Localized vibrational,edges and breathing modes of graphene nanoribbons with topological line defects

Peculiar vibrational modes of graphene nanoribbons (GNRs) with topological line defects were presented. We find that phonon dispersion relations of the topological defective GNRs are more similar to those of perfect armchair-edge GNR than to zigzag-edge GNR in spite of their zigzag edge. All vibrational modes at Γ point are assigned in detail by analyzing their eigenvectors and are presented by video. Three types of characteristic vibrational modes, namely, localized vibrational modes in defect sites, edges, and breathing modes, are observed. Five localized vibrational modes near the defect sites are found to be robust against the width of the topological line-defective GNR. The Raman D’ band just originates from one localized mode, 1622 cm^-1. The vibrational mode is sensitive to symmetry. The edge modes are related with structural symmetry but not with widths. Two edge modes are asymmetrical and only one is symmetrical. The breathing modes are inversely proportional to the width for wide-defect GNRs, and inversely proportional to the square root of the width for narrow-defect GNRs. The breathing mode frequencies of defective GNRs are slightly higher than those of perfect GNRs. These vibrational modes may be useful in the manipulation of thermal conductance and implementation of single phonon storage.     

Vibrational properties and Raman spectra of different edge graphene nanoribbons,studied by first-principles calculations

The vibrational properties and Raman spectra of graphene nanoribbons with six different edges have been studied by using the first-principles calculations. It is found that edge reconstruction leads to the emergence of localized vibrational modes and new topological defect modes, making the different edges identified by polarized Raman spectra. The radial breathing-like modes are found to be independent of the edge structures, while the G-band-related modes are affected by different edge structures. Our results suggest that the polarized Raman spectrum could be a powerful experimental tool for distinguishing the GNRs with different edge structures due to their different vibrational properties.     

三元合金缺陷层对有限超晶格中局域界面光学声子模的影响

在宏观介电连续近似下，采用转移距阵方法，研究了三元合金缺陷层对有限超晶格中局域界面光学声子模的影响.在这种有限超晶格结构中，可以清楚地看到所有界面模的演化轨迹.结果表明：存在两类局域模，它们的宏观静电势波函数分别局域在缺陷层和表面层附近，且这些模随着超晶格组分层和缺陷层的相对厚度和介电常数的改变，其局域位置和特性发生显著变化.此外，发现虽然能隙中局域模的数目不守恒，但所有界面模的总数守恒.     

Vibrational behaviour of self-interstitials infcc-metals

The vibrational properties of self-interstitials in the octahedral and 100-dumbbell configurations are studied for anfcc lattice with nearest neighbour interaction. Due to the local compression of the lattice in the vicinity of the interstitial both low-frequency resonant and high-frequency localized modes occur. The calculation of the local vibrational spectrum of the interstitial, with force constants fitted to the results of computer simulation, shows that the defect vibrates almost exclusively with resonant and localized frequencies and not with the typical eigenfrequencies of the ideal lattice. Analytical approximations for the resonant and localized modes are derived which show good agreement with the exact results. The low frequency resonances of the interstitial lead, even at low temperatures, to large thermal-displacements and to an remarkable increase of the specific heat.     

钉扎效应对聚噻吩中双空穴极化子附近局域振动模的影响

基于扩展的二维Su-Schrieffer-Heeger模型，研究了库仑钉扎作用对聚噻吩中双空穴极化子 附近的局域振动模的影响.除了与激发方式无关的本征振动模外，发现了与激发方式相关的 声子振动模式.计算结果与聚噻吩红外和拉曼光谱实验数据相当符合，从而对掺杂诱导和光 致激发下聚噻吩吸收光谱的区别给出了较好的理论阐释. 关键词： 聚噻吩 钉扎效应 吸收光谱 局域振动模     

First principles calculation of localized surface phonons and electron-phonon interaction at pb(111) thin films

A first principles calculation of the vibrational modes of Pb(111) thin films of thickness up to 14 layers reveals the existence of localized vibrational modes at the slab's surface. Both longitudinal and transverse surface modes localized a few atomic layers are found at energies above the bulk bands. The frequency of these modes presents a bilayer oscillatory behavior. The electron-phonon interaction of the slab's quantum well states is also calculated. We find a large (small) deformation potential for the lowest unoccupied (highest occupied) quantum well state. Its absolute value is also oscillatory with the number of layers.     

