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In this paper a comparative study of the electronic and magnetic propertiesof quasi-two-dimensional electrons in an artificial graphene-like superlatticecomposed of circular and elliptical quantum dots is presented. A completeorthonormal set of basis wave functions, which has previously been constructedin the frame of the Coulomb gauge for the vector potential has been implementedfor calculation of the energy dispersions, the Hofstadter spectra, the densityof states and the orbital magnetization of the considered systems, taking intoaccount both the translational symmetry of the superlattice and the wavefunction phase-shifts due to the presence of a transverse external magneticfield. Our calculations indicate a topological change in the miniband structuredue to the ellipticity of the quantum dots, and non-trivial modifications ofthe electron energy dispersion surfaces in reciprocal space with the change ofthe 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 considerablemodifications of the Hofstadter spectrum. The orbital magnetization is shown toreveal significant oscillations with the change of the magnetic flux. Thedeviation from the circular geometry of quantum dots has a qualitative impacton the dependencies of the magnetization on both the magnetic flux and thetemperature.

Hofstadter-like spectrum and Magnetization of Artificial Graphene constructed with cylindrical and elliptical quantum dots