From moiré superlattices to twistronic solids

自从2004年石墨烯被分离以来，许多其他层状材料已经在二维(2D)晶体的单层限制下实现。这些原子薄的材料几乎涵盖了从绝缘体到金属、磁体到超导体的所有性质类别。此外，由于层间的相互作用本质上是范德华作用，不涉及直接的化学键，任何两个层状晶体都可以放在彼此的顶部，形成原子锐利的界面，而不受晶格常数匹配或晶体方向相互取向的限制。对于相邻材料的二维原始矢量之间的一般夹角，相关晶格周期的拍打导致了准周期莫尔超晶格的形成，这为界面处的布拉格散射提供了一个新的来源。在堆叠的2D晶体中，莫尔可以显著影响堆叠的性能，近年来导致了新现象的发现，例如在六方氮化硼上观察到石墨烯中的霍夫斯塔特蝴蝶，以及在魔角扭曲的双层石墨层中出现相关的电子相。在这个项目中，我将致力于回答如何将莫尔超晶格物理用于范德华固体：具有嵌入扭曲界面的块状材料。这项工作具有挑战性，需要新的理论工具，因为固体物理的基石，布洛赫定理，不能应用于：(I)对于层之间的一般扭曲，云纹与面内晶格不相称，(Ii)半晶体之间的界面局部扰乱垂直于原子平面方向的平移周期。我将从理论上寻找在真正的三维结构中莫尔诱导效应得以存在的必要条件，并探索与彼此紧密相连的扭曲界面相关的现象。通过这样做，我的目标是建立一条途径，在3D设备中保护和利用2D材料的丰富物理学。

Since the isolation of graphene in 2004, many other layered materials have been realised in the single-layer limit of two-dimensional (2D) crystals. These atomically thin materials span virtually all classes of properties, from insulators to metals, magnets to superconductors. Moreover, because the interaction between the layers is van der Waals in nature and does not involve direct chemical bonds, any two layered crystals can be put on top of one another to form an atomically sharp interface without the normal constraints of lattice constant matching or mutual orientation of crystallographic directions. For a general angle between the 2D primitive vectors of neighbouring materials, beating of the associated lattice periodicities leads to the formation of a quasi-periodic moiré superlattice which provides a new source of Bragg scattering at the interface. In stacks of 2D crystals, moiré can significantly affect the properties of the stack and has in recent years led to the discovery of novel phenomena like the observation of Hofstadter's butterfly in graphene on hexagonal boron nitride and the appearance of correlated electronic phases in magic-angle twisted bilayer graphene.In this project, I will aim to answer the question of how moiré superlattice physics can be utilised in van der Waals solids: bulk materials with embedded twisted interfaces. This work is challenging and requires novel theoretical tools because the cornerstone of solid state physics, Bloch's theorem, cannot be applied as (i) for a general twist between layers the moiré is incommensurate with the in-plane lattices, (ii) an interface between half crystals locally disrupts translational periodicity in the direction normal to the atomic planes. I will search theoretically for the conditions necessary for the survival of the moiré-induced effects in truly three-dimensional structures and explore phenomena associated with twisted interfaces in close proximity to each other. In doing so, I aim to establish a route to preserve and exploit the rich physics of 2D materials in 3D devices.