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arXiv 1002.1688cond-mat.mes-hall
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单层和双层石墨烯量子环能级的简化模型

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

M. Zarenia, J. Milton Pereira, A. Chaves, F. M. Peeters, G. A. Farias

摘要:

在一个极小模型中,我们给出了单层和双层石墨烯中量子环中载流子本征态和本征值的解析表达式。计算是在连续介质模型的背景下进行的,通过求解零宽度环几何形状的狄拉克方程,即通过冻结载流子径向运动。我们包括外部磁场的影响,并显示Aharonov-Bohm振荡的外观和非零间隙的频谱。我们的极小模型给出了基于石墨烯的量子环的能谱的见解,并对有限宽度环的不同方面进行了建模。

英文摘要:

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 non-zero gap in the spectrum. Our minimal model gives insight in the energy spectrum of graphene-based quantum rings and models different aspects of finite width rings.

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