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The confinement effects on the electronic and donor states in GaAs–(Ga, Al)As quantum dots, in the presence of an applied magnetic field, are studied. Using the optical Bloch equations with damping, we study the time evolution of the 1s, 2p−, and 2p+ states in the presence of an applied magnetic field and of a terahertz laser. We discuss the conditions to obtain a bound 2p+ state in contrast to the bulk situation, where the 2p+ state is resonant with the continuum states (in this case, decoherence may be a serious problem for practical realizations). We show that the pronounced confining effects of semiconductor quantum dots lead to conditions such that the 2p+ excited donor state may lie below the continuum, originating a favourable situation concerning the coherence time of the corresponding Rabi oscillations. We also calculate the electric dipole transition moment, discuss the photosignal, and the possible experimental conditions under which decoherence is weak and qubit operations are efficiently controlled.

The variational and fractional-dimensional space approaches are used in a thorough study of the virial theorem value and scaling of the shallow-donor binding energies versus donor Bohr radius in GaAs/(Ga,Al)As semiconductor quantum wells (QWs) and quantum-well wires (QWWs). In the case of the fractional-dimensional space approach, in which the three-dimensional actual anisotropic semiconductor heterostructure is modelled by a fractional-dimensional isotropic effective medium, we have shown that if the ground-state wave function may be approximated by a D-dimensional hydrogenic wave function, the virial theorem value equals 2 and the scaling rule for the donor binding energy versus Bohr radius is hyperbolic, both for GaAs/(Ga,Al)As wells and wires. In contrast, calculations within the variational scheme show that the scaling of the donor binding energies with quantum-sized Bohr radius is in general nonhyperbolic and that the virial theorem value is nonconstant. Moreover, calculations for the donor binding energies versus well widths or wire radii, within both the fractional-dimensional and the variational approaches, indicate that any general conclusion based on a given virial theorem value or donor energy versus Bohr radius scaling rule should be examined with caution.

A theoretical resonant-tunnelling approach is used in a detailed study of the electronic and transmission properties of quasiperiodic Fibonacci GaAs-(Ga,Al)As semiconductor superlattices, under applied electric fields. The theoretical scheme is based upon an exact solution of the corresponding Schroedinger equations in different wells and barriers, through the use of Airy functions, and a transfer-matrix technique. The calculated quasibound resonant energies agree quite well with previous theoretical parameter-based results within a tight-binding scheme, in the particular case of isolated Fibonacci building blocks. Theoretical resonant-tunnelling results for and generations of the quasiperiodic Fibonacci superlattice reveal the occurrence of anticrossings of the resonant levels with applied electric fields, together with the conduction- and valence-level wave function localization properties and electric-field-induced migration to specific regions of the semiconductor quasiperiodic heterostructure. Finally, theoretical resonant-tunnelling calculations for the interband transition energies are shown to be in quite good quantitative agreement with previously reported experimental photocurrent measurements.

The effects of applied magnetic fields on the optical absorption spectra associated with transitions from the Landau valence magnetic levels to shallow donor states in GaAs - (Ga, Al)As quantum wells are studied for magnetic fields applied perpendicular to the heterostructure interfaces. The donor-related magneto-absorption spectra are calculated within the effective-mass approximation, and with a minimization procedure for evaluating donor energies and envelope wave functions. We consider a homogeneous donor distribution in the well and analyse the theoretical impurity-related magneto-absorption spectra for various quantum well widths and applied magnetic fields. The magneto-absorption lineshapes present features clearly associated with transitions involving donor states and different valence Landau magnetic levels.

An extensive theoretical study of the magneto-optical absorption spectra of periodic GaAs - (Ga, Al)As superlattices under magnetic fields parallel to the heterostructure interfaces is presented within the framework of the effective-mass approximation. The absorption coefficient associated with interband transitions between valence-hole and conduction-electron magnetic levels is calculated by considering an expansion of the envelope wavefunctions in terms of sine functions and by adopting a parabolic-band model for both electrons and holes. Results for the theoretical magneto-optical interband absorption spectra for varying in-plane magnetic fields compare qualitatively well with various experimental measurements. We present a detailed analysis of the effects of off-diagonal interband transitions involving conduction and valence Landau levels n and , respectively, with , and it is unambiguously shown that off-diagonal transitions may introduce significant contributions and extra features in the magneto-optical absorption spectra.

A theoretical study of the photonic band structure and transmission spectra for 1D periodic superlattices with an elementary cell composed of two layers of refractive indices n(a) and n(b), which may take on positive as well as negative values, has been performed within the transfer-matrix approach. The dependence on the angle of incidence of the electromagnetic wave for excitation of plasmon-polaritons as well as the properties of the (n) = 0 gap were thoroughly investigated. Results are found for the generalized conditions that must be satisfied by the ratio a/b of the layer widths of metamaterial photonic superlattices, for both transverse electric and transverse magnetic polarizations, in order to have an omnidirectional (n) = 0 gap. The present study indicates new perspectives in the design and development of future optical devices.

The hydrostatic-pressure effects on the electron-effective Lande factor and g-factor anisotropy in semiconductor GaAs–Ga1−xAlxAs quantum wells under magnetic fields are studied. The factor is computed by considering the non-parabolicity and anisotropy of the conduction band through the Ogg–McCombe effective Hamiltonian, and numerical results are displayed as functions of the applied hydrostatic pressure, magnetic fields, and quantum-well widths. Good agreement between theoretical results and experimental measurements in GaAs–(Ga, Al)As quantum wells for the electron g factor and g-factor anisotropy at low values of the applied magnetic field and in the absence of hydrostatic pressure is obtained. Present results open up new possibilities for manipulating the electron-effective g factor in semiconductor heterostructures.

The effects of confinement and magnetic fields on the effective electron Land? g factor of GaAs?Ga1?xAlxAs cylindrical quantum well wires are studied. Calculations were carried out via the Ogg?McCombe effective Hamiltonian which is used to describe the non-parabolicity and anisotropy effects on the electron states in the conduction band. The applied magnetic field is taken along the wire axis, and the Schr?dinger equation corresponding to electron spin projections parallel and antiparallel to the magnetic field is solved by using an expansion of the electron wavefunctions in terms of two-dimensional harmonic oscillator wavefunctions. Calculations for the electron factor in GaAs?Ga1?xAlxAs cylindrical quantum well wires are compared with results from previous theoretical work. Moreover, the present results clearly indicate the importance of taking into account the non-parabolicity/anisotropy of the conduction band if one is interested in a quantitative understanding of the electron g factor in GaAs?Ga1?xAlxAs quantum well wires.

The effects of hydrostatic pressure and growth-direction applied magnetic fields on the exciton dispersion and in-plane effective mass in coupled GaAs–(Ga, Al)As quantum wells are investigated. Calculations for spatially direct and indirect excitons were performed within the variational procedure in the effective-mass and nondegenerate parabolic band approximations and by taking into account the coupling between the exciton centre-of-mass momentum and its internal structure. The pressure coefficient is also obtained as a function of both the hydrostatic pressure and growth-direction applied magnetic field.

A theoretical study of the growth-direction magnetic-field effects on the exciton photoluminescence peak energies in GaAs–Ga1−xAlxAs quantum-dot/ultrathin quantum-well systems is presented. Calculations are performed within the effective-mass approximation and taking into account nonparabolicity effects for both the conduction-band and valence-band effective masses. We use a simple 'QD+ultrathin QW' model heterostructure to mimic the actual physical system, and calculated results for the exciton diamagnetic shifts are found in overall agreement with recent experimental measurements.