Intraband discrete breathers in disordered nonlinear systems. I. Delocalization

The existence of Discrete Breathers or DBs (also called Intrinsic Localized Modes or ILMs) and multibreathers, is investigated in a simple one-dimensional chain of random anharmonic oscillators with quartic potentials coupled by springs. When the breather frequency is outside and above the linearized (phonon) spectrum, the existence theorems and numerical methods previously used in periodic nonlinear models for finding time-periodic and spatially localized solutions, hold identically in random nonlinear systems. These solutions are extraband discrete breathers (EDBs). When the frequencies penetrate inside the linearized spectrum, the existence theorems do not hold. Our numerical investigations demonstrate that the strict continuation of (localized) EDBs as intraband discrete breathers (IDBs) is impossible because of cascades of bifurcations generating many discontinuities. A detailed analysis of these bifurcations for small systems with increasing sizes, shows that only a relatively small subset of the spatially extended multibreathers can be strictly continued while their frequency varies inside the phonon spectrum. We propose an ansatz for finding the coding sequences of these solutions and continuing safely these multibreathers in finite systems of any size. This continuation ends at a lower limit frequency where the solution annihilates through a bifurcation with another multibreather. A smaller subset of these multibreather solutions can be continued to amplitude zero and become linear localized modes at this limit. Conversely, any linear localized mode can be continued when increasing its frequency as an extended multibreather. Extrapolation of these results to infinite systems yields the main conclusion of this first part which is that nonlinearity in disordered systems (with localized eigenmodes only) restores their capability of energy transportation by generating infinitely many spatially extended time-periodic solutions. This approach yields mainly spatially extended solutions, except sometimes at their bifurcation points. In the second part of this work, which is presented in our next article, we develop an accurate method for calculating in situ localized IDBs.     

Influence of domain boundaries on polarity of GaN grown on sapphire

GaN films were grown on sapphire substrates by laser-induced reactive epitaxy. The domains in the films were determined to be the Ga-polarity by the convergent beam electron diffraction (CBED) technique, while the adjacent matrices had the N-polarity. The domain boundaries were characterized as inversion domain boundaries (IDBs). An atomic structure of the IDB is proposed based on high-resolution transmission electron microscopy (HRTEM) investigations. Control of the polarity of GaN/sapphire films was achieved by suppressing the formation of IDBs with an interlayer of AlGaN and a low-temperature GaN buffer layer.     

次近邻电子跳跃对孤子的电子束缚态和孤子附近局域模的影响

从SSH模型出发,考虑电子次近邻跳跃的影响,研究了聚乙炔中孤子的电子束缚态和孤子附近的局域振动模。结果发现:1.电子能谱中的电子-空穴对称性消失;2.孤子的电子束缚态的数目和位置发生了变化,且与孤子的类型有关;3.孤子附近出现了一个新的局域振动模G₆;4.次近邻电子跳跃改变了局域模的频率,增强了局域模的局域性。 关键词：     

Localized phonons due to the adsorption of a monolayer of atoms on a crystal surface

Localized surface phonons due to a monolayer of adsorbed atoms on a free surface are studied with a simple crystal model. Surface localized modes inside a ‘surface gap’ between the bulk bands of frequencies, and inside a bulk band are reported. Resonant surface states well defined in energy are also found.     

链间耦合对反式聚乙炔中孤子能谱及其局域振动模的影响

从计及了链间相互作用项的ＳＳＨ模型出发，讨论了相邻两条链间电子跃迁对反式聚乙炔中孤子能谱及孤子附近的局域振动模的影响，结果发现：（１）孤子能级偏离了禁带中心，能谱的对称性被破坏。（２）局域振动模发生劈裂，劈裂后两模的振动位形具有与原模相同的结构，但它们的频率和最大振幅均不同于原局域模。另外，模的频率还与两条链上的孤子类型以及链的相对序列有关。 关键词：     

Nonlinear electron-lattice interaction on excited states in polythiophene

In consideration of the effects of the square term of the electron-lattice interaction and the bond-bending term, the energy spectra and the localized vibrational modes around a bipolaron of the polythiophene are investigated based on the one-dimensional and two-dimensional extension SSH model. The results show that, with the influence of the square term, the energy gap increases, the frequencies of all the localized vibrational modes around a bipolaron decrease and their localizations also shift. It is noted that, an even-parity mode has been found which corresponds to absorption peak at 1220 cm⁻¹. When the bond-bending term is considered, the frequencies of the localized modes increase and five new localized modes appear. Among them, one Raman active mode and three infrared active modes may correspond the observed RRS absorption peaks at 1047 cm⁻¹ and three infrared absorption peaks at 370, 1020, 1120 cm⁻¹ in the experiments.     

