First-principles calculations based on density functional theory are used to explore the electronic-structure modulations in graphene on Ru(0001) by Au intercalation. We first use a lattice-matched model to demonstrate that a substantial band gap is induced in graphene by sufficiently strong A-B sublattice symmetry breaking. This band gap opening occurs even in the absence of hybridization between graphene $\pi$ states and Au states, and a strong sublattice asymmetry is established for a small separation ($d$) between the graphene and Au layer, typically, $d<3.0\AA$, which can actually be achieved for a low Au coverage. In realistic situations, which are mimicked using lattice-mismatched models, graphene $\pi$ states near the Dirac point easily hybridize with nearby (in energy) Au states even for a van der Waals distance, $d\sim 3.4\AA$, and this hybridization usually dictates a band gap opening in graphene. In that case, the top parts of the intact Dirac cones survive the hybridization and are isolated to form midgap states within the hybridization gap, denying that the band gap is induced by sublattice symmetry breaking. This feature of a band gap opening is similar to that found for the so-called “first” graphene layer on silicon carbide (SiC) and the predicted band gap and doping level are in good agreement with the experiments for graphene/Au/Ru(0001).

中文翻译：

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Au插层对Ru（0001）上石墨烯电子结构调制的第一性原理研究

基于密度泛函理论的第一性原理计算被用于探讨Au插层在Ru（0001）上石墨烯中的电子结构调制。我们首先使用晶格匹配模型来证明通过足够强的AB亚晶格对称性破坏在石墨烯中诱导了明显的带隙。即使在石墨烯之间不存在杂化的情况下，也会出现该带隙开口$\pi$ 态和Au态，并且为小间距建立了强烈的亚晶格不对称性（$d$）在石墨烯和Au层之间，通常， $d<3.0\mathrm{一个}$，实际上可以实现低Au覆盖率。在现实情况下（使用晶格不匹配模型进行模拟），石墨烯$\pi$ 狄拉克点附近的碳原子态很容易与附近的（能量）金原子态杂交，即使范德华斯距离也是如此， $d〜3.4\mathrm{一个}$，并且这种杂交通常决定了石墨烯中的带隙开口。在那种情况下，完整的狄拉克锥的顶部在杂交中幸存下来并被隔离，从而在杂交间隙内形成中间能隙状态，从而否认带隙是由亚晶格对称性破坏引起的。带隙开口的这一特征与在碳化硅（SiC）上的所谓“第一”石墨烯层发现的特征相似，并且预测的带隙和掺杂水平与石墨烯/ Au / Ru（ 0001）。