通过调节周期势强度，朗道“毛虫”如何转变为霍夫施塔特蝴蝶
How Landau caterpillars turn into Hofstadter butterflies by tuning the periodic potential strength
- University of Geneva（日内瓦大学）
- Leiden University（莱顿大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文通过调节周期势强度，将朗道能级与霍夫施塔特蝴蝶能谱联系，识别出拓扑相变，所得蝴蝶能谱与磁通φ>1的霍夫施塔特蝴蝶拓扑不同，其Wannier化方法可用于大磁场下的多体计算。
AI中文摘要：
众所周知，垂直磁场中二维电子的能谱由离散的平朗道能级给出。相比之下，二维紧束缚模型中的电子会产生分形的霍夫施塔特蝴蝶能谱。本文中，我们通过连续增大周期势强度，展示了蝴蝶能谱如何从展宽的朗道“毛虫”中产生，从而将这两个截然相反的极限联系起来。我们识别出一系列拓扑相变，这些相变分离出一个最低的平庸能带，这是蝴蝶能谱出现的必要条件。由于对角跳跃的反常行为，所得的蝴蝶能谱与磁通φ>1时的霍夫施塔特蝴蝶在拓扑上不同。此外，通过在大磁场下的Wannier化（维纳化）程序得到的有效紧束缚模型的跳跃参数高度依赖于磁通，这表明Wannier轨道本身会在施加的磁场下发生变化。我们的方法和结果与人工材料（如莫尔系统）相关，在这类系统中，每个晶格单胞的完整磁通量子在实验上是可实现的。在理论层面，针对每个特定磁通拥有Wannier化方法，可在大磁场下进行更精确的多体计算。
英文摘要：
It is well-known that the spectrum of two-dimensional electrons in a perpendicular magnetic field is given by discrete flat Landau levels. By contrast, electrons in a two-dimensional tight-binding model give rise to a fractal Hofstadter butterfly spectrum. In this paper, we connect these two opposite limits by showing how a butterfly spectrum emerges from broadened Landau `caterpillars', by continuously increasing the periodic potential strength. We identify a series of topological transitions that isolate a lowest trivial band, a necessary condition for the butterfly to emerge. The resulting butterfly is topologically distinct from the Hofstadter butterfly at fluxes $ϕ>1$, due to anomalous behavior of diagonal hopping. Moreover, the hopping parameters of an effective tight-binding model, obtained by a Wannierization procedure at large magnetic field, are highly dependent on the flux, revealing that Wannier orbitals themselves change under the applied magnetic field. Our methods and results are relevant for artificial materials, such as moiré systems, where a full quantum of flux per lattice unit cell is experimentally accessible. On a theoretical level, having Wannierization methods for each specific flux allows more accurate many-body calculations in large magnetic fields.
