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Simplified model for the energy levels of quantum rings in single layer and bilayer graphene

机译:单层和双层石墨烯中量子环能级的简化模型

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摘要

Within a minimal model, we present analytical expressions for the eigenstates and eigenvalues of carriers confined in quantum rings in monolayer and bilayer graphene. The calculations were performed in the context of the continuum model by solving the Dirac equation for a zero width ring geometry, i.e., by freezing out the carrier radial motion. We include the effect of an external magnetic field and show the appearance of Aharonov-Bohm oscillations and of a nonzero gap in the spectrum. Our minimal model gives insight on the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings.
机译:在一个最小的模型中,我们给出了限制在单层和双层石墨烯的量子环中的载流子的本征态和本征值的解析表达式。在连续体模型的上下文中,通过求解零宽度环几何的狄拉克方程,即冻结载体径向运动,来进行计算。我们包括外部磁场的影响,并显示Aharonov-Bohm振荡的出现以及频谱中的非零间隙。我们的最小模型可以洞悉基于石墨烯的量子环的能谱,并可以对有限宽度环的不同方面进行建模。

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