Electron-phonon interaction effect on optical absorption in cylindrical quantum wires

Electron-phonon interaction effects on linear and nonlinear optical absorption in cylindrical quantum wires are investigated. The linear and nonlinear optical absorption coefficients are obtained by using compact-density-matrix approach and iterative method, and the numerical results are presented for GaAs/AlAs cylindrical quantum-well wires. The results show that electron-phonon interaction not only influences the relaxation rate but also distinctly influences the wave functions and energies of the electron. The correction of electron-phonon interaction effect on the wave functions of the electron dominates the values of absorption coefficients. Moreover, the correction of electron-phonon interaction effect on the energies of the electron makes the absorption peaks blue shift and become wider.     

Cyclotron-resonance line-width due to electron-LO-phonon interaction in cylindrical quantum wires

The absorption power due to the electron-LO-phonon interaction in a cylindrical quantum wire (CQW) in the presence of a magnetic field is calculated. The dependence of absorption power on the photon energy is computationally calculated and graphically plotted for a specific CQW. From graphs of the absorption power, we determine cyclotron-resonance line-width (CRLW) as profiles of the curves. The numerical results show that the CRLW increases with increasing of the temperature and magnetic field, and CRLW decreases with increasing of the wire’s radius. The present results are in qualitative agreement with the existing theoretical and experimental results.     

Electron-phonon interaction in hemispherical quantum dot

Within the framework of the dielectric continuum (DC) model, the optical phonon modes and electron-optical-phonon interaction in hemispherical quantum dot are investigated. The proper eigenfunctions for longitudinal optical (LO) and interface optical (IO) phonon modes are constructed. After having quantized the eigenmodes, we derive the Hamiltonian operators describing the LO and IO phonon modes as well as the corresponding Fröhlich electron-phonon interaction. The dispersion relation of IO phonon modes is size independent. The potential applications of these results are also discussed.     

Electron Raman scattering in cylindrical quantum wires

Electron Raman scattering (ERS) is investigated in a free-standing semiconductor quantum wire of cylindrical geometry for two classes of materials CdS and GaAs. The differential cross section (DCS) involved in this process is calculated as a function of a scattering frequency and the radius of the cylinder. Electron states are considered to be confined within a free-standing quantum wire (FSW). Single parabolic conduction and valence bands are assumed. The selection rules are studied. Singularities in the spectra are found and interpreted for various radii of the cylinder.     

Modeling of Coulomb interaction in parabolic quantum wires

We study the exciton states in a parabolic quantum wire. An exactly solvable model is introduced for calculating the exciton state and the binding energy as a function of the radius of the quantum wire within the envelope-function approximation. In the calculation, we replace the actual Coulomb interaction between the electron and the hole by a Gaussian nonlocal separable potential and obtain closed expressions for both the envelope-function and the binding energy. Results are compared with those obtained by perturbative methods.     

Exciton-phonon interaction in cylindrical semiconductor quantum dots

The exciton-longitudinal optical phonon interaction is theoretically investigated for the case of polar semiconductor cylindrical quantum dots embedded in semiconductor matrix. The theory is developed within the dielectric continuum model considering the Fröhlich interaction between electrons and confined bulk longitudinal optical phonons for a configurational interaction model of quantum dot. Representative longitudinal optical phonon mode for the exciton-phonon interaction is predicted for cylindrical InAs/GaAs quantum dots.     

Electron-phonon interaction in non-polar quantum dots induced by the amorphous polar environment

We propose a Fröhlich-type electron-phonon interaction mechanism for carriers confined in a non-polar quantum dot surrounded by an amorphous polar environment. Carrier transitions under this mechanism are due to their interaction with the oscillating electric field induced by the local vibrations in the surrounding amorphous medium. We estimate the corresponding energy relaxation rate for electrons in Si nanocrystals embedded in a SiO₂ matrix as an example. When the nanocrystal diameter is larger than 4 nm then the gaps between the electron energy levels of size quantization are narrow enough to allow for transitions accompanied by emission of a single local phonon having the energy about 140 meV. In such Si/SiO₂ nanocrystals the relaxation time is in nanosecond range.     

