标题： 魔角扭曲双层石墨烯中带平度和各向异性量子几何的光学特征 显示英文标题

标题： Optical Signatures of Band Flatness and Anisotropic Quantum Geometry in Magic-Angle Twisted Bilayer Graphene

摘要： 我们通过改变扭转角度和晶格弛豫参数，利用光学电导率研究了魔角扭曲双层石墨烯的带宽平坦度和各向异性量子几何特性。 我们表明，带宽平坦度及其量子几何特性可以通过光学吸收及其产生的光学边界来揭示，这些光学边界基于量子几何中的迹条件。 更具体地说，低能区域光学吸收的窄而孤立峰提供了两个平坦带带宽的信息。 当该值小于电子相互作用时，它成为平坦带超导出现的关键条件。 此外，光学吸收还提供了平坦带与色散带之间的能隙值，当该能隙大于电子相互作用时，有助于实现分数陈绝缘相。 我们表明，零能附近光学边界狭窄且孤立的峰随着晶格弛豫的增加而减小。 同时，我们证明（广义）光学霍尔电导率的虚部揭示了贝里曲率负部分的消失，这由改进的迹-行列式不等式所强制。 因此，我们表明在单个理想平坦带情况下，贝里曲率负部分的总数量和分量趋近于零。 相比之下，当考虑所有占据带时，负分量的总数量略有不同。 最后，我们证明平坦带速度的消失和出现的手征对称性是迹条件饱和的充分条件，该条件涉及各向同性情况。 相反，行列式条件只能在各向异性系统中达到饱和。 显示英文摘要

摘要： We study the degree of band flatness and the anisotropic quantum geometry in magic-angle twisted bilayer graphene by varying the twist angle and the parameters of lattice relaxation using optical conductivity. We show that the degree of band flatness and its quantum geometry can be revealed through optical absorption and its resulting optical bounds, which are based on the trace condition in quantum geometry. More specifically, the narrow and isolated peak of optical absorption in the low-energy region provides information about the bandwidth of the two flat bands. When this value is smaller than the electron interaction, it serves as a critical condition for the emergence of flat band superconductivity. Furthermore, optical absorption also provides the gap value between the flat band and the dispersive band, and when this gap is larger than the electron interaction, it facilitates the realization of fractional Chern insulating phases. We show that the narrow and isolated peak of optical bound near zero energy decreases as lattice relaxation increases. Meanwhile, we demonstrate that the imaginary part of (generalized) optical Hall conductivity reveals the vanishing of the negative part of Berry curvature, which is enforced by the refined trace-determinant inequality. Accordingly, we show that the total amount of the negative part and component of the Berry curvature approaches zero in the single ideal flat-band case. In contrast, when considering all occupied bands, the total amount of the negative component is slightly different from zero. Lastly, we demonstrate that the vanishing of flat band velocity and the emergent chiral symmetry are sufficient conditions for the saturation of the trace condition, which pertains to the isotropic case. In contrast, the determinant condition can only be saturated in anisotropic systems.