The effects of an in-plane electric field and eccentricity on the electronic spectrum of a GaAs quantum ring in a perpendicular magnetic field are studied. The effective-mass equation is solved by two different methods: an adiabatic approximation and a diagonalization procedure after a conformal mapping. It is shown that the electric field and the eccentricity may suppress the Aharonov-Bohm oscillations of the lower energy levels. Simple expressions for the threshold energy and the number of flat energy bands are found. In the case of a thin and eccentric ring, the intensity of a critical field which compensates the main effects of eccentricity is determined. The energy spectra are found in qualitative agreement with previous experimental and theoretical works on anisotropic rings.

A systematic study of shallow-donor and excitonic states in semiconducting quantum wells within a fractional-dimensional space approach is presented. In this scheme, the Schrödinger equation is solved in a noninteger-dimensional space in which the interactions are assumed to occur in an isotropic effective environment, and the fundamental quantity is the parameter D, which defines the fractional dimension associated with the effective medium and the degree of anisotropy of the interactions. The fractional dimensionality of the isotropic effective space is derived via an unambiguous procedure in which one may obtain the exact solution for the energies of the actual physical system under consideration. Explicit calculations of the fractional-dimensional parameter are made in the case of shallow donors and excitons in finite-barrier GaAs - (Ga, Al)As quantum wells, with impurity and exciton binding energies found in good agreement with previous variational results and available experimental data.

The electronic states of quantum rings with centerlines of arbitrary shape and non-uniform width in a threading magnetic field are calculated. The solutions of the Schrödinger equation with Dirichlet boundary conditions are obtained by a variational separation of variables in curvilinear coordinates. We obtain a width profile that compensates for the main effects of the curvature variations in the centerline. Numerical results are shown for circular, elliptical, and limaçon-shaped quantum rings. We also show that smooth and tiny variations in the width may strongly affect the Aharonov-Bohm oscillations.

The polarization effects of in-plane electric fields and eccentricity on electronic and optical properties of semiconductor quantum rings (QRs) are discussed within the effective-mass approximation. As eccentric rings may appropriately describe real (grown or fabricated) QRs, their energy spectrum is studied. The interplay between applied electric fields and eccentricity is analysed, and their polarization effects are found to compensate for appropriate values of eccentricity and field intensity. The importance of applied fields in tailoring the properties of different nanoscale materials and structures is stressed.

Bloch and Wannier functions of the Kohn type for a quite general one-dimensional Hamiltonian with inversion symmetry are studied. Important clarifications on null minigaps and the symmetry of those functions are given, with emphasis on the Kronig–Penney model. The lack of a general selection rule on the miniband index for optical transitions between edge states in semiconductor superlattices is discussed. A direct method for the calculation of Wannier–Kohn functions is presented.