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Aichinger M.,Austrian Academy of Sciences | Aichinger M.,MathConsult GmbH | Aichinger M.,University Software Plus GmbH | Hernandez E.R.,CSIC - Institute of Materials Science
Physical Review B - Condensed Matter and Materials Physics | Year: 2013

The problem of two-dimensional, independent electrons subject to a periodic potential and a uniform perpendicular magnetic field unveils surprisingly rich physics, as epitomized by the fractal energy spectrum known as Hofstadter's butterfly. It has hitherto been addressed using various approximations rooted in either the strong potential or the strong field limiting cases. Here, we report calculations of the full spectrum of the single-particle Schrödinger equation without further approximations. Our method is exact, up to numerical precision, for any combination of potential and uniform field strength. We first study a situation that corresponds to the strong potential limit, and compare the exact results to the predictions of a Hofstadter-like model. We then go on to analyze the evolution of the fractal spectrum from a Landau-like nearly free electron system to the Hofstadter tight-binding limit by tuning the amplitude of the modulation potential. © 2013 American Physical Society. Source

Kylanpa I.,Tampere University of Technology | Aichinger M.,University Software Plus GmbH | Aichinger M.,Austrian Academy of Sciences | Janecek S.,University Software Plus GmbH | And 2 more authors.
Journal of Physics Condensed Matter | Year: 2015

We carry out a numerical real-space study on electrons confined in a two-dimensional triangular lattice of repulsive scattering centres. The system represents a qualitative model of molecular graphene, where the electron gas is confined between the scattering molecules in a hexagonal configuration. Our main interest is, on one hand, in the comparability of a finite system (flake) and a fully periodic one, and, on the other hand, in the role of the Coulombic electron-electron interactions and the relative strength of the scattering centres. Our real-space study shows in detail how the density of states of the fully periodic system - containing the Dirac point - is gradually formed as the size of the flake is increased. Good qualitative agreement with the experimental density of states is obtained. Our study confirms the minor role of the electron-electron interactions with selected system parameters, and shows in detail that large scattering amplitudes are required to obtain a distinctive Dirac point in the density of states. © 2015 IOP Publishing Ltd. Source

Aichinger M.,Austrian Academy of Sciences | Aichinger M.,MathConsult GmbH | Aichinger M.,University Software Plus GmbH | Janecek S.,Austrian Academy of Sciences | And 4 more authors.
Physical Review B - Condensed Matter and Materials Physics | Year: 2014

Artificial graphene is a recently realized, man-made nanosystem that exhibits graphene-like physics in a tunable setup. The system can be created by, e.g., positioning molecules in a triangular lattice on a metal surface. Here, we model finite flakes of artificial graphene on a real-space grid and calculate their single-electron properties as a function of the flake size and the strength of an external magnetic field. Our calculations reveal the gradual formation of Dirac cones as well as a self-similar Hofstadter butterfly as the flake size is increased. Moreover, the density of states qualitatively agrees with the experimental data with and without the magnetic field. © 2014 American Physical Society. Source

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