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.     

Topological phase transition and electrically tunable diamagnetism in silicene

The movement and relaxation of the localized energy on FPU lattices have been studied by using Wavelet transforms methods. The energy relaxation mechanism for nonlinear chains involves the degradation of higher frequency excitations into lower frequencies. It is shown that low frequency modes decay more slowly in nonlinear chains. The wavelet spectrum exhibits a behavior involving the interplay of phonon modes and breather modes.     

二维非晶光子材料的缺陷态

应用多重散射方法计算了二维介质柱构成的非晶光子材料的缺陷态。在非晶光子材料中抽掉不同位置的圆柱会产生频率不同的缺陷模，但缺陷模的能量都是非常局域的，能量基本上集中在以缺陷波长1／3为半径的圆内。这表明非晶光子材料中形成的缺陷模不仅具有周期性光子晶体的缺陷模的强局域化特征，同时缺陷模更富于变化。     

Observation of LO-phonon localization in GaAs quantum wires on faceted (311)A surfaces

The localization of longitudinal optical phonons in GaAs/AlAs lateral superlattices and quantum wires grown on faceted GaAs (311)A surfaces are investigated by means of Raman scattering spectroscopy. The frequencies of the localized phonons are found to decrease as the average thickness of the GaAs layer is decreased from 21 to 15 Å. As the GaAs thickness is decreased further to 11.3 and 8.5 Å, the frequencies of the localized phonons increases sharply in connection with the formation of an array of quantum wires. The frequencies calculated in a two-dimensional chain model agree with the experimental values. This makes it possible to interpret the increase in the frequencies of localized phonon states as being the result of the quantization of phonons in the array of one-dimensional objects. The results obtained support the model of GaAs (311)A surface faceting with a facet height of 10.2 Å. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 12, 942–946 (25 June 1996)     

On transmittance and localization of the electromagnetic wave in two-dimensional graphene-based photonic crystals

Two-dimensional graphene-based photonic crystal (GPC) formed by a periodic array of the homogeneous dielectric cylinders etched in the alternating graphene and dielectric layers and its inverse counterpart are considered. The transmittance of the photonic crystal is obtained. The waveguide due to the localization of the electromagnetic wave on the lattice defect that breaks the translational symmetry of the GPC of two different topologies is studied. The different topologies of GPC are characterized by different photonic band structures with different widths of photonic band gaps (PBG) and provide different frequencies for the localized electromagnetic wave due to the defect. The frequencies of the localized mode for both type of the GPC, located inside the lowest PBG, are in the range of THz or tens of THz depending on the topology of the GPC. It is shown that the photonic band gap always can be tuned by changing the chemical potential of graphene to provide formation of the localized photonic mode due to the defect. The technological advantages of the GPC, as well as the opportunity to tune the PBG and the frequency of the localized electromagnetic wave in the terahertz region of spectrum for the GPC are discussed.     

Localization of nonlinear waves in elastic bodies with inclusions

By the example of the problem of the motion of a semi-infinite string lying on an elastic base, a method for describing wave localization near inclusions is proposed for the case of a cubic nonlinearity of the base. The method applies the perturbation technique to the amplitude of a localized mode. The nature of the divergences is revealed, and the secular terms are found to belong to one of two types: inphase or antiphase with the localized wave. It is shown that a combination of the renormalization method and multiscale method provides a convergence of the solutions, which are sought for in the form of power series in the amplitude of the localized mode. It is found that the localization process is determined by the type of the discrete spectrum, type of the nonlinearity, and type of dispersion. The nonlinearity of the elastic base produces two characteristic effects. First, the frequency of the localized wave becomes dependent on the wave amplitude. Second, the system can generate traveling waves at multiple frequencies, which withdraw energy from the localized wave and cause it to decay. The decay behavior is determined by the minimum frequency of these traveling waves (because it must be higher than the cutoff frequency). The lifetime of the localized wave as a function of the mass of a dynamic inclusion exhibits a number of maxima. In particular, the first maximum corresponds to the minimum amplitude of the traveling wave at the triple frequency.     

Experimental observation of spatially localized dynamo magnetic fields

We report the first experimental observation of a spatially localized dynamo magnetic field, a common feature of astrophysical dynamos and convective dynamo simulations. When the two propellers of the von Kármán sodium experiment are driven at frequencies that differ by 15%, the mean magnetic field's energy measured close to the slower disk is nearly 10 times larger than the one close to the faster one. This strong localization of the magnetic field when a symmetry of the forcing is broken is in good agreement with a prediction based on the interaction between a dipolar and a quadrupolar magnetic mode.     

