The emergence of local moments in graphene zigzag edges, grain boundaries, vacancies and sp3 defects has been widely studied theoretically. However, conclusive experimental evidence is scarce. Recent progress in on-surface synthesis has made it possible to create nanographenes, such as triangulenes, with local moments in their ground states, and to probe them using scanning tunnelling microscope (STM) spectroscopy. Here we review the application of the theory of sequential and cotunneling transport to relate the dI/dV spectra with the spin properties of nanographenes probed by STM. This approach permits us to connect the dI/dV with the many-body energies and wavefunctions of the graphene nanostructures. We apply this method describing the electronic states of the nanographenes by means of exact diagonalization of the Hubbard model within a restricted Active Space. This permits us to provide a proper quantum description of the emergence of local moments in graphene and its interplay with transport. We discuss the results of this theory in the case of diradical nanographenes, such as triangulene, rectangular ribbons and the Clar goblet, that have been recently studied experimentally by means of STM spectroscopy. This approach permits us to calculate both the dI/dV spectra, that yields excitation energies, as well as the atomically resolved conductivity maps, that provide information on the wavefunctions of the collective spin modes.

中文翻译：

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用电子隧道光谱探测纳米石墨烯的局部矩

石墨烯锯齿形边缘、晶界、空位和 sp3 缺陷中局部矩的出现在理论上得到了广泛研究。然而，结论性的实验证据很少。表面合成的最新进展使得创建具有基态局部矩的纳米石墨烯（如三角烯）成为可能，并使用扫描隧道显微镜 (STM) 光谱对其进行探测。在这里，我们回顾了顺序和共隧道传输理论的应用，将 dI/dV 光谱与 STM 探测的纳米石墨烯的自旋特性联系起来。这种方法允许我们将 dI/dV 与石墨烯纳米结构的多体能量和波函数联系起来。我们通过在受限活动空间内对哈伯德模型进行精确对角化来应用这种方法来描述纳米石墨烯的电子状态。这使我们能够对石墨烯中局部矩的出现及其与输运的相互作用提供适当的量子描述。我们讨论了该理论在双自由基纳米石墨烯的情况下的结果，例如三角烯、矩形带和 Clar 高脚杯，最近通过 STM 光谱对其进行了实验研究。这种方法使我们能够计算产生激发能量的 dI/dV 谱，以及提供集体自旋模式波函数信息的原子分辨电导率图。这使我们能够对石墨烯中局部矩的出现及其与输运的相互作用提供适当的量子描述。我们讨论了该理论在双自由基纳米石墨烯的情况下的结果，例如三角烯、矩形带和 Clar 高脚杯，最近通过 STM 光谱对它们进行了实验研究。这种方法使我们能够计算产生激发能量的 dI/dV 谱，以及提供集体自旋模式波函数信息的原子分辨电导率图。这使我们能够对石墨烯中局部矩的出现及其与输运的相互作用提供适当的量子描述。我们讨论了该理论在双自由基纳米石墨烯的情况下的结果，例如三角烯、矩形带和 Clar 高脚杯，最近通过 STM 光谱对其进行了实验研究。这种方法使我们能够计算产生激发能量的 dI/dV 谱，以及提供集体自旋模式波函数信息的原子分辨电导率图。