Hofstadter蝴蝶在二维共价有机框架中的层次结构
Hierarchies of Hofstadter butterflies in 2D covalent-organic frameworks
摘要：
霍夫施塔特蝴蝶是被垂直磁场穿透的晶格中的自由电子的分形和自相似量子性质的第一个也是最迷人的例子之一。然而，这种效果的直接实验验证的单层材料仍然缺少非常强大的和不可访问的磁场是必要的。因此，它的间接实验验证仅在人工周期性2D系统中实现，如莫尔晶格。最近唯一合成的2D共价有机框架可能会避开这一限制：由于它们的大孔结构，检测霍夫施塔特蝴蝶的大多数特征所需的磁场确实可以通过今天的技术获得。这项工作打开了使这个来自70年代的异国情调和理论问题可测量的大门，并可能解决在单层材料中对霍夫施塔特蝴蝶的实验验证的探索。此外，2D共价有机框架中不同孔径的内在层次结构为原始蝴蝶增加了额外的复杂性和美丽性，并为新的物理观察提供了一个可直接访问的游乐场。
英文摘要：
The Hofstadter butterfly is one of the first and most fascinating examples of the fractal and self-similar quantum nature of free electrons in a lattice pierced by a perpendicular magnetic field. However, the direct experimental verification of this effect on single-layer materials is still missing as very strong and inaccessible magnetic fields are necessary. For this reason, its indirect experimental verification has only been realized in artificial periodic 2D systems, like moiré lattices. The only recently synthesized 2D covalent-organic frameworks might circumvent this limitation: Due to their large pore structures, magnetic fields needed to detect most features of the Hofstadter butterfly are indeed accessible with today's technology. This work opens the door to making this exotic and theoretical issue from the 70s measurable and might solve the quest for the experimental verification of the Hofstadter butterfly in single-layer materials. Moreover, the intrinsic hierarchy of different pore sizes in a 2D covalent-organic framework adds additional complexity and beauty to the original butterflies and leads to a directly accessible playground for new physical observations.
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