Huber Robin, Steffen Max-Niklas, Drienovsky Martin, Sandner Andreas, Watanabe Kenji, Taniguchi Takashi, Pfannkuche Daniela, Weiss Dieter, Eroms Jonathan
Institute of Experimental and Applied Physics, University of Regensburg, D-93040, Regensburg, Germany.
I. Institute of Theoretical Physics, University of Hamburg, Notkestraße 9-11, D-22607, Hamburg, Germany.
Nat Commun. 2022 May 23;13(1):2856. doi: 10.1038/s41467-022-30334-3.
Electrons exposed to a two-dimensional (2D) periodic potential and a uniform, perpendicular magnetic field exhibit a fractal, self-similar energy spectrum known as the Hofstadter butterfly. Recently, related high-temperature quantum oscillations (Brown-Zak oscillations) were discovered in graphene moiré systems, whose origin lies in the repetitive occurrence of extended minibands/magnetic Bloch states at rational fractions of magnetic flux per unit cell giving rise to an increase in band conductivity. In this work, we report on the experimental observation of band conductivity oscillations in an electrostatically defined and gate-tunable graphene superlattice, which are governed both by the internal structure of the Hofstadter butterfly (Brown-Zak oscillations) and by a commensurability relation between the cyclotron radius of electrons and the superlattice period (Weiss oscillations). We obtain a complete, unified description of band conductivity oscillations in two-dimensional superlattices, yielding a detailed match between theory and experiment.
暴露于二维（2D）周期性势和均匀垂直磁场中的电子表现出一种分形的、自相似的能谱，即霍夫施塔特蝴蝶。最近，在石墨烯莫尔系统中发现了相关的高温量子振荡（布朗 - 扎克振荡），其起源在于在每个晶胞磁通量的有理分数处扩展微带/磁布洛赫态的重复出现，从而导致带内电导率增加。在这项工作中，我们报告了在静电定义且栅极可调的石墨烯超晶格中带内电导率振荡的实验观测结果，这些振荡既受霍夫施塔特蝴蝶的内部结构（布朗 - 扎克振荡）控制，又受电子回旋半径与超晶格周期之间的可公度关系（魏斯振荡）控制。我们得到了二维超晶格中带内电导率振荡的完整、统一描述，实现了理论与实验的详细匹配。
