Chasing the Hofstadter Butterfly
Chasing the Hofstadter Butterfly
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追逐霍夫施塔特蝴蝶
DOI：
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发表时间：
2014
期刊：
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通讯作者：
I. Satija
中科院分区：
文献类型：
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作者：
I. Satija
我们重新审视问题的自相似性质的霍夫施塔特蝴蝶频谱，专注于频谱以及拓扑特征。在我们对所有磁通量值的研究中，我们挑出了频谱中最主要的层次，发现它与无理数= 2 − 3有关。表征在最小的能量尺度的内在挫折，这个隐藏的准晶体编码与霍尔电导率和它们的标度性质相关联的拓扑量子数的层次集。这种拓扑层次结构也被映射到一个积分阿波罗垫片（也称为Currency Sierpinski垫片），渐近地表现出D3对称性，揭示了一个隐藏的对称性的蝴蝶的能量和磁通量间隔收缩到零。随着周期性的驱动，诱导系统中的相变，蝴蝶的精细结构被放大，使状态与大拓扑不变量的实验访问。
We revisit the problem of self-similar properties of the Hofstadter butterfly spectrum, focusing on spectral as well as topological characteristics. In our studies involving all values of magnetic flux, we single out the most dominant hierarchy in the spectrum, which is found to be associated with an irrational number ζ = 2 − √ 3. Characterizing an intrinsic frustration at smallest energy scale, this hidden quasicrystal encodes hierarchical set of topological quantum numbers associated with Hall conductivity and their scaling properties. This topological hierarchy is also mapped to an integral Apollonian gasket ( also known as Curvilinear Sierpinski gasket ) that asymptotically exhibits D3 symmetry, revealing a hidden symmetry of the butterfly as the energy and the magnetic flux intervals shrink to zero. With a periodic drive that induces phase transitions in the system, the fine structure of the butterfly is shown to be amplified making states with large topological invariants accessible experimentally.