Confined states in quantum dots defined within finite flakes of bilayer graphene: Coupling to the edge, ionization threshold, and valley degeneracy

Abstract

We study quantum dots defined by external potentials within finite flakes of bilayer graphene using the tight-binding approach. We find that in the limit of large flakes containing zigzag edges the dot-localized energy levels appear within the energy continuum formed by extended states. As a consequence no ionization threshold for the carriers contained within the dot exists. For smaller flakes with zigzag boundaries the dot-localized energy levels appear interlaced with the energy levels outside the flake, so in a charging experiment the electrons will be added alternately to the dot area and to its neighborhood. We demonstrate that for flakes with armchair boundaries only, an energy window accessible uniquely to the dot-localized states is opened. Then a number of electrons can be added to the dot before the external states start to be occupied. We also discuss coupling of the dot-localized states to the edge states in the context of the valley degeneracy lifting. Moreover, we extract smooth envelope wave functions from the tight-binding solution and discuss their spatial symmetries. The coupling of the dot localized energy levels with reconstructed zigzag edges and atomic vacancies present within the layers is also considered.

9 pages,13 figures

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• Spin and valley manipulation in single and double electrostatic silicene quantum dots
• Confined states in graphene quantum blisters
• Persistent currents in topological and trivial confinement in silicene
• Spin-valley qubits in gated quantum dots in a single layer of transition metal dichalcogenides
• Tunneling Effect in Gapped Graphene Disk in Magnetic Flux and Electrostatic Potential