Origins of Electronic Localization and Superlattices in Misaligned 2D Heterostructures*

One can create a misaligned bilayer of 2D materials in many ways: from twist, strain, or lattice mismatch between layers. Experimental measurements of these materials (e.g. in bilayers of graphene or transition metal di-chalcogenides) have shown that the electrons' local density of states (LDoS) can be strongly influenced by the interlayer interaction. In some cases, the electronic wavefunction appears localized like an array of quantum dots. In others, a pattern of high-density regions connect like a network of Luttinger liquids.

In this talk, I will present theoretical results on the LDoS in these systems from both ab-initio tight-binding models (in a localized orbital basis) and ab-initio k-dot-p models (in a Bloch-state basis). In studying the duality between these two modeling approaches, we find that the general spatial dependence of the LDoS at a given energy can be inferred from the topology of the individual monolayers' band-structures at that energy.