We theoretically study the band structure and optical conductivity of twisted bilayer graphene (TBG) near the magic angle considering the effects of lattice relaxation. We show that the optical conductivity spectrum is characterized by a series of peaks associated with the van Hove singularities in the band structure, and the peak energies evolve systematically with the twist angle. Lattice relaxation effects in TBG modify its band structure, especially the flat bands, which leads to significant shifts of the peaks in the optical conductivity. These results demonstrate that spectroscopic features in the optical conductivity can serve as fingerprints for exploring the band structure, band gap, and lattice relaxation in magic-angle TBG as well as identifying its rotation angle.

We calculate the electronic band structures and topological properties of twisted homobilayer transition metal dichalcogenides(t-TMDs), in particular, bilayer MoTe2 and WSe2 based on a low-energy effective continuum model. We systematically show how the twist angle, vertical electric field and pressure modify the band structures of t-TMDs, often accompanied by topological transitions.We find the variation of topological transitions mainly take place in a limited range of parameters. The electric field can efficiently tune the energy of the topmost second valence band to motify the Chern numbers of the topmost three valance bands. The topological property of the topmost first valance band can be modified by electric field and pressure, but doesn’t depend on twist angle. We show the band gap between the topmost second and third valance bands that both change from non-trivial to trivial closes at κ − -point of the moiré Brillouin zone.

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We theoretically study the interference and propagation of phonon polaritons in hexagonal boron nitride (hBN) in van der Waals heterostructures composed of hBN and twisted bilayer graphene (TBG) with different interlayer spacing in TBG. We show that varying the interlayer spacing and, hence, the interlayer coupling strength results in dramatic modifications of the local optical conductivity at the domain walls (DWs) in TBG, which leads to significant changes in the polariton interference profile near DWs. Moreover, our simulation reveals that the two-dimensional near-field interference pattern generated by polariton propagation in hBN/TBG heterostructures can be dramatically changed by interlayer spacing and the superlattice period. Our study demonstrates that combining interlayer spacing modification with moiré superlattices is a valuable route to control light at the nanoscale and design nanophotonic devices with tunable functionalities.