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.     

Cyclotron Resonance of a Magnetopolaron in a Quantum Well at Finite Temperatures

Taking into account the interaction of an electron with both bulk longitudinal-optical (BO) and surface-optical (SO) phonons, the cyclotron resonance of a magnetopolaron in a quantum well at finite temperatures is investigated by using the generalized Larsen perturbationtheory method. It is shown that the absorption and emission resonances must be considered at the same time at finite temperatures. The results also show that the electron-SO phonon interaction plays an important role as well as the electron-BO phonon interaction, especially when the quantum well width is getting thinner. For an experimentally interesting GaAs/Ga_1-xAl_xAs sandwich structure, the splitting of the cyclotron resonance spectrum and the temperature dependence of two splitting cyclotron resonance mass of the magnetopolaron in the resonant magnetic field region have been studied.     

The scattering of phonons of arbitrary wavelength at a solid-solid interface: Model calculation and applications

A one-dimensional lattice model of a solid-solid interface is presented within which it is possible to characterize the scattering of phonons at the interface as a function of wavelength. The probability for a phonon to be transmitted across the interface is found generally to decrease with decreasing wavelength, although phenomena such as total reflexion and resonant transmission may occur. Conditions for the existence of a localized interface mode are given. The thermal boundary resistance for heat flow across the interface is expressed in terms of an average temperature-dependent phonon transmission coefficient which generally increases with decreasing temperature and approaches the continuum value at very low temperature. Applications of these results to three-dimensional interfaces in general, and particularly to heat dissipation in catalysts, high-frequency phonon radiators, and Kapitza resistance, are discussed.     

Magneto infrared absorption in high electron density GaAs quantum wells

Magneto infrared absorption measurements have been performed in a highly doped GaAs quantum well which has been lifted off and bonded to a silicon substrate, in order to study the resonant polaron interaction. It is found that the pinning of the cyclotron energy occurs at an energy close to that of the transverse optical phonon of GaAs. This unexpected result is explained by a model taking into account the full dielectric constant of the quantum well.     

Topological Phonon Modes in a Two-Dimensional Wigner Crystal

We investigate the spin-orbit coupling effect in a two-dimensional(2D)Wigner crystal.It is shown that sufficiently strong spin-orbit coupling and an appropriate sign of g-factor could transform the Wigner crystal to a topological phonon system.We demonstrate the existence of chiral phonon edge modes in finite size samples,as well as the robustness of the modes in the topological phase.We explore the possibility of realizing the topological phonon system in 2D Wigner crystals confined in semiconductor quantum wells/heterostructure.It is found that the spin-orbit coupling is too weak for driving a topological phase transition in these systems.It is argued that one may look for topological phonon systems in correlated Wigner crystals with emergent effective spin-orbit coupling.     

Size-dependent phonon transmission across dissimilar material interfaces

In this paper, we study the size effects on the phonon transmission across material interfaces using the atomistic Green's function method. Layered Si and Ge or Ge-like structures are modeled with a variety of confined sizes in both transverse and longitudinal directions. The dynamical equation of the lattice vibration (phonon waves) is solved using the Green's function method and the phonon transmission is calculated through the obtained Green's function. Phonon transmission across a single interface of semi-infinite Si and Ge materials is studied first for the validation of the methodology. We show that phonon transmission across an interface can be tuned by changing the mass ratio of the two materials. Multi-layered superlattice-like structures with longitudinal size confinement are then studied. Frequency-dependent phonon transmission as a function of both the number of periods and the period thickness is reported. A converged phonon transmission after ten periods is observed due to the formation of phonon minibands. Frequency-dependent phonon transmission with transverse size confinement is also studied for the interface of Si and Ge nanowire-like structures. The phonon confinement induces new dips and peaks of phonon transmission when compared with the results for a bulk interface. With increasing size in the transverse direction, the phonon transmission approaches that of a bulk Si/Ge interface.     

Study of Cyclotron Resonance of Interface Polarons

This paper presents a study of the cyclotron resonance of the interface polarons in a semiinfinite polar crystal. In the resonant magnetic field region the Landau-level corrections due to the resonant coupling of the electron with the bulk longitudinal-optical (LO) phonon and the surface optical (SO) phonon are calculated. At resonance the n-th Landau level (n > 0) splits into a triplet. The cyclotron-resonance mass of the electron is evaluated for an arbitrary magnetic-field strength. For the interface system the magneto-optical anomalies display three branches of the cyclotron-resonance mass spectra. The numerical results show that in the interface system the polaron effect is weakened with respect to the ideal twodimensional system. It is found that in the very weak magnetic fields the polaron effect is contributed mainly by the SO phonons, whereas in the large magnetic fields the LO-phonon contribution to the polaron.effect becomes predominant.     

