石墨烯中共振态的反常离域&空位磁矩
Anomalous delocalization of resonant states in graphene \& the vacancy magnetic moment
摘要：
石墨烯中的碳原子空位引起$σ+π$起源的局部磁矩，其大小尚不确定且有争议。在周期性的$first-principles$计算中，普遍报告了$π$磁性的部分淬灭，磁矩分散在1.0 - 2.0 $μ_{B}$的范围内，缓慢地收敛到下限或上限，这取决于如何接近稀释极限。相比之下，（系综）密度泛函理论计算集群模型整齐地收敛到$2$ $μ_{B}$的值时，增加系统的大小。这一惊人的差异引发了一场持续的争论，关于缺陷-缺陷相互作用和自掺杂的作用，以及自相互作用误差在空位诱导态的密度泛函理论描述中的重要性。在这里，我们解决这个难题，表明这个问题有一个基本的，单电子的起源，这是有关的特殊（周期性）安排的缺陷时，使用板超晶胞的方法。具体而言，我们报告的存在下，$anomalously$离域的晶格，使$π$的中隙带$unphysically$分散，因此易于自掺杂和淬火的$π$磁性的共振态。混合泛函通过加宽自旋分辨的$π$中间带隙之间的带隙而不减小它们的人工宽度来解决这个问题。因此，当磁矩与预期一致时，他们预测自旋分裂比实验中发现的大一个数量级。
英文摘要：
Carbon atom vacancies in graphene give rise to a local magnetic moment of $σ+π$ origin, whose magnitude is yet uncertain and debated. Partial quenching of $π$ magnetism has been ubiquitously reported in periodic $first-principles$ calculations, with magnetic moments scattered in the range 1.0 - 2.0 $μ_{B}$, slowly converging to the lower or the upper end, depending on how the diluted limit is approached. By contrast, (ensemble) density functional theory calculations on cluster models neatly converge to the value of $2$ $μ_{B}$ when increasing the system size. This stunning discrepancy has sparked an ongoing debate about the role of defect-defect interactions and self-doping, and about the importance of the self-interaction-error in the density-functional-theory description of the vacancy-induced states. Here, we settle this puzzle by showing that the problem has a fundamental, mono-electronic origin which is related to the special (periodic) arrangement of defects that results when using the slab-supercell approach. Specifically, we report the existence of resonant states that are $anomalously$ delocalized over the lattice and that make the $π$ midgap band $unphysically$ dispersive, hence prone to self-doping and quenching of the $π$ magnetism. Hybrid functionals fix the problem by widening the gap between the spin-resolved $π$ midgap bands, without reducing their artificial widths. As a consequence, while reconciling the magnetic moment with expectations, they predict a spin-splitting which is one order of magnitude larger than found in experiments.
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