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.
 S.S. Sunku, G.X. Ni, B.Y. Jiang, H. Yoo, A. Sternbach, A.S. McLeod, T. Stauber, L. Xiong, T. Taniguchi, K. Watanabe, P. Kim, M.M. Fogler, D.N. Basov, Photonic crystals for nano-light in moiré graphene superlattices,
Science 362, 1153-1156 (2018).
 G. X. Ni, H. Wang, B.-Y. Jiang, L. X. Chen, Y. Du, Z. Y. Sun, M. D. Goldflam, A. J. Frenzel, X. M. Xie, M. M. Fogler, D. N. Basov, Soliton superlattices in twisted hexagonal boron nitride, Nat. Commun. 10, 4360 (2019).