▎ 摘　　要

Advancement toward opening a bandgap at the Dirac point induced by symmetry breaking paved the way to realize 2D heterostructures with graphene and hexagonal boron nitride (h-BN). An alternate arrangement of graphene and h-BN layers in a 3D stacking can tune the bandgaps of these composites depending on the position of B and N atoms with respect to C atoms of graphene. Herein, a unique possibility of arranging graphene and h-BN atomic layers in a quasiperiodic Fibonacci sequence to study the possibilities of controlling the electronic properties of these heterostructures is explored. Density functional theory calculations combined with van der Waals corrections reveal that these quasiperiodic heterostructures are more stable than normal periodic stacking of monolayers of graphene and h-BN. Moreover, for certain arrangements of atomic layers, sizeable bandgaps can be obtained.