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In this paper a comparative study of the electronic and magnetic properties of quasi-two-dimensional electrons in an artificial graphene-like superlattice composed of circular and elliptical quantum dots is presented. A complete orthonormal set of basis wave functions, which has previously been constructed in the frame of the Coulomb gauge for the vector potential has been implemented for calculation of the energy dispersions, the Hofstadter spectra, the density of states and the orbital magnetization of the considered systems, taking into account both the translational symmetry of the superlattice and the wave function phase-shifts due to the presence of a transverse external magnetic field. Our calculations indicate a topological change in the miniband structure due to the ellipticity of the quantum dots, and non-trivial modifications of the electron energy dispersion surfaces in reciprocal space with the change of the number of magnetic flux quanta through the unit cell of the superlattice. The ellipticity of the QDs leads to an opening of a gap and considerable modifications of the Hofstadter spectrum. The orbital magnetization is shown to reveal significant oscillations with the change of the magnetic flux. The deviation from the circular geometry of quantum dots has a qualitative impact on the dependencies of the magnetization on both the magnetic flux and the temperature.

The miniband Aharonov-Bohm oscillations and the interminiband absorption coefficient have been considered theoretically for one-layer superlattices of square and rectangular symmetries, composed of cylindrical quantum rings in the external transverse magnetic field with a periodic vector potential by the lattice constants. The crossings and anticrossings of the energies corresponding to different values of quasimomentum are observed. It is shown that the energy gap between the minibands and the sequence of the energies in each miniband can be tuned by the magnetic field. The interminiband absorption coefficient qualitatively depends on the symmetry of the superlattice, magnetic field induction and the incident light polarization. The obtained results indicate on the possibility to control the electronic and optical characteristics of the devices based on quantum ring superlattices.

The effect of Rashba spin-orbit interaction and anisotropic strain on the electronic, optical and thermodynamic properties of artificial graphene-like superlattice composed of InAs-GaAs quantum dots has been considered theoretically. The electronic energy dispersions have been obtained using Green's function formalism in combination with Fourier transformation to the reciprocal space and an exact diagonalization technique. We have observed a splitting of Dirac points and appearance of edditional Dirac-like points due to the Rashba spin-orbit interaction. Breaking of the hexagonal symmetry of the dispersion surfaces caused by the strain anisotropy is observed as well. It is shown that both the spin-orbit interaction and strain anisotropy have a qualitative impact on the measurable characteristics of the considered structure and can be used as effective tools to control the performance of devices based on artificial graphene.

The simultaneous effect of intense THz laser and in-plane electric fields on Aharonov-Bohm effect in single isotropic quantum rings is investigated using the non-perturbative Floquet theory in high-frequency limit. It is shown that in isotropic quantum rings the intense THz laser and in-plane electric field create unusual Aharonov-Bohm oscillations. For fixed values of intense THz laser field parameter, the amplitudes of Aharonov-Bohm oscillations can be effectively tuned by changing the electric field direction. Furthermore, for fixed values of electric field strength and laser field parameter the intraband optical properties can be effectively tuned by changing the electric field direction. Thus, it can be argued that a circular QR in the intense THz laser field is equivalent to the anisotropic quantum ring, and the electric field direction effectively tunes the unusual Aharonov-Bohm oscillations and intraband optical properties of the ring.

The problem of an electron-hole system interacting through a contact potential and moving in a one-dimensional quantum ring threaded by an Aharonov-Bohm flux is considered, both with respect to the system's energetics as well as its optical properties. An exact analytical expression for the energy spectrum is derived using a straightforward method based on boundary conditions for wavefunctions and their derivatives along the ring. The optical properties of this exciton system, namely the linear dynamic polarizability and absorption spectrum are investigated demonstrating certain unusual features. It is shown, for example, that for special values of the magnetic flux there are energies in the spectrum that correspond to the dark excitonic states., 12 pages, 4 figures

In the present work the interband optical absorption in the ensemble of spherical quantum layers with weak quantum interaction is investigated. The distribution of layers by their inner radii is taken into account. The effect of weak electric field on the energy levels coupling and absorption character is investigated as well. It is shown that the energy spectrum 1s1p1d2s1f2p... for spherical quantum dot turns to the spectrum 1s1p1d1f2s2p... for spherical quantum layer with enough large value of inner radius. It is also shown that in spherical quantum layer, where the coupling between neighboring states is not negligible, there is no square low dependence of Stark shift on electric field strength in contrast to the rotator model.