Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
Hierarchy of Hofstadter states and replica quantum Hall ferromagnetism in graphene superlattices
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DOI：
10.1038/nphys2979
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发表时间：
2014-07-01
期刊：
影响因子：
19.6
通讯作者：
Mishchenko, A.
中科院分区：
文献类型：
--
作者：
Yu, G. L.;Gorbachev, R. V.;Mishchenko, A.
自相似性和分形引起了各个学科研究人员的兴趣。在置于氮化硼上并受到磁场作用的石墨烯中，自相似性以原始狄拉克光谱的大量复制品的形式出现，它们的量子化产生了朗道能级的分形图案，被称为霍夫施塔特蝴蝶。在这里，我们采用电容光谱直接探测态密度（DoS）和能隙在这个频谱。在没有磁场的情况下，复制品光谱被视为由货车霍韦奇点包围的明显的DoS最小值。霍夫施塔特蝴蝶在高磁场中表现为反复出现的朗道扇形图。电子-电子相互作用为自相似行为增加了另一个扭曲。我们观察到量子霍尔铁磁性的抑制，在可重复的磁通量和额外的铁磁性内副本光谱的反向斯通纳过渡。分形狄拉克系统中相互作用的强度和多样性为研究多体物理提供了广阔的空间。
Self-similarity and fractals have fascinated researchers across various disciplines. In graphene placed on boron nitride and subjected to a magnetic field, self-similarity appears in the form of numerous replicas of the original Dirac spectrum, and their quantization gives rise to a fractal pattern of Landau levels, referred to as the Hofstadter butterfly. Here we employ capacitance spectroscopy to probe directly the density of states (DoS) and energy gaps in this spectrum. Without a magnetic field, replica spectra are seen as pronounced DoS minima surrounded by van Hove singularities. The Hofstadter butterfly shows up as recurring Landau fan diagrams in high fields. Electron-electron interactions add another twist to the self-similar behaviour. We observe suppression of quantum Hall ferromagnetism, a reverse Stoner transition at commensurable fluxes and additional ferromagnetism within replica spectra. The strength and variety of the interaction effects indicate a large playground to study many-body physics in fractal Dirac systems.