Isolated and hybrid bilayer graphene rings

Abstract

Using the continuum model, we investigate the electronic properties of two types of bilayer graphene (BLG) quantum ring (QR) geometries: (i) an isolated BLG QR and (ii) a monolayer graphene (MLG) with a QR put on top of an infinite graphene sheet (hybrid BLG QR). Solving the Dirac-Weyl equation in the presence of a perpendicular magnetic field and applying the infinite-mass boundary condition at the ring boundaries, we obtain analytical results for the energy levels and corresponding wave spinors for both structures. In the case of isolated BLG QR, we observe a sizeable and magnetically tunable band gap which agrees with the tight-binding transport simulations. Our analytical results also show the intervalley symmetry $E_e^K(m)=-E_h^{K^{\prime }}(m)$ between the electron (e) and hole (h) states ($m$ being the angular momentum quantum number) for the energy spectrum of the isolated BLG QR. The presence of interface boundary in a hybrid BLG QR modifies drastically the energy levels as compared to that of an isolated BLG QR. Its energy levels are tunable from MLG dot, to isolated BLG QR, and to MLG Landau energy levels as magnetic field is varied. Our predictions can be verified experimentally using different techniques such as by magnetotransport measurements.

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