School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, United States.
Nano Lett. 2012 Jul 11;12(7):3833-8. doi: 10.1021/nl301794t. Epub 2012 Jun 25.
The Hofstadter butterfly spectrum for Landau levels in a two-dimensional periodic lattice is a rare example exhibiting fractal properties in a truly quantum system. However, the observation of this physical phenomenon in a conventional material will require a magnetic field strength several orders of magnitude larger than what can be produced in a modern laboratory. It turns out that for a specific range of rotational angles twisted bilayer graphene serves as a special system with a fractal energy spectrum under laboratory accessible magnetic field strengths. This unique feature arises from an intriguing electronic structure induced by the interlayer coupling. Using a recursive tight-binding method, we systematically map out the spectra of these Landau levels as a function of the rotational angle. Our results give a complete description of LLs in twisted bilayer graphene for both commensurate and incommensurate rotational angles and provide quantitative predictions of magnetic field strengths for observing the fractal spectra in these graphene systems.
二维周期格子中朗道能级的霍夫施塔特蝴蝶谱是在真正的量子体系中表现出分形性质的罕见例子。然而，在常规材料中观察到这一物理现象需要的磁场强度比现代实验室能够产生的磁场强度大几个数量级。事实证明，对于特定范围的扭转角，扭曲双层石墨烯作为一个特殊的系统，在实验室可达到的磁场强度下具有分形能谱。这种独特的性质源于由层间耦合引起的有趣的电子结构。使用递归紧束缚方法，我们系统地描绘了这些朗道能级作为旋转角的函数的谱。我们的结果为扭曲双层石墨烯中的 LL 提供了完全的描述，无论是在相容还是不相容的旋转角下，并对这些石墨烯系统中观察分形谱所需的磁场强度提供了定量预测。
