Moire quasicrystals in graphene encapsulated by hexagonal boron nitride

Interference of double moire patterns of graphene (G) encapsulated by hexagonal boron nitride (BN) can alter the electronic structure features near the primary/secondary Dirac points and the electron-hole symmetry introduced by a single G/BN moire pattern depending on the relative stacking arrangements of the top/bottom BN layers. For equal moire periods and commensurate patterns with Δφ = 60° angle differences, the patterns can add up constructively or cancel out destructively depending on their relative sliding, while moire quasicrystals are expected for Δφ = 30° differences. We present calculations on the double moire interference effects in the density of states and magnetic oscillations in nearly aligned BN/G/BN systems giving rise to moire quasicrystals and their evolution as a function of moire superlattice twist angles.