C. Trallero-Giner

Polar optical oscillations in quantum wires and free-standing wires: the electron-phonon interaction Hamiltonian

By applying a phenomenological theory for long-wavelength polar optical oscillations to mesoscopic layered semiconductor structures, we calculate the normal modes of a quantum wire and of a free-standing wire, the cylindrical geometry is adopted with circular cross-section of radius r0. The displacement field u and the electric potential phi are calculated for the different modes, as well as the dispersion relation curves. The case of the GaAs/AlAs structure is analysed. We limit ourselves to the study of oscillations perpendicular to the wire axis. The electron-phonon interaction Hamiltonian is derived for the present problem using the second-quantization formalism.

Interface optical phonons in spheroidal quantum dots

Interface optical phonons are studied in the case of a quantum dot (QD) with prolate and oblate spheroidal geometries within the dielectric continuum approach. We considered CdSe or CdS QDs imbedded in a host material which is modelled as an infinite medium. The surface optical phonon modes, the corresponding frequencies, and the electron-phonon interaction Hamiltonian are reported. Comparison is made with previous works which only considered strictly spherical dots. We conclude that deviations from the perfect spherical shape could be responsible for observable physical effects in Raman spectra.

Electron Raman scattering in cylindrical quantum wires

The differential cross-section (DCS) for an electron Raman scattering (ERS) process in a semiconductor quantum wire (QW) of cylindrical geometry is calculated for T=0 K and neglecting phonon-assisted transitions. Electron states are considered assuming complete confinement within the QW. We also assume single parabolic conduction and valence bands. Two kinds of spectrum are discussed: emission spectra DCS as a function of emitted photon energy) and excitation spectra (DCS as a function of incident photon energy). In both cases we analyse the DCS for different scattering configurations. We study selection rules for the processes. Singularities in the spectra are found and interpreted. The ERS studied here can be used to provide direct information about the electron band structure of the system.

Polar optical oscillations of layered semiconductor structures in the long-wavelength limit

Polar optical oscillations coupled to unretarted electric fields are discussed for the long-wavelength limit with application to layered semiconductor structures (quantum wells, superlattice, etc.). A Lagrangian formalism is adopted for the deduction of the equations of both mechanical and electrical quantities. The obtained equations bear the form of second-order coupled differential equations for the fundamental quantities, displacement field u and electric potential г. Matching boundry conditions are rigorously derived from the equations and interpreted physically. The particular case of materials belonging to the cubic symmetry is discussed with special application to the double heterostructure. Some comments are also made about the case of isotropic constituent materials. We have thus settled a theory for long- wavelength oscillations taking into account dispersion up to quadratic terms in the wave vector (through the introduction of medium internal stresses) with the aim of avoiding some problems which have been detected and discussed in earlier treatments of this subject.

Energy levels of a quantum ring in a lateral electric field

Abstract The electronic states of a semiconductor quantum ring (QR) under an applied lateral electric field are theoretically investigated and compared with those of a quantum disk of the same size. The eigenstates and eigenvalues of the Hamiltonian are obtained from a direct matrix diagonalization scheme. Numerical calculations are performed for a hard-wall confinement potential and the electronic states are obtained as a function of the electric field and the ratio r2/r1, where r2 (r1) is the outer (inner) radius of the ring. The effects of decreasing symmetry and mixing on the energy levels and wave functions due to the applied electric field are also studied. The direct optical absorption are reported as a function of the electric field.

Optical transition in self-assembled InAs/GaAs quantum lens under high hydrostatic pressure

We present a simulation to characterize the dependence on hydrostatic pressure for the photoluminescence spectra in self-assembled quantum dots with lens shape geometry. We have tested the physical effects of the band offset and electron-hole effective masses on the optical emission in dot lens. The model could be implemented to get qualitative information of the parameters involved in the quantum dot or the measured optical properties as function of pressure.

Formal analytical solutions for the Gross–Pitaevskii equation

Abstract Considering the Gross–Pitaevskii integral equation we are able to formally obtain an analytical solution for the order parameter Φ ( x ) and for the chemical potential μ as a function of a unique dimensionless non-linear parameter Λ . We report solutions for different ranges of values for the repulsive and the attractive non-linear interactions in the condensate. Also, we study a bright soliton-like variational solution for the order parameter for positive and negative values of Λ . Introducing an accumulated error function we have performed a quantitative analysis with respect to other well-established methods as: the perturbation theory, the Thomas–Fermi approximation, and the numerical solution. This study gives a very useful result establishing the universal range of the Λ -values where each solution can be easily implemented. In particular, we showed that for Λ − 9 , the bright soliton function reproduces the exact solution of GPE wave function.

Feynman diagrams and Fano interference in light scattering from doped semiconductors

We present a diagrammatic approach to the calculation of quantum interference contributions to the Raman light scattering efficiency of doped semiconductors. A three-band model within a parabolic approximation is used to account for the electronic and optical phonon Raman scatterings under the condition of resonance coupling of an optical phonon with an inter-valence-band electronic continuum. Diagram techniques allow us to compare the roles of various processes contributing to an asymmetrical scattering profile.

Exciton polaritons in two-dimensional dichalcogenide layers placed in a planar microcavity: Tunable interaction between two Bose-Einstein condensates

CNPq (Brazil), FCT (Portugal), EC Graphene Flagship Project (Contract No. CNECTICT- 604391)

Excited states in the infinite quantum lens potential: conformal mapping and moment quantization methods

The conformal mapping method (CMM) and the eigenvalue moment method (EMM) are employed to study the eigenvalue problem defined by a free particle in a quantum lens geometry. The characteristics of the spectrum and the corresponding spatial properties of wavefunctions are studied for varying symmetry quantization numbers and lens parameter values. It is shown that the states belong to two independent Hilbert subspaces corresponding to even and odd azimuthal, m, quantum numbers. The CMM analysis is used to reduce the Dirichlet problem for the Helmholtzs equation into a 2D problem defined by a region with semicircular geometry. This approach allows one to obtain explicit analytical solutions in terms of the lens geometry. In the case of small geometry deformations (relative to the semicircular case), the solutions can be found by a perturbative method. The exact and approximate solutions are compared for different values of the lens parameters. We compare these results with those derived through the EMM approach, which, although more computationally expensive, can yield converging lower and upper bounds. The particular formulation developed here differs significantly from an earlier application of EMM to the ground state case (within each symmetry class). Accordingly, we develop the new formulation and apply it to a limited number of states in order to confirm the results derived by the other, aforementioned, methods.