A copper- and boron-related defect in silicon

The resistivity of boron-doped silicon can be significantly increased by polishing such material with an appropriate amine- and copper-containing slurry. This effect is ascribed to a passivation of the boron acceptors by a defect produced or introduced by the polishing process. Three new, so far unknown localized vibrational modes at 691, 720, and 1038 cm^–1 are observed in highly boron-doped silicon samples after such a polishing treatment. Two of these localized modes can be identified as due to a boron-containing defect. High concentrations of copper found in the samples after appropriate polishing indicate a participation — either directly or indirectly — of this metal in the passivation process.     

Interlayer vacancy effects on the phonon modes in AB stacked bilayer graphene nanoribbon

We explore the effects of interlayer vacancy defects on the vibrational properties of Bernal (AB) stacking bilayer armchair graphene nanoribbons (BiAGNRs) using the forced vibrational method. It is observed that the Raman active longitudinal optical (LO) phonon of BiAGNR is shifted downward with the decrease of the ribbon width and an increase of the vacancy concentrations. We find that vacancies induce some new peaks in the low frequency regime of the phonon density of states. Our calculated typical mode patterns elucidate that the localized transverse optical phonon at the K-point is shifted towards the defect sites from the edges with increased vacancy concentrations. In addition, the impact of defect induced phonon modes on the specific heat capacity and thermal conductivity of BiAGNRs are discussed. These results present a new way of understanding the heat dissipation phenomena of graphene-based high-performance nanodevices and to clarify the Raman and the experiments related to the phonon properties.     

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.     

Localized modes in a one-dimensional sphalerite-structure lattice with anharmonicity

The nonlinear localized vibrational modes of a one-dimensional atomic chain with two periodically alternating masses and force constants are analytically investigated using a discrete multiple-scale expansion method. This model simulates a row of atoms in the <1 1 1>-direction of sphalerite, or zinc blende, crystals. Owing to the structural asymmetry, the vibrational amplitude is governed by a perturbed nonlinear Schr?dinger equation instead of the standard one found in one-dimensional lattices with two alternating masses but uniform force constant. Although the stationary localized modes with carrier wavevector at the Brillouin-zone boundary are similar to those of ionic lattices, the moving localized modes with wavevectors within the zone are different owing to the perturbation. The calculation shows that the height of the moving localized modes in this lattice dampens with time. Received 14 May 2001 and Received in final form 12 July 2001     

Excess entropy for a vacancy in a crystal

The following topics are discussed: (1) Within the harmonic theory a general expression is given for excess entropy of a localized detect in any crystal with cyclic boundary conditions and in the small perturbation limit. For a single vacancy defect Stripp and Kirkwood's formula is obtained, ΔS/k_B = d/2,d being the dimension of the space. For other localized defects the perturbation formula requires calculation of the unperturbed Green's matrix. (2) It is argued that the effect of free surface boundary conditions, as well as other surface changes, leaves ΔS effectively invariant. (3) Using the vacancy perturbation result for ΔS and Lawson's formula, a value for the vacancy formation volume is obtained only in terms of known measured parameters; this result is compared to experimental and other calculated values of ΔV_f. (4) If localized vibrational modes are present due to the vacancy, what effect these might have on ΔS, and, from this, what materials might be candidates for observing localized modes.     

Possible Propagating Intrinsic Localized Vibrational Modes for One-Dimensional Klein-Gordon Lattice

A11 possible existed propagating intrinsic localized vibrational modes for the discrete Klein-Gordon lattice are obtained analytically in the whole w(q) space of the system by means of the so-called semidiscrete approximation, with which the carrier wave is treated explicitly while the envelope is described in the continuum approximation. Our investigation shows that, in general, both the pulse-like and kink (antikink) envelope types of the vibrational modes for the system can occur with certain carrier wavenumbers and frequencies in the separated parts of the ω(q) space. And the propagating velocity of the pulse-like modes is either subsonic or nearsonic, abd that of the kink (antikink) modes is either subsonic or supersonic. Our results are similar to or consistent with some results for Klein-Gordon lattice model or other related nonlinear lattice systems by some different methods.     

TWO-DIMENSIONAL LOCALIZED VIBRATIONAL MODES AROUND A POLARON WITH THE NEXT-NEAREST-NEIGHBOR HOPPING INTERACTIONS

We have calculated the vibrational modes around a polaron to test the effects of the next-nearest-neighbor hopping interactions on the localized medes within a framework of the two-dimensional mode. The results show that: (1) For a negative polaron, eleven localized modes have been found, compared with ten modes obtained on a previous work without non-nearest neighbor hopping. (2) For a positive polaron, two additional localized modes occur. (3) The localization of localized modes are strengthened and their frequencies move after turning on the next-nearest-neighbor hopping interactions.     

