Physics of graphene/hexagonal boron nitride heterostructures

电子学的基础是观察到，电子在具有规则、周期性原子排列的材料中传播的能量被量子化并限制在电子能带内。通过这种方式，根据这些带的排列和实验条件，一些材料导电，一些材料绝缘。同时，我们知道磁场可以对运动带电粒子的能量施加另一种量子化限制。非常有趣的物理学预测是，这两种效应以相似的强度竞争，并形成与磁能级相互作用的带，导致一种自我重复的图案，类似于树叶上的自相似图案或雪花形成的图案。不幸的是，由于系统周期性和磁场需要同时满足的条件，这种电子能带结构模式仍然难以捉摸。最近，有研究表明，石墨烯和六方氮化硼这两种原子薄材料制成的三明治中的电子能带结构变成了这样的自相似图案。这是因为，除了每种材料中原子的规则排列外，由于两个原子层之间的复杂覆盖而出现了另一个称为莫尔的周期性，由于这些材料的出色质量，可以进行探测。在这个项目中，我将研究石墨烯/六方氮化硼体系的电子性质，以了解这些结构中周期性和磁场量子化之间的相互作用。我将从理论上探索通过重新排列相互之间的层来操纵后者的结果，并建议使用什么实验工具来最充分地了解所起作用的物理知识。最后，我将模拟在外加磁场中形成的自相似电子能带结构，并探索它所描述的迷人的物理。

At the foundation of electronics lies the observation that energies of electrons travelling in materials with regular, periodic arrangement of atoms are quantized and restricted to electronic bands. This way, depending on the arrangement of those bands and experimental conditions, some materials conduct and some are insulating. At the same time, we know that another quantizing restriction on the energy of a travelling charged particle can be imposed with magnetic field. Very interesting physics has been predicted for the situation in which those two effects compete with similar strength and the formation of bands interplays with that of magnetic levels, leading to a self-repetitive pattern bearing likeness to self-similar patterns on leaves or those formed by snowflakes. Unfortunately, such electronic band structure patterns remained elusive due to the conditions on the periodicity of the system and magnetic field that need to be fulfilled simultaneously. Recently, it has been shown that the electronic band structure in sandwiches made of graphene and hexagonal boron nitride, two atomically thin materials, becomes such a self-similar pattern. This is because, apart from regular arrangement of atoms within each of the materials, another periodicity known as moiré arises due to complicated overlay between the two atomic layers and can be probed thanks to the outstanding quality of those materials. In this project, I will investigate the electronic properties of graphene/hexagonal boron nitride systems in order to understand the interplay between periodicity and magnetic field quantizations in those structures. I will explore theoretically the result of manipulating the latter by rearranging the layers with respect to each other and suggest what experimental tools give the fullest knowledge of the physics at play. Finally, I will model the self-similar electronic band structure formed in external magnetic field and explore the fascinating physics it is describing.