One can create a misaligned bilayer of 2D materials in many ways: from twist, strain, or lattice mismatch between layers. Recent experiments have shown that the careful construction of a misaligned bilayer can cause correlated electronic phases (Mott insulator, superconductor).

In this talk, I will present theoretical results on the density of states in this class of systems from both ab-initio tight-binding models (in a localized orbital basis) and 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 individual monolayer band-structure and the effective interlayer coupling strength.