Ab initio rovibrational spectrum of LiNC and LiCN

Rovibrational calculations are performed on an ab initio potential energy surface for lithium cyanide. Vibrational states localized about both the isocyanide structure and the metastable cyanide structure are found. Calculated fundamental frequencies are LiNC 126.6 cm^?1 (bend) and 754.3 cm^?1 (stretch); LiCN 165.8 cm^?1 (bend) and 688.8 cm^?1 (stretch). Many states are found in the region of the barrier to isomerization, some of which are delocalized (polytopic).     

Lattice vibrational analysis of polyacene

Within an extended Su-Schrieffer-Heeger model, we made a lattice vibrational analysis of polyacene. In a singly-charged polyacene, the ground state contains an interchain-coupled polaron of quasi-D2h symmetry, around which we found thirteen localized modes in total. Among these localized modes, five (three B2u and two B3u) are infrared active, six (four Ag and two B1g) modes are Raman active, and the other two localized modes are asymmetric, which are both infrared active and Raman active. For the case a charged polaron is coupled with a neutral soliton in a finite polyacene chain, the vibrational modes are also calculated to display the coupling effect between self-trapping excitations on phonons. It is found that the localized phonons are determined mainly by the charged polaron, but the number and frequencies of the localized modes are influenced by the existence of the neutral soliton.     

Low-frequency resonance increase in the resistance of a microcontact between ferromagnetic and nonmagnetic metals

The magnetic dynamics of a mesoscopic three-dimensional magnet has been studied by measuring the resistance of a nanodimensional (point) microcontact between paramagnetic and ferromagnetic metals. The resistance was measured by a modulation technique under conditions where a significant role was played by dipole-dipole interaction, magnetic field, and dissipation. It was found that the resistance of the microcontact exhibits resonance growth at low frequencies (～10³ s^?1). The properties of resonances are described by a model of microcontact gyromagnetic oscillations (MCGMOs) based on mutual transformation of spin and mechanical angular momentum. Experimental techniques, basic properties, and the MCGMO model are described. The passage of an electric current through the interface between paramagnetic and ferromagnetic metals leads to nonequilibrium magnetization localized at the interface. A high current density in the microcontact determines the strong excitation of magnetization (high density of magnons) at which the interaction between magnons becomes significant. In a uniaxial magnet, the attraction of magnons leads to the formation of a spatially localized configuration of gapless long-wavelength magnons (magnetic soliton). At a given excitation of magnetization, the vector structure of a magnetic soliton possesses a minimum free energy (configuration energy minimum). The configuration energy minimum of a magnetic soliton is responsible for the radical increase in the soliton spin relaxation time, which determines the fundamental possibility of exciting stationary low-frequency MCGMOs.     

Rotating electrons in quantum dots: Classical limit

We solve the problem of a few electrons in a two-dimensional harmonic confinement using a quantum mechanical exact diagonalization technique, on the one hand, and classical mechanics, on the other. The quantitative agreement between the results of these two calculations suggests that, at low filling factors, all the low energy excitations of a quantum Hall liquid are classical vibrations of localized electrons. The Coriolis force plays a dominant role in determining the classical vibration frequencies.     

Quasiadiabatic decay of capillary turbulence on the charged surface of liquid hydrogen

We study the free decay of capillary turbulence on the charged surface of liquid hydrogen. We find that decay begins from the high frequency end of the spectral range, while most of the energy remains localized at low frequencies. The apparent discrepancy with the self-similar theory of nonstationary wave turbulent processes is accounted for in terms of a quasiadiabatic decay wherein fast nonlinear wave interactions redistribute energy between frequency scales in the presence of finite damping at all frequencies. Numerical calculations based on this idea agree well with experimental data.     

Lokalisierte Schwingungszustände in kubischen Kristallen mit Punktdefekten

The localized modes of vibration are discussed for a face centered and a body centered cubic lattice, if the ideal crystal is perturbated by a substitutional impurity. The eigenvectors are found by group-theoretical considerations, the frequencies can be calculated approximately by a variational principle, which gives good results, if the mode is strongly localized. It is discussed, which changes in mass and coupling parameters can give rise to localized modes of vibration. It turns out that in the model, which is considered here (nearest neighbour interaction and no changes in lattice structure), a vacancy does not show localized vibrations.