School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, Shandong, People's Republic of China.
J Phys Condens Matter. 2014 Mar 5;26(9):095002. doi: 10.1088/0953-8984/26/9/095002. Epub 2014 Feb 12.
The interface between graphene and hexagonal boron nitride (h-BN) substrate plays an important role in device applications. Previously, theoretical studies have suggested that a small gap is opened at Dirac cones of graphene, but there is no detectable band gap in experiments. To explain the experimental result, we used two models from the views of lattice match and lattice mismatch between graphene and h-BN by first-principles calculations. We first studied the landscapes of the sliding energy surface (SES) and band gap of graphene on h-BN substrate within a lattice match approximation, which mimics continuously variable stacking sequences in a long-period graphene/BN Moiré superstructure arising from minor lattice mismatch. The plausibility of the long-period Moiré superstructure was evidenced by the smooth SES. The main features of the SES landscape can be captured by means of a simple registry index method. For most stacking patterns, the interactions between graphene and h-BN substrate open a band gap at the Dirac cones of graphene. However, there are special stacking modes in the landscape that preserve the Dirac cones of graphene. To further simulate the long-period graphene/BN Moiré superstructure observed in experiments, we also employed a rotation model within the lattice mismatch approximation. At the equilibrium interlayer spacing, the Dirac cones of graphene are preserved in all the rotational graphene/BN superstructures. The zero-band-gap feature is independent of the translation and rotation of graphene with respect to the h-BN substrate, which clearly agrees with the results of zero band gap in experiments.
石墨烯与六方氮化硼（h-BN）衬底之间的界面在器件应用中起着重要作用。以前的理论研究表明，在石墨烯的狄拉克锥处会打开一个小间隙，但在实验中没有检测到带隙。为了解释实验结果，我们从石墨烯和 h-BN 之间的晶格匹配和晶格失配的角度使用了两种模型，通过第一性原理计算进行了研究。我们首先在晶格匹配近似下研究了石墨烯在 h-BN 衬底上的滑动能量表面（SES）和带隙的形貌，这模拟了由小晶格失配引起的长周期石墨烯/BN 莫尔超结构中连续变化的堆叠序列。SES 的平滑性证明了长周期莫尔超结构的合理性。SES 形貌的主要特征可以通过简单的注册索引方法来捕获。对于大多数堆叠模式，石墨烯和 h-BN 衬底之间的相互作用在石墨烯的狄拉克锥处打开了带隙。然而，在景观中有特殊的堆叠模式，保留了石墨烯的狄拉克锥。为了进一步模拟实验中观察到的长周期石墨烯/BN 莫尔超结构，我们还在晶格失配近似下采用了旋转模型。在平衡层间间距下，所有旋转的石墨烯/BN 超结构都保留了石墨烯的狄拉克锥。零带隙特征与石墨烯相对于 h-BN 衬底的平移和旋转无关，这与实验中零带隙的结果完全一致。
