High-order fractal states in graphene superlattices
High-order fractal states in graphene superlattices
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DOI：
10.1073/pnas.1804572115
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发表时间：
2018-05-15
影响因子：
11.1
通讯作者：
Geim, A. K.
中科院分区：
文献类型：
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作者：
Kumar, R. Krishna;Mishchenko, A.;Geim, A. K.
石墨烯超晶格显示出高温量子振荡，这是由于在高磁场中周期性地出现离域布洛赫态，使得通量量子的单位分数穿透超晶格晶胞。在这些条件下，半经典电子轨迹再次变得笔直，类似于零磁场的情况。在这里，我们报告的磁输运测量，揭示了第二，第三和第四阶磁布洛赫态在高电子密度和温度高于100 K。这些状态的重复产生了一种与霍夫施塔特蝴蝶的起源密切相关的分形图案。分形态的层次结构由磁微带的宽度决定，与我们的能带结构计算定性一致。
Graphene superlattices were shown to exhibit high-temperature quantum oscillations due to periodic emergence of delocalized Bloch states in high magnetic fields such that unit fractions of the flux quantum pierce a superlattice unit cell. Under these conditions, semiclassical electron trajectories become straight again, similar to the case of zero magnetic field. Here, we report magnetotransport measurements that reveal second-, third-, and fourth-order magnetic Bloch states at high electron densities and temperatures above 100 K. The recurrence of these states creates a fractal pattern intimately related to the origin of Hofstadter butterflies. The hierarchy of the fractal states is determined by the width of magnetic minibands, in qualitative agreement with our band-structure calculations.