Long-wavelength Optical Phonons Research Articles

Optical phonon mixing in bilayer graphene with a broken inversion symmetry

Pristine bilayer graphene is a centrosymmetric material in which parity is a conserved quantity. The high sensitivity of this atomic scale structure to external perturbations that break the inversion symmetry enables significant potentials for device applications. Raman spectroscopy is used here to probe the breakdown of parity conservation in a direct and quantitative manner via a phonon mixing phenomenon. The striking broken-symmetry effects display anticrossing coupling between two opposite parity long-wavelength optical phonons. The spectral intensity transfer between the two observed Raman peaks offers quantitative measurements of the evolution of the phonon wave function and demonstrates a manifestation of broken inversion symmetry in graphene layers.

Quantized long-wavelength optical phonon modes in graphene nanoribbon in the elastic continuum model

This paper presents an analytical displacements and dispersion relations for optical phonons of a graphene sheet. These results are used to derive the optical deformation potential interactions for graphene as well as to obtain descriptions of the confined optical phonons for graphene.

Long-wavelength optical phonons in single-walled boron nitride nanotubes

A unified macroscopic continuum model is proposed to calculate the long-wavelength optical phonons of single-walled boron nitride nanotubes. The effect of the polarity in the boron nitride nanotubes on optical vibrations is considered by this model. We obtain the dispersion relation of the optical phonons. The avoided crossing between longitudinal and transverse optical phonon branches arises from the indirectly coupling between different phonon branches. The diameter dependence of the optical phonon frequency is derived. Our results are in agreement well with the experiment ones [R. Arenal, A.C. Ferrari, S. Reich, L. Wirtz, J.-Y. Mevellec, S. Lefrant, A. Rubio, A. Loiseau, Nano Lett. 6 (2006) 1812].

Anomaly of Optical Phonons in Bilayer Graphene

The frequency shift and broadening of long-wavelength optical phonons are calculated for varying Fermi level in a bilayer graphene. Symmetric modes with displacements of two layers in phase are affected strongly. In the absence of a magnetic field, the broadening disappears and the frequency shift exhibits a logarithmic singularity when the Fermi energy is a half of the phonon energy, and the shift increases in proportion to the Fermi energy for sufficiently high electron density. In magnetic fields, the broadening is resonantly enhanced and the frequency shift exhibits a rapid change when the phonon energy becomes the energy separation of Landau levels between which optical transitions are allowed.

Dielectric constants and phonon modes of amorphous hafnium aluminate deposited by metal organic chemical vapor deposition

Dielectric constants and long-wavelength optical phonon modes of amorphous hafnium aluminate films with a maximum aluminum content of 19at.% are studied by infrared spectroscopic ellipsometry (IRSE). The hafnium aluminate films were prepared by metal organic chemical vapor deposition on silicon substrates. IRSE revealed one polar lattice mode and one impurity-type mode, which show all a systematic shift in frequency with varying Al content. The static dielectric constant decreases from 10.1 for 4.6at.% Al to 8.1 for 19at.% Al. The absolute values were found to be between 50% and 70% smaller than the values obtained from electrical measurements.

Symmetry-based approach to electron-phonon interactions in graphene

We use the symmetries of monolayer graphene to write a set of constraints that must be satisfied by any electron-phonon interaction Hamiltonian. The explicit solution as a series expansion in the momenta gives the most general, model-independent couplings between electrons and long-wavelength acoustic and optical phonons. As an application, the possibility of describing elastic strains in terms of effective electromagnetic fields is considered in detail, with an emphasis on group-theory conditions and the role of time-reversal symmetry.

Exotic electronic and transport properties of graphene

A brief review is given on electronic and transport properties of monolayer graphene from a theoretical point of view. The topics include the effective-mass description of electronic states, topological anomaly associated with Berry's phase, singular diamagnetic susceptibility, zero-mode anomalies and their removal due to level broadening effects, screening effect and charged impurity scattering, the symmetry crossover among symplectic, unitary, and orthogonal due to the presence of special time reversal symmetry, and anomaly and magnetic oscillation of long-wavelength optical phonons.

Magnetic Oscillation of Optical Phonon in Graphene

The frequency shift and broadening of long-wavelength optical phonons due to interactions with electrons are calculated in a monolayer graphene in magnetic fields. The broadening is resonantly enhanced and the frequency shift exhibits a rapid change when the phonon energy becomes the energy separation of Landau levels between which optical transitions are allowed.

