Momentum space techniques are fundamental to the understanding of electronic structure of materials. The basic formulation of momentum space comes from the Bloch operator for periodic materials. It has been shown momentum space can be formulated for homogenous incommensurate bilayers, and has even begun to be extended to homogenous trilayers, thus extending momentum space beyond the periodic regime. Here we go further by removing the requirement for homogeneity in the layers, extending momentum space to include mechanical relaxation effects in the incommensurate bilayer systems. We also fully formalize the momentum space technique, showing it is composed of a scattering description coming directly from the monolayer Bloch operators. This formalism can be easily extended to other problems with scattering such as phonons and multilayers.
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