Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes as well as the corresponding Fro^ehlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-well wire (QWW) are derived and studied. Numerical calculations on GaAs/AlzGa1-x As cylindrical QWW are performed. Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersion frequencies of IO or SO phonon modes sensitively depend on the Al mole fraction x in AlzGa1-x As material and the wavevector in z direction, kz. With the increasing of kz and quantum number m, the frequency of each IO mode approaches one of the two frequency values of the single GaAs/AlxGa1-x As heterostructure, and the electrostatic potential distribution of the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the coupling between the electron-IO and -SO phonons becomes weaker.     

Electron-Phonon Interaction in an Annular Quantum Dot

The confined longitudinal-optical （LO） phonon and surface-optical （SO） phonon modes of a free-standing annular cylindrical quantum dot are derived within the framework of dielectric continuum approximation. It is found that there exist two types of SO phonon modes： top SO （TSO） mode and side SO（SSO） mode in a cylindrical quantum annulus. Numerical calculation on CdS annulus system has been performed. Results reveal that the two different solutions of SSO mode distribute mainly at the inner or outer surfaces of the annulus. The dispersion relations and the coupling intensions of phonons in a quantum annulus are compared with those in a cylindrical quantum dot. It is found that the dispersion relations of the two different structures are similar, but the coupling intension of the phonon-electron interaction in quantum annulus is larger than that in quantum dot. The Hamiltonians describing the free phonon modes and their interactions with electrons in the system are also derived.     

Energy of a Polaron in a Wurtzite Nitride Finite Parabolic Quantum Well

The effects of electron-phonon interaction on energy levels of a polaron in a wurtzite nitride finite parabolic quantum well （PQW） are studied by using a modified Lee-Low-Pines variational method. The ground state, first excited state, and transition energy of the polaron in the GaN/Al0.3Ga0.7N wurtzite PQW are calculated by taking account of the influence of confined LO（TO）-like phonon modes and the half-spaee LO（TO）-like phonon modes and considering the anisotropy of all kinds of phonon modes. The numerical results are given and discussed. The results show that the electron-phonon interaction strongly affects the energy levels of the polaron, and the contributions from phonons to the energy of a polaron in a wurtzite nitride PQW are greater than that in an A1GaAs PQW. This indicates that ehe electron-phonon interaction in a wurtzite nitride PQW is not negligible.     

Growth and Optical Properties of Double Heterostructure GaN／InGaN／GaN Films with Large Composition

The double heterostructure GaN/InGaN/GaN films with different thicknesses of the InGaN layer were grown at 780℃ or 800℃ by metal-organic chemical vapour deposition.The samples were investigated using x-ray diffraction (XRD),room-temperature photoluminescence (PL) and Raman scattering.The dependences of the samples on both the growth temperature and the thickness of the InGaN layer were studied.The composition of InGaN was determined by the results of XRD,and the bowing parameter of InGaN was calculated in terms of the PL spectra.When the thickness of the InGaN layer was reduced,the phase separation of InGaN was found in some samples.The raman frequency of the A1(LO) and E2(low) modes in all the samples shifted and did not agree with Vegard‘s law.     

OPTICAL-PHONON MODES AND ELECTRON-OPTICAL-PHONON INTERACTION IN A COUPLED QUANTUM WELL

By applying the dielectric continuum model, optical-phonon modes of the lattice vibration and a complete interaction Frohlich-like Harniltonian between an electron and the optical phonons including the interface phonons, the confined LO phonons and the half-space LO phonons are derived for a general coupled quantum well (GCQW) structure of polar crystals. The dispersion curves of the interface modes and the electron-interface-phonon coupling function as functions of coordinate z and wavenumber k are given and discussed for a GCQW. We find that there are eight (not ten) frequency solutions for the interface optical-phonon modes in GCQW and that, in the long-wavelength limit, the longitudinal and transverse modes in the two side materials 1 and 5 are forbidden and two new frequency solutions ω± are obtained instead. Moreover, we also find that the electron-interface-phonon coupling functions are complicated functions of k and that the phonons with long wavelengths are important and the higher-frequency modes are more important than the lower-frequency modes for the electron-phonon interaction.     

