One of the amazing properties of graphene is the ultrarelativistic behavior of its loosely bound electrons, mimicking massless fermions that move with a constant velocity, inversely proportional to a fine-structure constant ${\alpha }_g$ of the order of unity. The effective interaction between these quasiparticles is, however, better controlled by the coupling parameter ${\alpha }_g^{*}={\alpha }_g/\epsilon$, which accounts for the dynamic screening due to the complex permittivity $\epsilon$ of the many-valence electron system. This concept was introduced in a couple of previous studies [Reed et al., Science 330, 805 (2010) and Gan et al., Phys. Rev. B 93, 195150 (2016)], where inelastic x-ray scattering measurements on crystal graphite were converted into an experimentally derived form of ${\alpha }_g^{*}$ for graphene, over an energy-momentum region on the $\mathrm{eV}\AA {}^{-1}$ scale. Here, an accurate theoretical framework is provided for ${\alpha }_g^{*}$, using time-dependent density-functional theory in the random-phase approximation, with a cutoff in the interaction between excited electrons in graphene, which translates to an effective interlayer interaction in graphite. The predictions of the approach are in excellent agreement with the above-mentioned measurements, suggesting a calibration method to substantially improve the experimental derivation of ${\alpha }_g^{*}$, which tends to a static limiting value of $\sim 0.14$. Thus, the ab initio calibration procedure outlined demonstrates the accuracy of perturbation expansion treatments for the two-dimensional gas of massless Dirac fermions in graphene, in parallel with quantum electrodynamics.

中文翻译：

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时变密度泛函理论校正石墨烯的精细结构常数

石墨烯的令人惊奇的特性之一是其松散结合的电子的超相对论行为，模仿了以恒定速度运动的无质量费米子，该费率与精细结构常数成反比 ${\alpha }_G$统一秩序。但是，这些准粒子之间的有效相互作用可以通过耦合参数更好地控制${\alpha }_G^{*}={\alpha }_G/\epsilon$，由于介电常数复杂，因此可以进行动态筛选 $\epsilon$多价电子系统 这个概念是在先前的一些研究中引入的[Reed等。，Science 330，805（2010）和Gan等。，物理 Rev. B 93，195150（2016） ]，其中将晶体石墨上的非弹性X射线散射测量结果转换为实验衍生的形式${\alpha }_G^{*}$ 石墨烯的能量动量区域 $\mathrm{电子伏特}\mathrm{一个}{}^{-\mathrm{1个}}$规模。在这里，提供了一个准确的理论框架${\alpha }_G^{*}$，在随机相近似中使用时间相关的密度泛函理论，石墨烯中激发电子之间的相互作用截止，这转化为石墨中有效的层间相互作用。该方法的预测与上述测量非常吻合，这表明一种校正方法可以大大改善实验的推导性。${\alpha }_G^{*}$，其趋向于静态极限值 $〜0.14$。因此，概述的从头算起校准过程证明了石墨烯中无质量的狄拉克费米子二维气体的扰动膨胀处理的准确性，以及量子电动力学的并行性。