We report on experimental and theoretical studies of 2D van der Waals materials with a very small rotational misalignment, the twisted bilayer graphene (TBG) and twisted hexagonal boron nitride (hBN). The lattice mismatch of the layers in such materials gives rise to a periodic network of dislocations (solitons) with periods as larger as few hundred nanometers. The solitons and their effect on collective modes of the systems are visualized by infrared nano-imaging experiments. In TBG, the solitons are seen to alter propagation of plasmons. We explain this in terms of a strong infrared response of chiral electron states bound to the solitons. In hBN, the solitons are observed to shift and broaden phonon-polariton modes. We interpret this as evidence of local strain effects on the phonon spectra.
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