一维准晶中的拓扑critical states和反常电子透射率
Topological critical states and anomalous electronic transmittance in one dimensional quasicrystals
摘要：
由于缺乏周期尺度，人们对准晶中的电子态及其拓扑性质知之甚少。在这里，我们专注于一维准晶，并揭示其电子临界态是拓扑鲁棒的。本文利用平铺空间上同调理论，讨论了一维非周期平铺特别是Fibonacci准晶的情形，证明了拓扑临界态的存在性。此外，我们还显示了奇异的电子透射行为附近的拓扑临界状态。在微扰区域，我们讨论了平移对称性的缺乏和拓扑临界态的存在导致透射率的非常规标度行为。考虑到解析分析和数值计算，电子透射率的情况下，该系统被放置在空气中，或连接的半无限周期性的引线。最后，我们还讨论了我们的分析推广到其他准晶。我们的发现开辟了一类新的拓扑量子态，它们只存在于准晶中，由于奇异的平铺图案，在没有周期性的长度尺度，其异常的电子输运性质适用于许多实验。
英文摘要：
Due to the absence of periodic length scale, electronic states and their topological properties in quasicrystals have been barely understood. Here, we focus on one dimensional quasicrystal and reveal that their electronic critical states are topologically robust. Based on tiling space cohomology, we exemplify the case of one dimensional aperiodic tilings especially Fibonacci quasicrystal and prove the existence of topological critical states at zero energy. Furthermore, we also show exotic electronic transmittance behavior near such topological critical states. Within the perturbative regime, we discuss lack of translational symmetries and presence of topological critical states lead to unconventional scaling behavior in transmittance. Considering both analytic analysis and numerics, electronic transmittance is computed in cases where the system is placed in air or is connected by semi-infinite periodic leads. Finally, we also discuss generalization of our analysis to other quasicrystals. Our findings open a new class of topological quantum states which solely exist in quasicrystals due to exotic tiling patterns in the absence of periodic length scale, and their anomalous electronic transport properties applicable to many experiments.
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