The electronic structures of systems consisting of hexagonal boron nitride layers and graphite sheets have been investigated in detail using density functional theory methods with two exchange correlation functions (local density approximation and generalized gradient approximation). The experimental data of graphene, graphite, monolayer hexagonal BN, and hexagonal BN were reproduced well with computational models. The commensurate models used in the investigation were generated by taking the averages of the lattice constants for graphite and h-BN.

Carbon and boron nitride layers were placed in a unit cell designed to isolate the layer systems from adjacent neighbors along the stacking dimension. Most importantly, a non-zero band gap was successfully predicted with density functional theory (DFT) methods in a bilayer consisting of one graphene sheet and one hexagonal BN sheet. The bilayer system is sensitive to the interlayer distance and to conformational effects, making it a promising structure with an easily tunable band gap. A set of simple equations, based on perturbation theory, has been derived from the bilayer data and was used to predict band gaps at K in graphene of BN/C/BN trilayers in excellent agreement with full band structure computations.

Trilayer structures consisting of graphene and hexagonal BN layers were used to identify the factors responsible for the observed band gap in graphene sheets.