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Artificially constructed van der Waals heterostructures (vdWHs) provide anideal platform for realizing emerging quantum phenomena in condensed matterphysics. Two methods for building vdWHs have been developed: stackingtwo-dimensional (2D) materials into a bilayer structure with different latticeconstants, or with different orientations. The interlayer coupling stemmingfrom commensurate or incommensurate superlattice pattern plays an importantrole in vdWHs for modulating the band structures and generating new electronicstates. In this article, we review a series of novel quantum states discoveredin two model vdWH systems -- graphene/hexagonal boron nitride (hBN)hetero-bilayer and twisted bilayer graphene (tBLG), and discuss how theelectronic structures are modified by such stacking and twisting. We alsoprovide perspectives for future studies on hetero-bilayer materials, from whichan expansion of 2D material phase library is expected.

Progress on band structure engineering of twisted bilayer and two-dimensional moir\'e heterostructures