Polar Mixing Optical Phonon Spectra in Wurtzite GaN Cylindrical Quantum Dots： Quantum Size and Dielectric Effects

The interface-optical-propagating （IO-PR） mixing phonon modes of a quasi-zero-dimensional （QOD） wurtzite cylindrical quantum dot （QD） structure are derived and studied by employing the macroscopic dielectric continuum model. The analytical phonon states of IO-PR mixing modes are given. It is found that there are two types of IO-PR mixing phonon modes, i.e. p-IO//z-PR mixing modes and the z-IO//p-PR mixing modes existing in QOD wurtzite QDs. And each IO-PR mixing modes also have symmetrical and antisymmetrieal forms. Via a standard procedure of field quantization, the Frohlich Hamiltonians of electron-（IO-PR） mixing phonons interaction are obtained. Numerical calculations on a wurtzite GaN cylindrical QD are performed. The results reveal that both the radial-direction size and the axial-direction size as well as the dielectric matrix have great influence on the dispersive frequencies of the IO-PR mixing phonon modes. The limiting features of dispersive curves of these phonon modes are discussed in depth. The phonon modes ＂reducing＂ behavior of wurtzite quantum confined systems has been observed obviously in the structures. Moreover, the degenerating behaviors of the IO-PR mixing phonon modes in wurtzite QOD QDs to the IO modes and PR modes in wurtzite Q2D QW and QID QWR systems are analyzed deeply from both of the viewpoints of physics and mathematics.     

Polar Interface Optical Phonon Modes and Froehlich Electron－Phonon Interaction Hamiltonians in an Arbitrary Layer－Number Quantum Well System

By using determinant method as in our recent work, the IO phonon modes, the orthogonal relation for polarization vector, electron-IO phonon F~6hlich interaction Hamiltonian, the dispersion relation, and the electron-phonon coupling function in an arbitrary layer-number quantum well system have been derived and investigated within the framework of dielectric continuum approximation. Numerical calculation on seven-layer AlxGal-xAs/GaAs systems have been performed. Via the numerical results in this work and previous works, the general characters of the IO phonon modes in an n-layer coupling quantum well system were concluded and summarized. This work can be regarded as a generalization of previous works on IO phonon modes in some fLxed layer-number quantum well systems, and it provides a uniform method to investittate the effects of IO phonons on the multi-layer coupling quantum well systems.     

Study on lattice vibrational properties and Raman spectra of Bi_2Te_3 based on density-functional perturbation theory

We present a variational density-functional perturbation theory(DFPT) to investigate the lattice dynamics and vibrational properties of single crystal bismuth telluride material. The phonon dispersion curves and phonon density of states(DOS) of the material were obtained. The phonon dispersions are divided into two fields by a phonon gap. In the lower field,atomic vibrations of both Bi and Te contribute to the DOS. In the higher field, most contributions come from Te atoms. The calculated Born effective charges and dielectric constants reveal a great anisotropy in the crystal. The largest Born effective charge generates a significant dynamic charge transferring along the c axis. By DFPT calculation, the greatest LO–TO splitting takes place in the infrared phonon modes and reaches 1.7 THz in the Brillouin zone center. The Raman spectra and peaks corresponding to respective atomic vibration modes were found to be in good agreement with the experimental data.     

Graphene films grown on sapphire substrates via solid source molecular beam epitaxy

A method for growing graphene on a sapphire substrate by depositing an SiC buffer layer and then annealing at high temperature in solid source molecular beam epitaxy (SSMBE) equipment was presented. The structural and electronic properties of the samples were characterized by reflection high energy diffraction (RHEED), X-ray diffraction Φ scans, Raman spectroscopy, and near edge X-ray absorption fine structure (NEXAFS) spectroscopy. The results of the RHEED and Φ scan, as well as the Raman spectra, showed that an epitaxial hexagonal α-SiC layer was grown on the sapphire substrate. The results of the Raman and NEXAFS spectra revealed that the graphene films with the AB Bernal stacking structure were formed on the sapphire substrate after annealing. The layer number of the graphene was between four and five, and the thickness of the unreacted SiC layer was about 1--1.5 nm.     

