From moiré superlattices to twistronic solids

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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.