▎ 摘　　要

Using the van der Waals density functional theory method (DFT-D2), we have investigated thickness dependent energy band gaps and effective masses of multilayer BN/graphene/BN structures by changing the stacking order. The band gap is substantially dependent on the stacking order. For instance, the calculated band gap in ABA stacking is about 150 meV, whereas it becomes 31 meV in ABC stacking. No significant thickness dependent band gap is observed in both ABA and ABC stackings although the band gap is gradually increasing with the BN thickness in ABA stacking. In addition, the effective mass is found to be strongly dependent on the stacking order. The effective mass in ABA stacking is much larger than that found in ABC stacking. On the other hand, the effective mass along K-M direction is smaller than that along K-Gamma direction in ABA stacking. However, it is independent on the band direction in ABC stacking. We have found that the inclusion of van der Waals interaction alters thickness dependent band gap and effective mass of BN/graphene/BN multilayer systems compared with those found with standard density functional theory. (C) 2014 AIP Publishing LLC.