Effects of electron–optical phonon interactions on the polaron energy in a wurtzite ZnO/Mg_xZn_(1-x)O quantum well

We investigated the properties of polarons in a wurtzite ZnO/MgxZn1-xO quantum well by adopting a modified Lee–Low–Pines variational method, giving the ground state energy, transition energy, and phonon contributions from various optical-phonon modes to the ground state energy as functions of the well width and Mg composition. In our calculations, we considered the effects of confined optical phonon modes, interface-optical phonon modes, and half-space phonon modes, as well as the anisotropy of the electron effective band mass, phonon frequency, and dielectric constant. Our numerical results indicate that the electron–optical phonon interactions importantly affect the polaronic energies in the ZnO/MgxZn1-xO quantum well. The electron–optical phonon interactions decrease the polaron energies. For quantum wells with narrower wells, the interface optical phonon and half-space phonon modes contribute more to the polaronic energies than the confined phonon modes. However, for wider quantum wells, the total contribution to the polaronic energy mainly comes from the confined modes. The contributions of the various phonon modes to the transition energy change differently with increasing well width. The contribution of the half-space phonons decreases slowly as the QW width increases, whereas the contributions of the confined and interface phonons reach a maximum at d ≈ 5.0 nm and then decrease slowly. However,the total contribution of phonon modes to the transition energy is negative and increases gradually with the QW width of d.As the composition x increases, the total contribution of phonons to the ground state energies increases slowly, but the total contributions of phonons to the transition energies decrease gradually. We analyze the physical reasons for these behaviors in detail.     

Surface optical phonon—assisted electron Raman scattering in a semiconductor quantum disc

We have carried out a theoretical calculation of the differential cross section for the electron Raman scattering process associated with the surface optical phonon modes in a semiconductor quantum disc.electron states are considered to be confined within a quantum disc with infinite potential barriers.The optical phonon modes we have adopted are the slab phonon modes by taking into consideration the Frohlich interaction between an electron and a phonon.The selection rules for the Raman process are given.Numerical results and a discussion are also presented for various radii and thicknesses of the disc,and different incident radiation energies.     

Interaction of a pair coherent state with a three-level Λ-type atom and generation of a modified Bessel-Gaussian state with a vortex structure

The evolution of a system state is derived based on the nonresonant interaction of a three-level "Λ" type atom with two cavity modes at a pair coherent state and two classic fields,and a cavity field state is analyzed in detail under conditional detecting.It is found that the quantized modified Bessel-Gaussian states as well as the superposition states consisting of the quantized vortex states with different weighted coefficients may be prepared through carefully preparing an initial atomic state and appropriately adjusting the interaction time.The scheme provides an additional choice to realize the two-mode quantized vortex state within the context of cavity quantum electrodynamics(QED).     

Study of （Ga,Mn）N prepared by Mn-ion implantation using optical techniques

This paper reports that （Ga, Mn）N is prepared using implantation of 3at.% Mn Ions into undoped GaN. Structural characterization of the crystals was performed using x-ray diffraetion（XRD）. Detailed XRD measurements have revealed the characteristic of Mn-ion implanted GaN with a small contribution of other compounds. With Raman spectroscopy measurements, the spectra corresponding to the intrinsic GaN layers demonstrate three Raman active excitations at 747, 733 and 566 cm-1 identified as EI（LO）, A1 （LO） and E~, respectively. The Mn-doped GaN layers exhibit additional excitations at 182, 288, 650 725, 363, 506cm^-1 and the vicinity of E~ mode. The modes observed at 182, 288, 650 725em 1 are assigned to macroscopic disorder or vacancy-related defects caused by Mn-ion implantation. Other new phonon modes are assigned to Mnx-Ny, Gax-Mny modes and the local vibrational mode of Mn atoms in the （Ga, Mn）N, which are in fair agreement with the standard theoretical results.     

Interaction of pair coherent state with a three-level Λ-type atom and generation of a modified Bessel-Gaussian state with a vortex structure

The evolution of a system state is derived based on the nonresonant interaction of a three-level "Λ" type atom with two cavity modes at a pair coherent state and two classic fields, and a cavity field state is analysed in detail under conditional detecting. It is found that the quantized modified Bessel-Gaussian states as well as the superposition states consisting of the quantized vortex states with different weighted coefficients may be prepared through carefully preparing an initial atomic state and appropriately adjusting the interaction time. The scheme provides an additional choice to realize the two-mode quantized vortex state within the context of cavity quantum electrodynamics (QED).     

Polarons with Spatially Dependent Mass in a Finite Parabolic Quantum Well

We study the energy levels of an electron (or hole) polaron in a parabolic quantum well structure,including the spatial dependence of the effective mass.We also consider the two-mode behaviour of longitudinal optical phonon modes of the ternary mixed crystals in the structure,in the calculation of the effect of the electron phonon interaction.We calculate the ground state,the first excited state and the transition energy of an electron (or hole) in the GaAs/AlxGa1-xAs parabolic quantum well structure.The numerical results show that the electron-phonon interaction obviously affects the energy levels of the electron (or hole),which are in agreement with experimental results.     

