In graphene, charged defects break the electron-hole symmetry and can even give rise to exotic collapse states when the defect charge exceeds a critical value which is proportional to the Fermi velocity. In this work, we investigate the electronic properties of twisted bilayer graphene (tBLG) with charged defects using tight-binding calculations. Like monolayer graphene, tBLG exhibits linear bands near the Fermi level but with a dramatically reduced Fermi velocity near the magic angle (approximately 1.1°). This suggests that the critical value of the defect charge in magic-angle tBLG should also be very small. We find that charged defects give rise to significant changes in the low-energy electronic structure of tBLG. Depending on the defect position in the moiré unit cell, it is possible to open a band gap or to induce an additional flattening of the low-energy valence and conduction bands. Our calculations suggest that the collapse states of the two monolayers hybridize in the twisted bilayer. However, their in-plane localization remains largely unaffected by the presence of the additional twisted layer because of the different length scales of the moiré lattice and the monolayer collapse state wavefunctions. These predictions can be tested in scanning tunneling spectroscopy experiments.

在石墨烯中，带电缺陷会破坏电子空穴对称性，当缺陷电荷超过与费米速度成正比的临界值时，甚至会产生奇异的塌缩态。在这项工作中，我们使用紧束缚计算研究了带有带电缺陷的扭曲双层石墨烯（tBLG）的电子特性。与单层石墨烯一样，tBLG 在费米能级附近呈现线性带，但在魔角（约 1.1°）附近费米速度显着降低。这表明魔角tBLG中缺陷电荷的临界值也应该非常小。我们发现带电缺陷会导致 tBLG 的低能电子结构发生显着变化。根据莫尔晶胞中的缺陷位置，有可能打开带隙或引起低能价带和导带的额外平坦化。我们的计算表明两个单层的塌缩态在扭曲的双层中杂交。然而，由于莫尔晶格和单层塌陷态波函数的不同长度尺度，它们的面内定位在很大程度上不受附加扭曲层存在的影响。这些预测可以在扫描隧道光谱实验中得到检验。由于莫尔晶格和单层塌陷态波函数的长度尺度不同，它们的面内定位在很大程度上不受附加扭曲层存在的影响。这些预测可以在扫描隧道光谱实验中得到检验。由于莫尔晶格和单层塌陷态波函数的长度尺度不同，它们的面内定位在很大程度上不受附加扭曲层存在的影响。这些预测可以在扫描隧道光谱实验中得到检验。