Electron-phonon interaction in LaAg

Magnetoacoustic de Haas-van Alphen data on LaAg are compared with a new relativistic band structure calculation including La-4f states. We find convincing agreement of the measured and calculated dHvA frequencies. The deformation of the Fermi surface under strain is determined from the magnetoacoustic dHvA amplitude. The strongest deformation potential coupling is found for three equivalent pockets which become inequivalent under orthorhombic strain. The lifting of their degeneracy leads to the softening of theT ₃ elastic constant. This is different from the useual band Jahn-Teller effect which is based on the lifting of subband degeneracy at a single point ink-space.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Third-harmonic generation in cylindrical parabolic quantum wires with static magnetic fields

The third-harmonic generation (THG) and its conversion efficiency in Al_xGa_1-xAs/GaAs cylindrical parabolic quantum wires with static magnetic fields are studied in detail. The calculated results show that the parabolic confining potential and the static magnetic field have evident influence on the THG and its conversion efficiency. In addition, the conversion efficiency of the THG is also related to the input optical intensity. It is noted that very high conversion efficiency of the THG can be obtained by increasing properly the input optical intensity and choosing an optimized parabolic confining potential and applied static magnetic field.     

The magnetoexciton binding energy dependency on aluminium concentration in cylindrical quantum wires

A calculation of the binding energy of an exciton confined in cylindrical quantum wires of GaAs surrounded by (Ga, Al) As in the presence of a uniform magnetic field is reported as a function of wire radius, potential height and magnetic field strength, using effective mass approximation and variational approach techniques. For larger magnetic field strength and aluminium (Al) concentration values, the binding energies get larger as expected and are found to be in good agreement with previous theoretical reports. However, we also observed a shift in the binding energy maxima position to smaller wire radii with increasing magnetic field strength and Al concentration.     

Electron-phonon interaction in tetrahedral semiconductors

Considerable progress has been made in recent years in the field of ab initio calculations of electronic band structures of semiconductors and insulators. The one-electron states (and the concomitant two-particle excitations) have been obtained without adjustable parameters, with a high degree of reliability. Also, more recently, the electron-hole excitation frequencies responsible for optical spectra have been calculated. These calculations, however, are performed with the constituent atoms fixed in their crystallographic positions and thus neglect the effects of the lattice vibrations (i.e. electron-phonon interaction) which can be rather large, even larger than the error bars assumed for ab initio calculations.Effects of electron-phonon interactions on the band structure can be experimentally investigated in detail by measuring the temperature dependence of energy gaps or critical points (van Hove singularities) of the optical excitation spectra. These studies have been complemented in recent years by observing the dependence of such spectra on isotopic mass whenever different stable isotopes of a given atom are available at affordable prices. In crystals composed of different atoms, the effect of the vibration of each separate atom can thus be investigated by isotopic substitution. Because of the zero-point vibrations, such effects are present even at zero temperature (T=0).In this paper, we discuss state-of-the-art calculations of the dielectric function spectra and compare them with experimental results, with emphasis on the differences introduced by the electron-phonon interaction. The temperature dependence of various optical parameters will be described by means of one or two (in a few cases three) Einstein oscillators, except at the lowest temperatures where the T⁴ law (contrary to the Varshni T² result) will be shown to apply. Increasing an isotopic mass increases the energy gaps, except in the case of monovalent Cu (e.g. CuCl) and possibly Ag (e.g. AgGaS₂). It will be shown that the gaps of tetrahedral materials containing an element of the first row of the periodic table (C,N,O) are strongly affected by the electron-phonon interaction. It will be conjectured that this effect is related to the superconductivity recently observed in heavily boron-doped carbon.     

Electron-phonon interaction and antiferromagnetic correlations

We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.     

Electron-phonon interaction in impure metals

Making use of the theory for the phonon damping in an impure metal developed recently by Eisenriegler, we study the interaction between electrons and long wave-length longitudinal phonons, and its effects on electronic properties at low temperatures. On account of the inelastic scattering of electrons by impurity ions, a minimum in the electrical resistivity is found when plottedvs temperature, although its value is extremely small.     

Electron-phonon interaction in carbon schwarzites

The recent synthesis of random schwarzites has stimulated the present ab initio calculation of the electronic structure and electron-phonon interaction in two different periodic D-type schwarzites, fcc-(C₂₈)₂ (made of 24 seven-membered rings per unit cell) and fcc-(C₆₄)₂ (made of 12 eight membered and 48 six-membered rings per unit cell). Like in fullerenes, also in schwarzites the electron-phonon interaction potential is found to increase with the absolute Gauss curvature, though it remains smaller than for doped fullerenes. Received 19 December 2002 Published online 1st April 2003 RID="a" ID="a"e-mail: marco.bernasconi@unimib.it