Raman scattering study of two-dimensional magnetic van der Waals compound VI_3

The layered magnetic van der Waals materials have generated tremendous interest due to their potential applications and importance in fundamental research. Previous x-ray diffraction(XRD) studies on the magnetic van der Waals compound VI_3, revealed a structural transition above the magnetic transition but output controversial analysis on symmetry. In this paper we carried out polarized Raman scattering measurements on VI_3 from 10 K to 300 K, with focus on the two Ag phonon modes at ～ 71.1 cm~(-1) and 128.4 cm~(-1). Our careful symmetry analysis based on the angle-dependent spectra demonstrates that the crystal symmetry can be well described by C_(2h) rather than D_(3d) both above and below structural phase transition. We further performed temperature-dependent Raman experiments to study the magnetism in VI_3. Fano asymmetry and anomalous linewidth drop of two Ag phonon modes at low temperatures, point to a significant spin–phonon coupling. This is also supported by the softening of 71.1-cm~(-1) mode above the magnetic transition. The study provides the fundamental information on lattice dynamics and clarifies the symmetry in VI_3. And spin–phonon coupling existing in a wide temperature range revealed here may be meaningful in applications.     

Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will convert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.     

Polar Oscillation of Interface and Surface Optical Phonons in Free-Standing Cylindrical Quantum-Well Wires

Under dielectric continuum approximation, interface optical (IO) and surface optical (SO) phonon modes aswell as the corresponding Frohlich electron-phonon interaction Hamiltonian in a free-standing cylindrical quantum-wellwire (Q WW) are derived and studied. Numerical calculations on GaAs/AlxGa1-xAs cylindrical QWW are performed.Results reveal that there are two branches of IO phonon modes and one branch of SO phonon mode, and the dispersionfrequencies ofIO or SO phonon modes sensitively depend on the Al mole fraction x in Alx Ga1-x As material and the wave-vector in z direction, kz. With the increasing of κz and quantum number m, the frequency of each IO mode approaches oneof the two frequency values of the single GaAs/Alx Ga1-xAs heterostructure, and the electrostatic potential distributionof the phonon mode tends to be more and more localized at a certain interface or surface, meanwhile, the couplingbetween the electron-IO and -SO phonons becomes weaker.     

Polar interface and surface optical vibration spectra in multi-layer wurtzite quantum wires： transfer matrix method

The polar interface optical （IO） and surface optical （SO） phonon modes and the corresponding Froehlich electron phonon-interaction Hamiltonian in a freestanding multi-layer wurtzite cylindrical quantum wire （QWR） are derived and studied by employing the transfer matrix method in the dielectric continuum approximation and Loudon＇s uniaxial crystal model. A numerical calculation of a freestanding wurtzite GaN/AlN QWR is performed. The results reveal that for a relatively large azimuthal quantum number m or wave-number kz in the free z-direction, there exist two branches of IO phonon modes localized at the interface, and only one branch of SO mode localized at the surface in the system. The degenerating behaviours of the IO and SO phonon modes in the wurtzite QWR have also been clearly observed for a small kz or m. The limiting frequency properties of the IO and SO modes for large kz and m have been explained reasonably from the mathematical and physical viewpoints. The calculations of electron-phonon coupling functions show that the high-frequency IO phonon branch and SO mode play a more important role in the electron phonon interaction.     

Infrared active phonon modes and ionicity of single crystal MgAl2O4

Near-normal incident infrared reflectivity spectra of （100） MgAl2O4 spinel single crystal have been measured at different temperatures in the frequency region between 50 and 6000 cm^-1. Eight infrared-active phonon modes are identified, which are fitted with the factorized form of the dielectric function. The dielectric property and optical conductivity of the MgAl2O4 crystal are analysed. From TO/LO splitting, the effective Szigeti charges and Born effective charges at different temperatures are calculated for studying the ionicity and the effect of polarization. Based on the relationship between the （LO-TO）1 splitting, which represents the transverse and longitudinal frequencies splitting of the highest energy phonon band in the reflectivity spectrum, and the ionic-covalent parameter, the four main phonon modes are assigned. MgA1204 can be considered as a pure ionic crystal and its optical characters do not change with decreasing temperature, so it may be used as a suitable substrate for high-Tc superconducting thin films.