The electronic structure of GaAs, InAs and InSb nanowires is studied using the six-band and the eight-band k·p models. The effect of the different Luttinger-like parameters (in the eight-band model) on the hole band structure is investigated. Although GaAs nanostructures are often treated within a six-band model because of the large bandgap, it is shown that an eight-band model is necessary for a correct description of its hole spectrum. The camel-back structure usually found in the six-band model is not always present in the eight-band model. This camel-back structure depends on the interaction between light and heavy holes, especially the ones with opposite spin. The latter effect is less pronounced in an eight-band model, but could be very sensitive to the Kane inter-band energy (E(P)) value.

The exciton states in strained (In,Ga)As nanorings embedded in a GaAs matrix are computed. The strain distribution is extracted from the continuum mechanical model, and the exact diagonalization approach is employed to compute the exciton states. Weak oscillations of the ground exciton state energy with the magnetic field normal to the ring are an expression of the excitonic Aharonov-Bohm effect. Those oscillations arise from anticrossings between the ground and the second exciton state and can be enhanced by increasing the ring width. Simultaneously, the oscillator strength for exciton recombination exhibits oscillations, which are superposed on a linear increase with magnetic field. The obtained results are contrasted with previous theoretical results for 1D rings, and differences are explained to arise from different confinement potentials for the electron and the hole, and the large diamagnetic shift present in the analyzed type-I rings. Furthermore, our theory agrees qualitatively well with previous photoluminescence measurements on type-II InP/GaAs quantum dots.

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The energy spectrum and eigenstates of single-layer black phosphorous nanoribbons in the presence of perpendicular magnetic field and in-plane transverse electric field are investigated by means of a tight-binding method and the effect of different types of edges is analytically examined. A description based on a new continuous model is proposed by expansion of the tight-binding model in the long-wavelength approximation. The wavefunctions corresponding to the flatband part of the spectrum are obtained analytically and are shown to approach agree well with the numerical results from the tight-binding method. Analytical expressions for the critical magnetic field at which Landau levels are formed and the ranges of wavenumbers in the dispersionless flat-band segments in the energy spectra are derived. We examine the evolution of the Landau levels when an in-plane lateral electric field is applied and determine analytically how the edge states shift with magnetic field.