论文标题
磁化石墨烯双层中的霍夫史塔特蝴蝶：代数方法
Hofstadter butterflies in magnetically modulated graphene bilayer: an algebraic approach
论文作者
论文摘要
已经表明，在均匀磁场中的Bernal堆叠双层石墨烯（BLG）表现出整数量子霍尔效应，其零降级异常\ cite {geimbielayer}。在本文中，我们将这种系统以二维的周期性磁调制，并具有方形对称性。从代数表明，所得的霍夫史塔特光谱可以用相似的磁调制中的单层石墨烯的相应光谱表示。在弱场极限中，使用紧密结合模型，我们还在周期性的磁调制中得出了这种BLG系统的Harper-Hofstadter方程。我们进一步证明了在这种系统中霍尔电导率的拓扑定量，并指出量化的霍尔高原在所有量子数方面都均等，用于定量霍尔电导率。
It has been shown that Bernal stacked bilayer graphene (BLG) in a uniform magnetic field demonstrates integer quantum Hall effect with a zero Landau-level anomaly \cite{Geimbilayer}. In this article we consider such system in a two dimensional periodic magnetic modulation with square lattice symmetry. It is shown algebraically that the resulting Hofstadter spectrum can be expressed in terms of the corresponding spectrum of monolayer graphene in a similar magnetic modulation. In the weak-field limit, using the tight-binding model, we also derive the Harper-Hofstadter equation for such BLG system in a periodic magnetic modulation. We further demonstrate the topological quantisation of Hall conductivity in such system and point out that the quantised Hall plateaus are equally spaced for all quantum numbers for the quantised Hall conductivity.
