▎ 摘　　要

The recent bottom-up synthesis of atomically precise nanoporous graphene (NPG) offers a way of tuning graphene's properties by forming NPG/graphene (Grp) bilayers. Depending on the size, shape, and periodicity of the nanopores in NPG, the heterobilayers can exhibit various functionalities. This theoretical work presents an inverse design of NPG/Grp bilayers with electric-field-tunable bandgaps as a target property. The interlayer interaction in such heterobilayers can induce a bandgap in graphene either by breaking inversion symmetry (type I) or by moving and merging Dirac points of graphene (type II). The bandgap opening also requires electron-hole symmetry breaking induced by an applied perpendicular electric field, leading to two distinct, linear versus nonlinear, field dependences of the bandgap for the type-I and type-II cases, respectively. To translate the underlying physics of the bandgap opening in graphene into real atomic structures, the authors develop an inverse design method and find NPG/Grp bilayers with the target functionality. The field-tunable bandgap in graphene, supported by first-principles calculations for the inverse-designed systems, holds promise for new types of graphene transistors.