Effect of Gaussian acoustic nanocavities in a narrow constriction on ballistic phonon transmission

We investigate the effect of Gaussian acoustic nanocavities in a narrow constriction on ballistic phonon transport through a semiconductor nanowire at low temperatures. When the transverse width of acoustic nanocavities takes a Gaussian function, it is found that the resonant peaks and band gaps in transmission spectra are obvious, indicating that the system has selective transmission and filters actions for ballistic phonons. The number and length of nanocavities have significant effects on the phonon transmission and thermal conductance. The results are compared with those in uniform width acoustic nanocavities. The Gaussian acoustic nanocavities are therefore a promising phononic device to manipulate ballistic phonons in nanophononics.     

Surface effects on optical phonons and on phonon-plasmon modes

The size and shape dependence of the properties of long wave optical phonons in polar crystals is discussed. The main effect occurring due to the presence of surfaces is the appearance of a surface optical phonon band in the frequency region between the frequencies ω_t and ω_l of the long wave transverse and longitudinal bulk modes. The surface modes give rise to strong absorption peaks in the infrared absorption spectra of small samples. For very small crystallites the surface mode absorption is dominant, and as the size of the specimens is increased, the ratio of surface to bulk mode absorption decreases. It is shown that the large spread in particle sizes usually encountered in experimental work and the increased damping of the phonon modes in small samples both tend to obscure the fine structure of the absorption spectrum. The surface phonon-plasmon modes in polar crystals containing free carriers are treated in an analogous manner.     

Dispersion and the electron–phonon interaction in a single heterostructure

We investigate the electron–phonon interaction in a polar–polar single heterostructure through the use of the linear combination of hybrid phonon modes, considering the role of longitudinal optical, transverse optical and interface modes, using a continuum model that accounts for both mechanical and electrical continuity over a heterostructure interface. We discuss the use of other models for such systems, such as the bulk phonon (3DP) and dielectric continuum (DC) models, using previously developed sum-rules to explain the limitations on their validity. We find that our linear combination (LC) model gives an excellent agreement with scattering rates previously derived using the 3DP and DC models when the lattice dispersion is weak enough to be ignored, however, when there is a noticeable lattice dispersion, the LC model returns a different answer, suggesting that interface modes play a much greater part in the scattering characteristics of the system under certain conditions. We also discuss the remote phonon effect in polar/polar heterostructures.     

Optical absorption weak coupling theory of polarons bound to defects

We calculate the infrared absorption of large polarons bound to defects in the weak coupling limit. Polar crystals with more than one longitudinal optical phonon branch coupled to the electrons are considered. Oscillator strengths corresponding to defect transitions without phonons and to transitions with emission of phonons are calculated using the Larsen wave-functions. The results are applied to infrared data in strontium titanate and it is found that weak coupling calculations are in better agreement than strong coupling ones.     

Cyclotron Resonance of an Interface Magnetopolaron at Finite Temperatures

Taking into account the interaction of an electron with both bulk longitudinal-optical (LO) and interface-optical (IO) phonons, the cyclotron resonance of an interface magnetopolaron at finite temperatures is investigated by using the generalized Larsen perturbation-theory method. It is shown that the absorption and emission resonance must be considered at the same time at finite temperatures. The results also show the important role played by the electron-IO phonon interaction. For the GaAa/GaSb structure, splitting of the cyclotron resonance spectrum and temperature dependence of the threefold splitting cyclotron resonance mass of the magnetopolaron in the resonant magnetic field region are studied.     

Phonon-assisted combined resonance in magneto-photoconductivity of n-InSb

A combined cyclotron-spin resonance assisted by an emission of LO phonon has been observed in the longitudinal and transverse magneto-photoconductivity of n-InSb. The theoretical analysis predicts a resonance in magneto-optical absorption for light polarization e 6 H and a weakly resonant behavior for e ⊥ H. This agrees with the observations.     

Phonons and periodons in IV–VI semiconductor superlattices

We have calculated the phonon and periodon dispersion relations in IV–VI semi-conducting bulk PbTe and SnTe and their superlattice structure. The model used here is a one-dimensional lattice which includes harmonic interactions up to second neighbours as well as on-site nonlinear electron-ion interactions at the anion site. We calculate the phonon and periodon dispersion relations in bulk and PbTe-SnTe superlattice for the transverse optic and acoustic modes using the transfer matrix method. Our analysis has predicted correct nature of the folding of acoustic and confinement of optical phonons at various frequency intervals corresponding to pass and stop bands of the superlattices.     

Investigation on thermal conductivity of graphene/Si heterostructure with different defect ratios and sizes

The thermal conductivity (TC) of graphene/Si heterostructures with different defect ratios and sizes was investigated using the molecular dynamics method. As the defect ratio of heterostructure increased, the TC decreased first sharply and then slowly under a high temperature stage. The TC of heterostructure also showed a significant size effect. This phenomenon was explained by phonon dispersion and flip competition. The phonon density of states for the graphene heterostructure with different defect ratios and sizes was obtained to understand the thermal transport mechanism. Analysis showed that with the increase in the defect ratio and when the flexural modes of the heterostructure became weak, the longitudinal and transverse modes gradually dominated the phonon transport. This phenomenon can be explained that the Si atom vibration was harder in the vertical plane than that of graphene. The vibration mode hindered the heat carrier of graphene and affected heat transport to the heterostructure.     

