of heat capacity from the theoretical prediction in the high temperature range. In the present work, with the use of molecular dynamics, the existence of DBs in α-uranium is demonstrated and their properties are studied. It is found that DB frequency lies above the phonon band and increases with DB amplitude. DB is localized on half a dozen of atoms belonging to a straight atomic chain. DB in uranium, unlike DBs in fcc, bcc and hcp metals, is almost immobile. Thus, the DB reported in this study cannot contribute to thermal conductivity and the search for other types of DBs in α-uranium should be continued. Our results demonstrate that even metals with low-symmetry crystal lattices such as the orthorhombic lattice of α-uranium can support DBs.     

An atomistic model for the simulation of acoustic phonons, strain distribution, and Grüneisen coefficients in zinc-blende semiconductors

An accurate modeling of phonons, strain distributions, and Grüneisen coefficients is essential for the qualitative and quantitative design of modern nanoelectronic and nanooptoelectronic devices. The challenge is the development of a model that fits within an atomistic representation of the overall crystal yet remains computationally tractable. A simple model for introducing the anharmonicity of the interatomic potential into the Keating two-parameter valence-force-field model is developed. The new method is used for the calculation of acoustic phonon and strain effects in zinc-blende semiconductors. The model is fitted to the Grüneisen coefficients for long-wavelength acoustic phonons and reproduces the response to strain throughout the Brillouin zone in reasonable agreement with experiment.     

Unusual slow energy relaxation induced by mobile discrete breathers in one-dimensional lattices with next-nearest-neighbor coupling

We study the energy relaxation process in one-dimensional (1D) lattices with next-nearest-neighbor (NNN) couplings. This relaxation is produced by adding damping (absorbing conditions) to the boundary (free-end) of the lattice. Compared to the 1D lattices with on-site potentials, the properties of discrete breathers (DBs) that are spatially localized intrinsic modes are quite unusual with the NNN couplings included, i.e. these DBs are mobile, and thus they can interact with both the phonons and the boundaries of the lattice. For the interparticle interactions of harmonic and Fermi–Pasta–Ulam–Tsingou-β (FPUT-β) types, we find two crossovers of relaxation in general, i.e. a first crossover from the stretched-exponential to the regular exponential relaxation occurring in a short timescale, and a further crossover from the exponential to the power-law relaxation taking place in a long timescale. The first and second relaxations are universal, but the final power-law relaxation is strongly influenced by the properties of DBs, e.g. the scattering processes of DBs with phonons and boundaries in the FPUT-β type systems make the power-law decay relatively faster than that in the counterparts of the harmonic type systems under the same coupling. Our results present new information and insights for understanding the slow energy relaxation in cooling the lattices.     

氢化锆(ZrH1.7)和钯氢(PdH0.7)光学声子的温度效应

在本院重水堆旁的铍过滤探测器中子非弹性散射谱仪上,对氢化锆(ZrH_1.7)(含碳0.2％)和钯氢(PdH_0.7)两种金属氢化物在室温和低温(97K)两种温度下,分别测定了光学声子能谱。结果表明:氢化锆的光学声子能级是等间距的,能级宽度基本上不随温度变化,即光学声子的非谐性是微弱的,较好地遵从爱因斯坦的谐振模型;而钯氢的第二个光学声子能级间距大于第一个能级间距约8meV,并且光学声子能级的宽度从室温下的38meV变化到低温(97K)下的20meV,这表明对钯氢的超导性起决定作用的光学声子,存在较明显的非谐性。 关键词：     

YVO4晶体及其掺Nd的喇曼光谱

本文报道了对YVO4晶体及其掺Nd的喇曼光谱的测量结果,用这些结果可以了解到这种材料的声子能谱情况,在与其它基质材料比较中可以看出它的特点是：分立的低声子在500－800cm^-1之间有一个间隙,主要部分分布在800－900cm^-1附近,根据群论分析可以得出各喇曼谱线相应的对称性,而且可看出这些喇曼谱线主要来源于VO4^3-的振动,对这种不均匀分布的声子能变对于其光谱性能可能产生的影响也作了分析讨论,测量结果还发现掺杂能抑制原有的高能声子。     

Discrete breathers in biatomic crystals of <Emphasis Type="Italic">AB</Emphasis> and <Emphasis Type="Italic">A</Emphasis><Subscript>3</Subscript><Emphasis Type="Italic">B</Emphasis> composition

The conditions for the existence of discrete breathers (DBs) in biatomic crystals of AB and A ₃ B composition are established, and their properties are studied by means of molecular mechanics using the examples of CuAu and Pt₃Al, respectively. The phonon spectra of the crystals are analyzed, and a gap in the phonon spectrum of CuAu is obtained via considerable homogeneous elastic strain. There is a gap in the phonon spectrum of the Pt₃Al crystal at zero strain, due to the considerable difference between the atomic weights of its components. The frequencies at which discrete breathers can exist in the considered crystals are determined. The energy localized on different types of DBs is estimated. The propagation of a current pulse through Pt₃Al resulting in the excitation of DBs with mild nonlinearity is simulated.     

