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Multilayered van der Waals structures often lack periodicity, whichdifficults their modeling. Building on previous work for bilayers, we develop atight-binding based, momentum space formalism capable of describingincommensurate multilayered van der Waals structures for arbitrary latticemismatch and/or misalignment between different layers. We demonstrate how thedeveloped formalism can be used to model angle-resolved photoemissionspectroscopy measurements, and scanning tunnelling spectroscopy which can probethe local and total density of states. The general method is then applied toincommensurate twisted trilayer graphene structures. It is found that thecoupling between the three layers can significantly affect the low energyspectral properties, which cannot be simply attributed to the pairwisehybridization between the layers.

Electronic spectral properties of incommensurate twisted trilayer graphene