Effect of structural defect on phonon transmission quantization in low-dimensional superlattices

Using the scattering-matrix cascading method, we investigate the effect of structural defect on the acoustic phonon transmission quantization in a low-dimensional superlattice quantum waveguide. In the present system, the phonon transmission exhibits rather complex resonant behaviors. It is found that a lateral defect in an otherwise periodic structure modifies the transversal phonon transmission spectra nontrivially and completely washes away the transmission quantization due to the strong additional scattering by defect. However, the appreciable quantization survives in the presence of a longitudinal defect. Our results also show that by adjusting the geometric parameters of the structural defect, one can control the phonon transport of the structure to match practical requirements in devices.     

First-order Raman scattering in cylindrical wurtzite nanowire

We have presented a theoretical study on electron resonant Raman scattering (ERRS) process associated with the bulk longitudinal optical (LO), surface optical (SO) and quasi-confined (QC) phonon modes in a free-standing wurtzite nanowire (NW). We consider the Fröhlich electron–phonon interaction in the framework of the dielectric continuum model. Numerical calculations on the GaN material reveal that differential cross-section (DCS) is sensitive to the wire size. The bulk LO and high-frequency quasi-confined (QC₊) phonons make main contributions to the DCS and the impact of the SO phonon can be negligible in the ERRS process. Moreover, scattering intensity of the bulk LO phonon is strongly enhanced as the incident photon energy approaches the energy band-gap of the GaN.     

Thermal properties of carbon nanotubes and nanotube-based materials

The thermal properties of carbon nanotubes are directly related to their unique structure and small size. Because of these properties, nanotubes may prove to be an ideal material for the study of low-dimensional phonon physics, and for thermal management, both on the macro- and the micro-scale. We have begun to explore the thermal properties of nanotubes by measuring the specific heat and thermal conductivity of bulk SWNT samples. In addition, we have synthesized nanotube-based composite materials and measured their thermal conductivity. The measured specific heat of single-walled nanotubes differs from that of both 2D graphene and 3D graphite, especially at low temperatures, where 1D quantization of the phonon bandstructure is observed. The measured specific heat shows only weak effects of intertube coupling in nanotube bundling, suggesting that this coupling is weaker than expected. The thermal conductivity of nanotubes is large, even in bulk samples: aligned bundles of SWNTs show a thermal conductivity of >200 W/m K at room temperature. A linear K(T) up to approximately 40 K may be due to 1D quantization; measurement of K(T) of samples with different average nanotube diameters supports this interpretation. Nanotube–epoxy blends show significantly enhanced thermal conductivity, showing that nanotube-based composites may be useful not only for their potentially high strength, but also for their potentially high thermal conductivity. Received: 17 October 2001 / Accepted: 3 December 2001 / Published online: 4 March 2002     

Relaxation of quasi-transverse phonons in the Herring mechanism and ultrasound absorption in cubic crystals with positive and negative anisotropies of the second-order elastic moduli

The phonon relaxation and quasi-transverse ultrasound absorption in the course of Herring and Landau-Rumer anharmonic scattering processes in cubic crystals with positive (Ge, Si, diamond, InSb, LiF, MgO) and negative (KCl, NaCl, CaF₂) anisotropies of the second-order elastic moduli have been investigated. A new mechanism of transverse phonon relaxation, according to which the fusion of a transverse (slow or fast) phonon with a slow phonon generates a fast transverse phonon, has been considered in the long-wave-length approximation. This mechanism is similar to the Herring relaxation mechanism for longitudinal phonons. It has been demonstrated that, for crystals of the first group with a considerable anisotropy of the elastic energy (Ge, Si, InSb, LiF, MgO), “anomalous” relaxation processes in which the fusion of a slow transverse phonon with a fast phonon generates a slow transverse phonon are possible in contrast to the Herring relaxation mechanism for longitudinal phonons. These relaxation processes appear to be impossible for all crystals of the second group (KCl, NaCl, CaF₂), as well as for crystals of the first group with a small anisotropy of the elastic energy, such as diamond. The angular dependences of the ultrasound absorption coefficient for the Herring and Landau-Rumer mechanisms have been analyzed using the anisotropic-continuum model. It has been shown that, for the crystals of the first group under consideration, the contribution of the Herring mechanism to the long-wavelength ultrasound absorption is small compared to the contribution of the Landau-Rumer mechanism. However, for the KCl and NaCl crystals of the second group in directions of the [001] type, the contribution of the Herring mechanism can significantly exceed the contribution of the Landau-Rumer mechanism.     

Linear Boltzmann Equation as the Long Time Dynamics of an Electron Weakly Coupled to a Phonon Field

We consider the long time evolution of a quantum particle weakly interacting with a phonon field. We show that in the weak coupling limit the Wigner distribution of the electron density matrix converges to the solution of the linear Boltzmann equation globally in time. The collision kernel is identified as the sum of an emission and an absorption term that depend on the equilibrium distribution of the free phonon modes.