It was recently argued that Bernal stacked bilayer graphene (BLG) exposed to a two-dimensional superlattice (SL) potential exhibits a variety of intriguing behaviors [Ghorashi et al., Phys. Rev. Lett. 130, 196201 (2023)]. Chief among them is the appearance of flat Chern bands that are favorable to the appearance of fractional Chern insulator states. Here, we explore the application of spatially periodic out-of-plane orbital magnetic fields to the model of Ghorashi et al. to find additional means of inducing flat Chern bands. We focus on fields that vary on length scales much larger than the atomic spacing in BLG, generating what we refer to as magnetic SLs. The magnetic SLs we investigate either introduce no net magnetic flux to the SL unit cell or a single quantum of flux. We find that magnetic SLs acting on their own can induce topological flat bands, but richer behavior, such as the appearance of flat and generic bands with high Chern numbers, can be observed when the magnetic SLs act in conjunction with commensurate electric SLs. Finally, we propose a method of generating unit-flux-quantum magnetic SLs along with concomitant electric SLs. The magnetic SL is generated by periodic arrays of flux vortices originating from type II superconductors, while the electric SL arises due to a magnetic SL-induced charge density on the surface of a magnetoelectric material. Tuning the vortex lattice and the magnetoelectric coupling permits control of both SLs, and we study their effects on the band structure of BLG.

中文翻译：

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在具有电和磁性超晶格的双层石墨烯中诱导拓扑平坦带


最近有人认为，暴露于二维超晶格 （SL） 电位的 Bernal 堆叠双层石墨烯 （BLG） 表现出各种有趣的行为 [Ghorashi et al.， Phys. Rev. Lett.130， 196201 （2023）]。其中最主要的是平坦的陈带的出现，这有利于分数陈绝缘态的出现。在这里，我们探讨了空间周期性面外轨道磁场在 Ghorashi 等 人模型中的应用，以寻找诱导平坦陈带的其他方法。我们专注于在长度尺度上变化的场，这些场的长度尺度远大于 BLG 中的原子间距，从而产生我们所说的磁性 SL。我们研究的磁性 SL 要么没有向 SL 晶胞引入净磁通量，要么只引入单一量子磁通量。我们发现，磁 SL 自身作用可以诱导拓扑平坦带，但当磁性 SL 与相应的电 SL 一起作用时，可以观察到更丰富的行为，例如出现具有高陈数的平坦和通用带。最后，我们提出了一种产生单位磁通量量子磁 SL 以及伴随电 SL 的方法。磁性 SL 是由源自 II 型超导体的磁通涡流的周期性阵列产生的，而电 SL 是由于磁电材料表面的磁性 SL 感应电荷密度而产生的。调整涡旋晶格和磁电耦合可以控制两个 SL，我们研究了它们对 BLG 能带结构的影响。