Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
Magic angles in twisted bilayer graphene near commensuration: Towards a hypermagic regime
复制标题
DOI：
10.1103/physrevb.106.115418
复制
发表时间：
2022-03
影响因子：
3.7
通讯作者：
M. Scheer;Kaiyuan Gu;Biao Lian
中科院分区：
文献类型：
--
作者：
M. Scheer;Kaiyuan Gu;Biao Lian
Bistritzer-MacDonald连续介质模型（BM模型）描述了在小扭转角下扭曲双层石墨烯（TBG）的低能涡流带。我们推导了一个广义连续体模型，该模型具有相应$AA$层的复杂层间跳变（而不是BM模型中的真实跳变）、相应$AB/BA$层的真实层间跳变和全局能量转移的特征。$AA$叠加跳跃的复相和扭转角共同定义了一个单一的角度参数$\phi_0$。我们计算了前六种不同的相称的TBG构型的模型参数，其中$38.2^\circ$构型可能在实验可观察的能量尺度内。在类似于BM模型的条件下，我们确定了任何$\phi_0$的第一个魔角。在这个角度下，电荷中性的最低两个莫尔维尔带变得平坦，除了$\boldsymbol\Gamma_M$点附近，并且保留了脆弱的拓扑结构，但失去了粒子-空穴对称性。我们进一步确定了一个以$\phi_0 = \pm\pi/2$为中心的超魔法参数区，其中围绕电荷中性（通常为$8$或更多）的许多波纹带同时变平。许多平坦带类似于kagome晶格和$p_x$, $p_y$ 2轨道蜂窝晶格紧密结合模型。
The Bistritzer-MacDonald continuum model (BM model) describes the low-energy moir\'e bands for twisted bilayer graphene (TBG) at small twist angles. We derive a generalized continuum model for TBG near any commensurate twist angle, which is characterized by complex interlayer hoppings at commensurate $AA$ stackings (rather than the real hoppings in the BM model), a real interlayer hopping at commensurate $AB/BA$ stackings, and a global energy shift. The complex phases of the $AA$ stacking hoppings and the twist angle together define a single angle parameter $\phi_0$. We compute the model parameters for the first six distinct commensurate TBG configurations, among which the $38.2^\circ$ configuration may be within experimentally observable energy scales. We identify the first magic angle for any $\phi_0$ at a condition similar to that of the BM model. At this angle, the lowest two moir\'e bands at charge neutrality become flat except near the $\boldsymbol\Gamma_M$ point and retain fragile topology but lose particle-hole symmetry. We further identify a hypermagic parameter regime centered at $\phi_0 = \pm\pi/2$ where many moir\'e bands around charge neutrality (often $8$ or more) become flat simultaneously. Many of these flat bands resemble those in the kagome lattice and $p_x$, $p_y$ 2-orbital honeycomb lattice tight-binding models.