Size dependent ultrasonic absorption in superfluid helium

Ultrasonic waves in liquid He II at temperatures below 0.6°K can be absorbed by thermal phonons in 3- or 4-phonon processes. For the case that the mean free path of thermal phonons is sufficiently long 3-phonon processes are generally excluded because energy and momentum cannot be conserved. The conservation requirements cannot be fullfilled because the group velocity of thermal phonons is lower than the ultrasonic velocity due to dispersion. — The purpose of this note is to point out that insmall samples of liquid the uncertainty in phonon energy prevents a violation of the conservation laws for 3-phonon processes. In small volumes of liquid, ultrasonic waves are therefore strongly absorbed in 3-phonon processes, while in larger volumes of liquid this contribution to the absorption is absent. — A similiar size dependent absorption is to be expected for longitudinal waves at low temperatures in ideal crystals.     

Measurement of a phonon hot spot in photoexcited Si

High frequency phonons are produced by the thermalization of photoexcited electronhole pairs in a semiconductor. Inelastic and elastic scattering processes determine the frequency down-conversion and diffusion of this thermal energy. Simple estimates of the anharmonic and isotope scattering processes suggest that the acoustic phonons will undergo a quasi-diffusive propagation process. In particular, non-equilibrium phonons high-resolution phonon-imaging experiments presented here show well defined ballistic pulses and sharp phonon-focusing caustics. We explain this discrepancy in terms of a phonon hot spot which acts to efficiently down-convert the high-frequency phonons very near the excitation spot. We present the first measurements of the size of a phonon hot spot, which depends upon excitation power.     

Effect of dispersion on the phonon focusing and anisotropy of thermal conductivity of silicon single crystals in the boundary scattering regime

The effect of dispersion on the focusing of thermal phonons and on the thermal conductivity of silicon single crystals in the boundary scattering regime has been investigated. Analysis of the spectra of acoustic modes obtained for silicon single crystals from inelastic neutron scattering data has demonstrated that, upon transition from long-wavelength phonons to short-wavelength phonons, the directions of their focusing change. With an increase in temperature, this leads to a change in the anisotropy of thermal conductivity of phonons with different polarizations and, consequently, to a change in the anisotropy of the total thermal conductivity. Analysis of the temperature dependence of the thermal conductivity has revealed that the presence of extended flattened sections in the spectrum of short-wavelength transverse phonons indicates anomalously low values of the group velocity and, accordingly, a significant decrease in the contribution from these phonons to the thermal conductivity with increasing temperature. The contribution from longitudinal phonons to the thermal conductivity also significantly increases even at temperatures higher than 110 K and becomes dominant.     

Dynamical two electron states in a Hubbard-Davydov model

We study a model in which a Hubbard Hamiltonian is coupled to the dispersive phonons in a classical nonlinear lattice. Our calculations are restricted to the case where we have only two quasi-particles of opposite spins, and we investigate the dynamics when the second quasi-particle is added to a state corresponding to a minimal energy single quasi-particle state. Depending on the parameter values, we find a number of interesting regimes. In many of these, discrete breathers (DBs) play a prominent role with a localized lattice mode coupled to the quasiparticles. Simulations with a purely harmonic lattice show much weaker localization effects. Our results support the possibility that DBs are important in HTSC.Received: 14 August 2004, Published online: 26 November 2004PACS: 71.38.-k Polarons and electron-phonon interactions - 63.20.Pw Localized modes - 63.20.Ry Anharmonic lattice modes     

Characterization of single-crystalline GaAs by imaging with ballistic phonons

Ballistic phonon propagation in single-crystalline [001]-oriented gallium arsenide has been studied using low-temperature scanning electron microscopy for imaging. Deviations in the phonon focusing pattern due to dispersion effects were found by comparing the phonon images to theoretical calculations of the long-wavelength limit. The phonon propagation behavior in, samples cut from differently prepared wafers has been investigated. For highly impure crystals we found a pronounced increase of the diffusive signal component at the expense of the ballistic one. Samples with varying dislocation densities also showed a sensitive dependence, of the ballistic phonon propagation on these crystal defects. For focusing calculations considering elastic scattering processes the diffusivity of the phonons could be determined as a function of the mean scattering length. We have found phonon mean free paths of 0.35 mm to 0.80 mm for the various GaAs crystals.     