First-principles calculations of pseudolocal vibrational modes: the case of Cu and Cu pairs in Si

Pseudolocal vibrational modes (pLVMs) are defect-related vibrational modes which are localized despite being below the phonon maximum. Such modes are sometimes seen as phonon replicas in photoluminescence spectra. The pLVMs associated with two copper-related defects are calculated from first-principles density-functional theory in periodic supercells. The localization of the pLVMs is quantified using the magnitude of the eigenvectors of the dynamical matrix.     

Moving nonlinear localized vibrational modes for a one-dimensional homogenous lattice with quartic anharmonicity

Moving nonlinear localized vibrational modes (i.e. discrete breathers) for the one-dimensional homogenous lattice with quartic anharmonicity are obtained analytically by means of a semidiscrete approximation plus an integration. In addition to the pulse-envelope type of moving modes which have been found previously both analytically and numerically, we find that a kink-envelope type of moving mode which has not been reported before can also exist for such a lattice system. The two types of modes in both right- and left-moving form can occur with different carrier wavevectors and frequencies in separate parts of the plane. Numerical simulations are performed and their results are in good agreement with the analytical predictions. Received 13 October 1999 and Received in final form 15 May 2000     

Optomechanical coupling in a two-dimensional photonic crystal defect cavity

Periodically structured materials can sustain both optical and mechanical modes. Here we investigate and observe experimentally the optomechanical properties of a conventional two-dimensional suspended photonic crystal defect cavity with a mode volume of ~3(λ/n)3. Two families of mechanical modes are observed: flexural modes, associated to the motion of the whole suspended membrane, and localized modes with frequencies in the GHz regime corresponding to localized phonons in the optical defect cavity of diffraction-limited size. We demonstrate direct measurements of the optomechanical vacuum coupling rate using a frequency calibration technique. The highest measured values exceed 80 kHz, demonstrating high coupling of optical and mechanical modes in such structures.     

Resonant interaction between localized and extended vibrational modes in Si: 18O under pressure

The interaction between localized and extended vibrational modes in solids is of central importance in understanding how local vibrational modes decay into phonons. Interstitial oxygen (O(i)) in silicon is a model system for studying such interactions. Using hydrostatic pressure, we have brought the antisymmetric stretch mode of (18)O(i) in silicon into resonance with the second harmonic of the (18)O(i) resonant mode. Infrared spectroscopy was used to observe an anticrossing between these two vibrational modes at pressures near 4 GPa. A model of the interaction between these modes produced excellent agreement with the experimentally observed frequencies and linewidths.     

Two-dimensional photonic crystals with a lattice defect: Spectrum of defect modes, localization of light, and formation of evanescent waves

Properties of an electromagnetic field localized in the defect modes of two-dimensional photonic crystals are studied. The defect-mode spectrum of these structures is calculated, electromagnetic field localization and channeling effects are analyzed, and the properties of the field inside and beyond a photonic crystal with a lattice defect are also studied. The calculations show that the electromagnetic field is localized in the defect mode of a photonic crystal in a region smaller than the wavelength. The dependence of the defect-mode spectrum on the parameters of the photonic crystal is investigated and possibilities for controlling the spectrum of defect modes are indicated. It is shown that the optical field leaving a photonic crystal possesses the properties of a evanescent wave, which means that spatial resolution substantially greater than the wavelength of the radiation can be achieved in the near field and opens up possibilities for using photonic crystals with a lattice defect in near-field optical microscopy. The possibility of externally controlling an optical field localized in the defect modes of a photonic crystals is demonstrated.     

MOVING NONLINEAR LOCALIZED MODES FOR ONE-DIMENSIONAL KLEIN－GORDON DIATOMIC LATTICE

We study analytically the moving nonlinear localized vibrational modes (discrete breathers) for a one-dimensional Klein－Gordon diatomic lattice in the whole ω(q) plane of the system by means of a semi- discrete approximation, in which the carrier wave of the modes is treated explicitly while the envelope is described in the continuum approximation. We find that both pulse and kink envelope moving modes for this lattice system can occur with certain carrier wave vectors and vibrational frequencies in separate regions of the ω(q) plane. However, the kink envelope moving modes have not been reported previously for this lattice system.     

Localized defect modes of water waves through two-dimensional periodic bottoms with point defects

In this Letter, the localized defect modes of water waves over two-dimensional periodic bottoms with a point defect are investigated by supercell calculations and plane-wave expansion method. Two kinds of defects are introduced, one is a radius defect created by changing radius of cylinder, and another is a depth defect created by changing its depth. The results indicate that both can create defect modes, and the amplitude distributions of the defect modes are well localized in the vicinity of the defects with various patterns. The influences of radius and depth of defect cylinder on the defect modes are investigated in detail.