From moiré superlattices to twistronic solids

自2004年石墨烯分离以来，许多其他层状材料已经在二维（2D）晶体的单层极限中实现。这些原子级薄的材料几乎涵盖了从绝缘体到金属，从磁铁到超导体的所有性质。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相互叠加，形成一个原子尖锐的界面，而不受晶格常数匹配或晶体学方向相互取向的常规约束。对于相邻材料的二维基元矢量之间的一般角度，相关晶格周期的变化导致形成准周期莫尔<s:1>超晶格，这为界面上的布拉格散射提供了新的来源。在二维晶体堆叠中，莫尔流可以显著影响堆叠的性质，近年来导致了一些新现象的发现，如在六方氮化硼上观察到石墨烯中的霍夫施塔特蝴蝶，以及在魔角扭曲双层石墨烯中出现相关电子相。在这个项目中，我的目标是回答如何在范德华固体中使用摩尔超晶格物理的问题：具有嵌入扭曲界面的块状材料。这项工作是具有挑战性的，需要新的理论工具，因为固体物理学的基石，布洛赫定理，不能应用于(i)层之间的一般扭曲，莫尔条纹与平面内晶格不相称，（ii）半晶体之间的界面局部破坏了原子平面垂直方向的平移周期性。我将从理论上寻找在真正的三维结构中莫尔海姆诱发的效应存在的必要条件，并探索与彼此靠近的扭曲界面相关的现象。在这样做的过程中，我的目标是建立一条路线，以保存和利用3D设备中2D材料的丰富物理特性。

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.