Electric field effect tuning of electron-phonon coupling in graphene

Gate-modulated low-temperature Raman spectra reveal that the electric field effect (EFE), pervasive in contemporary electronics, has marked impacts on long-wavelength optical phonons of graphene. The EFE in this two-dimensional honeycomb lattice of carbon atoms creates large density modulations of carriers with linear dispersion (known as Dirac fermions). Our EFE Raman spectra display the interactions of lattice vibrations with these unusual carriers. The changes of phonon frequency and linewidth demonstrate optically the particle-hole symmetry about the charge-neutral Dirac point. The linear dependence of the phonon frequency on the EFE-modulated Fermi energy is explained as the electron-phonon coupling of massless Dirac fermions.     

YVO_4晶体及其掺Nd的喇曼光谱

本文报道了对YVO4 晶体及其掺Nd的喇曼光谱的测量结果 ,用这些结果可以了解到这种材料的声子能谱情况 ,在与其它基质材料比较中可以看出它的特点是 :分立的低声子在 5 0 0～ 80 0cm-1之间有一个间隙 ,主要的部分分布在 80 0～ 90 0cm-1附近 ,根据群论分析可以得出各喇曼谱线相应的对称性 ,而且可看出这些喇曼谱线主要来源于VO3 -4 的振动。对这种不均匀分布的声子能谱对于其光谱性能可能产生的影响也作了分析讨论。测量结果还发现掺杂能抑制原有的高能声子。     

Gyroscopic dynamics of antiferromagnetic vortices in domain boundaries of yttrium orthoferrite

It is established experimentally that the magnetic field directed along the b axis has little effect on the velocities of antiferromagnetic vortices in the domain boundary (DB) of yttrium orthoferrite and fails to explain the presence of an appreciable gyroscopic force acting on these vortices. This force is induced by the dynamic canting of magnetic sublattices proportional to the DB velocity. Due to the canting, the velocities of antiferromagnetic vortices depend initially quadratically on the DB velocity, as was experimentally found in this work. The dynamics of antiferromagnetic vortices in the yttrium orthoferrite DBs is gyroscopic and quasi-relativistic, with the limiting velocity of 20 km/s equal to the velocity of spin waves at the linear portion of their dispersion curve.     

Energy Transport in Weakly Anharmonic Chains

We investigate the energy transport in a one-dimensional lattice of oscillators with a harmonic nearest neighbor coupling and a harmonic plus quartic on-site potential. As numerically observed for particular coupling parameters before, and confirmed by our study, such chains satisfy Fourier’s law: a chain of length N coupled to thermal reservoirs at both ends has an average steady state energy current proportional to 1/N. On the theoretical level we employ the Peierls transport equation for phonons and note that beyond a mere exchange of labels it admits nondegenerate phonon collisions. These collisions are responsible for a finite heat conductivity. The predictions of kinetic theory are compared with molecular dynamics simulations. In the range of weak anharmonicity, respectively low temperatures, reasonable agreement is observed.     

双模瑞利-泰勒不稳定性的预热烧蚀效应研究

针对双模扰动下的烧蚀瑞利-泰勒不稳定性增长问题,采用高精度的数值计算方法,研究了不同预热程度下模耦合产生的多个高次谐波幅值的发展和演化问题。研究表明,三种预热烧蚀条件下,当扰动基模满足长波与短波耦合方式时,谐波中的长波模态占主导,而短波模发展明显受到抑制;当满足短波与短波耦合时,耦合结果带来了许多新的增长较快的长波模态,此时短波模增长呈现小幅震荡形式。比较两种耦合方式可以发现,长波结构在烧蚀瑞利-泰勒不稳定性弱非线性阶段都占主导地位,尤其是短波与短波耦合中气泡与尖钉表现出不同于两个基模的长波模结构。进一步分析预热效应对模耦合增长的影响,发现预热程度越强就越能削弱耦合谐波的增长,这说明预热对烧蚀瑞利-泰勒不稳定性具有致稳作用,这对惯性约束聚变工程中控制烧蚀瑞利-泰勒不稳定性发展具有重要意义。     

声子色散对量子点中弱耦合磁极化子声子平均数的影响

利用线性组合算符和幺正变换相结合的方法,研究了声子色散对抛物量子点中弱耦合磁极化子电子周围光学声子平均数的影响。计及纵光学（ LO）声子色散,在抛物近似下导出了基态能量与量子点有效受限长度、声子色散系数、回旋共振频率以及电子－声子耦合常数之间的关系,电子周围光学声子平均数与声子色散系数以及电子－声子耦合常数的关系。数值计算结果表明在弱耦合情况下抛物量子点中磁极化子的基态能量随声子色散系数的增大而减小;电子周围光学声子平均数随声子色散系数增大而增大,随电子－声子耦合常数的增大而增大。