Hierarchies of Hofstadter butterflies in 2D covalent organic frameworks

Abstract The Hofstadter butterfly is one of the first and most fascinating examples fractal self-similar quantum nature free electrons in a lattice pierced by perpendicular magnetic field. However, direct experimental verification this effect on single-layer materials still missing as very strong inaccessible fields are necessary. For reason, its indirect has only been realized artificial periodic 2D systems, like moiré lattices. recently synthesized covalent organic frameworks might circumvent limitation: Due to their large pore structures, needed detect features indeed accessible with today technology. This work opens door make exotic theoretical issue from 70s measurable solve quest for materials. Moreover, intrinsic hierarchy different sizes framework adds additional complexity beauty original butterflies leads playground new physical observations.