Electronic structure of twisted graphene nanoflakes and nanoribbons

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Doctoral Thesis
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Landgraf, Wolfgang

A mutual rotation of two layers of graphene introduces a geometric superstructure, a so-called moiré pattern, which may be visualized as a periodic array of patches of different stacking orders. The electronic properties of the resulting system, a twist bilayer, are very rich. This physics of the ideal twist bilayer includes both a large angle decoupling limit, in which the bilayer system behaves as two single graphene layers, as well as a small angle strongly coupled limit characterized by a zero mode structure in the density of states and localization of electrons on specific regions of the moiré. The question we address in this work is how the physics of the ideal twist bilayer is changed by (i) finite size effects and (ii) an out-of-plane magnetic field. We show that in the small angle regime the magnetic field induces persistent currents in the bulk of the twist bilayer. These currents can be visualized as “convection cells” centered on the AA patches of the moiré where the current distribution has a component parallel to the magnetic field. Such persistent currents occur for magnetic fields for which the magnetic length is greater than the moiré length, and for which the Landau spectrum resembles closely that of the single graphene layer. We furthermore investigate how the electron localization and the density of states of the ideal twist system are modified by finite size effects in twist nanoribbons and twist flakes. Calculations of the density of states and of the real space distribution of the electron density at low energies (E < 0.5eV) reveal that, at these energies, the twist bilayer behaves essentially as a lattice of independent moiré quantum wells.

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