Hofstadter butterfly of graphene with point defects
Hofstadter butterfly of graphene with point defects
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具有点缺陷的石墨烯霍夫施塔特蝴蝶
DOI：
10.1103/physrevb.85.235414
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发表时间：
2012
影响因子：
3.7
通讯作者：
O. Gülseren
中科院分区：
文献类型：
--
作者：
S. Aslamoğlu;M. Oktel;O. Gülseren
我们研究了垂直磁场下具有点缺陷的霍夫施塔特蝴蝶石墨烯的结构。我们使用紧束缚方法，交互作用达到第二近邻。首先，我们展示了纯石墨烯的霍夫施塔特蝴蝶谱，包括具有二阶跳跃的所有四个价轨道。为了模拟缺陷，我们在由七个碳原子和一个缺陷原子组成的放大晶胞内进行计算。我们发现具有较小跳跃常数的杂质原子会导致高度局域化的状态，这些状态与系统的其余部分解耦。与这些状态相关的能带形成一条几乎 E = 0 eV 的线。另一方面，具有较高跳跃常数的杂质原子与邻近原子强耦合。这些状态通过形成与原始蝶形解耦的两个自相似带，围绕能量的最小值和最大值修改霍夫施塔特蝶形。我们还表明，由于杂质态而产生的能带和能隙对于二阶跳变是稳健的。
We investigate the structure of Hofstadter’s butterfly of graphene with point defects under a perpendicular magnetic field. We use a tight-binding method with interactions up to second-nearest neighbors. First of all, we present the Hofstadter butterfly spectrum of pure graphene, including all four valence orbitals with second-order hopping. To model defects, we perform calculations within an enlarged unit cell of seven carbon atoms and one defect atom. We find that impurity atoms with smaller hopping constants result in highly localized states which are decoupled from the rest of the system. The bands associated with these states form a nearly E = 0 eV line. On the other hand, impurity atoms with higher hopping constants are strongly coupled with the neighboring atoms. These states modify the Hofstadter butterfly around the minimum and maximum values of the energy by forming two self-similar bands decoupled from the original butterfly. We also show that the bands and gaps due to the impurity states are robust with respect to the second-order hopping.