Kagome network of miniband-edge states in double-aligned graphene–hexagonal boron nitride structures

Twistronic heterostructures have recently emerged as a new class of quantum electronic materials with properties determined by the twist angle between the adjacent two-dimensional materials. Here, we study moir\'e superlattice minibands in graphene (G) encapsulated in hexagonal boron nitride (hBN) with an almost perfect alignment with both the top and bottom hBN crystals. We show that, for such an orientation of the unit cells of the hBN layers that locally breaks inversion symmetry of the graphene lattice, the hBN/G/hBN structure features a kagome network of topologically protected states with energies near the miniband edge, propagating along the lines separating the areas with different miniband Chern numbers.