Dispersion of confined optical phonons in semiconductor nanowires in the framework of a continuum approach

Confined optical phonons are discussed for a semiconductor nanowire of the Ge (Si) prototype on the basis of a theory developed some years ago. In the present work this theory is adapted to a nonpolar material and generalized to the case when the phonon dispersion law involves both linear and quadratic terms in the wave vector. The treatment is considered along the lines of a continuous medium model and leads to a system of coupled differential equations describing oscillations of mixed nature. The nanowire is modeled in the form of an infinite circular cylinder and the solutions of the fundamental equations are found. We are thus led to a description of long-wavelength optical phonons, which should show a closer agreement with experimental data and with calculations along atomistic models. The presented theory is applied to the calculation of optical phonons in a Ge nanowire. We have found the dispersion curves for various optical phonon modes. We also normalize the modes and discuss the electron-phonon interaction within the deformation potential approximation.

Interface-phonon-limited two-dimensional mobility in AlGaN∕GaN heterostructures

The room temperature polar-optical-phonon-limited two-dimensional electron mobility in AlxGa1−xN∕GaN heterostructures is calculated taking into account the interaction of conduction electrons and interface-phonon modes. The polar optical oscillations are described via the uniaxial dielectric continuum model. Electron–polar-optical-phonon scattering rates are evaluated from a general expression that is always valid as long as the interaction Hamiltonian matrix elements depend only on the magnitude of the phonon wave vector. Values for the 300K low-field mobility (μ) of a few hundreds cm2∕Vs are obtained within a simplified relaxation time scheme involving electron-phonon absorption scattering rates. It is found that the way of describing the electronic states in the conduction band strongly affects the calculation of μ. The typical triangular well model gives the poorest results compared with a previously proposed analytical approximation of the conduction band potential profile. We present a discussion on the relevance of an appropriate model for long-wavelength polar optical phonons in the obtention of realistic values of the electron mobility in wurtzite heterostructures.

Anomaly of Optical Phonon in Monolayer Graphene

The frequency shift and broadening of long-wavelength optical phonons due to interactions with electrons are calculated in a monolayer graphene as a function of the electron density. The broadening disappears and the frequency shift exhibits a logarithmic singularity when the Fermi energy is half of the energy of the optical phonon. The shift increases in proportion to the Fermi energy for sufficiently high electron density.

Infrared optical properties of MgxZn1−xO thin films (0⩽x⩽1): Long-wavelength optical phonons and dielectric constants

Infrared spectroscopic ellipsometry in the spectral range from ω=360cm−1toω=1500cm−1 and Raman scattering spectroscopy are applied to study the long-wavelength optical phonon modes and dielectric constants of MgxZn1−xO thin films in the composition range 0⩽x⩽1. The samples were grown by pulsed laser deposition on sapphire substrates. X-ray diffraction measurements of the thin film samples reveal the hexagonal wurtzite crystal structure for x⩽0.53 and the cubic rocksalt crystal structure for x⩾0.67. A systematic variation of the phonon mode frequencies with Mg-mole fraction x is found for both hexagonal and cubic MgxZn1−xO thin films. The modified random isodisplacement model matches the observed composition dependence of the phonon mode frequencies for the hexagonal structure thin films [J. Chen and W. Z. Shen, Appl. Phys. Lett. 83, 2154 (2003)], whereas a simple linear approximation scheme is sufficient for the cubic structure part. We observe a discontinuous behavior of the transverse optical phonon modes (decrease), and the static and high-frequency dielectric constants (increase) within the phase transition composition region from the wurtzite structure part to the rocksalt structure part. On the contrary, the longitudinal phonon mode parameters increase almost linearly, and upon phase transition the splitting between the transverse and longitudinal modes increases. We associate this discontinuous behavior with the change of the nearest-neighbor coordination number from fourfold (wurtzite structure) to sixfold (rocksalt structure) in our samples and the associated increase in bond ionicity from ZnO to MgO. Accordingly, we propose that the reduced exciton mass parameter should approximately double upon changing from wurtzite to rocksalt crystal structure.

Phonon modes, dielectric constants, and exciton mass parameters in ternary MgxZn1−xO

ABSTRACTThe long-wavelength optical phonons and dielectric constants of PLD-grown MgxZn1−xO films are studied by combination of infrared spectroscopic ellipsometry and Raman scattering spectroscopy. The ternary alloy MgxZn1−xO exhibits a phase transition with change of coordination number from four-fold coordinated, hexagonal wurtzite structure (ZnO) to six-fold coordinated, cubic rocksalt structure (MgO). It is found that both phonon mode frequencies and dielectric constants change abruptly upon phase transition, which is assigned to the change of coordination number. The change of dielectric constants can be related to the change of electronic properties, for instance, the exciton binding energy. In a simple approach, the exciton binding energy depends on the reduced exciton mass and the static dielectric constant. By comparison with experimental values of the exciton binding energies it is found that the reduced exciton mass must increase by a factor of about two upon face transition from wurtzite to rocksalt structure.

Nonpolar optical scattering of positronium in magnesium fluoride

We report the results of the analysis of the temperature broadening of the momentum distribution of delocalized Positronium (Ps) in Magnesium Fluoride in terms of optical deformation-potential scattering model (long-wavelength optical phonons). The Ps optical deformation-potential coupling constant $D_{o}$ in MgF$_{2}$ has been determined to be $(1.8\pm0.3)\times10^{9}$ eV/cm. We also show that the Ps momentum distribution is sensitive to second-order phase transitions in those crystals where optical deformation-potential scattering is allowed in one and forbidden in another crystalline phase.

Determination of the composition of lithium tantalate by means of Raman and OH − absorption measurements

Two optical methods for determination of the composition in lithium tantalate were discussed. Quantitative relationships between the line width of Raman peaks (142 cm −1 for E phonon and 861 cm −1 for A 1 phonon) and the crystal composition were firstly presented. The comparison of the Raman data obtained for the congruent and the near-stoichiometric crystals reveals some differences in the shape and the number of Raman peaks, which lead to a new assignment of the long-wavelength optical phonons. The OH − absorption bands of lithium tantalate crystals were measured at room temperature, and the line width of one decomposed peak was found to change considerably with the crystal composition, irrespective of the hydrogen concentration. The quantitative relationship between the line width of this peak and the crystal composition is also presented.

The composition dependence and new assignment of the Raman spectrum in lithium tantalate

The Raman scattering spectra of lithium tantalate crystals with different compositions were investigated. The comparison of the Raman data obtained for the congruent and the near-stoichiometric crystals reveals some differences in the shape and the number of Raman peaks, which lead to a new assignment of the long-wavelength optical phonons. And quantitative relationships between the linewidth of Raman peaks (142 cm −1 for E-phonon and 861 cm −1 for A 1-phonon) and the crystal composition were firstly presented. Two local Raman lines, 278 and 750 cm −1, were found for the congruent crystals and attributed to the intrinsic defects, Li vacancy and anti-site Ta ion, respectively.

Continuum model for long-wavelength phonons in two-dimensional graphite and carbon nanotubes

A continuum model yielding dispersion relations for long-wavelength acoustic and optical phonons in two-dimensional graphite and achiral single-walled carbon nanotubes is developed. Close relations with the theory of thin elastic plates and cylindrical shells are established. The effective thickness of a nanotube determining the limits of validity of the continuum model is estimated. A qualitative analysis of vibrations of chiral nanotubes is presented.

Long-wavelength nonequilibrium optical phonon dynamics in cubic and hexagonal semiconductors

We have investigated the relaxation of zone-center nonequilibrium optical phonons in bulk cubic and hexagonal semiconductors. Our theory is based on the application of Fermi's golden rule formula involving anharmonic interaction between phonons. Calculations of the lifetimes of the zone-center longitudinal optical (LO) and transverse optical (TO) phonons in cubic materials have been performed by modeling acoustic phonon modes within Debye's isotropic continuum scheme. Lifetimes of ${A}_{1}(\mathrm{LO})$, ${E}_{1}(\mathrm{TO})$, ${A}_{1}(\mathrm{TO})$, ${E}_{2}^{2}$ and ${E}_{2}^{1}$ modes in wurtzite semiconductors have also been calculated by employing Debye's scheme within a semi-isotropic continuum model for acoustic modes. We have obtained a few trends in the lifetime results within a crystal phase (cubic or hexagonal), and between the two crystal phases. Our results support and explain available experimental data over a large temperature range, and make some predictions.

Continuum model for long-wavelength optical phonons in cylinders: Application to carbon nanotubes

A continuum model for long-wavelength nonpolar optical phonons in systems with cylindrical symmetry is presented. The eigenfrequencies and modes for hollow cylinders with free surfaces are obtained, choosing parameters that model single-wall carbon nanotubes. A strong mixing of longitudinal and transverse modes is found for nonzero wave vectors; in fact, the mixing is present for certain modes even at the center of the Brillouin zone. The results show the need to treat on an equal footing all optical modes in these systems of reduced dimensionality.

Intrinsic lifetimes and anharmonic frequency shifts of long-wavelength optical phonons in polar crystals

Quantitative calculations of phonon lifetimes due to anharmonic three-phonon processes require knowledge of cubic anharmonic coupling coefficients. In order to determine the temperature dependence of phonon frequencies, anharmonic force constants of up to fourth order are needed. In polar crystals, the macroscopic electric field gives rise to nonanalytic terms in these coefficients. It is shown how these non-analytic terms can be determined from other physical quantities including higher-order dipole moments, Raman coefficients, and nonlinear susceptibilities. The contribution of these terms to the intrinsic damping of the long-wavelength optical phonon modes in GaAs has been determined by an ab initio calculation.