Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes.
Physical Properties of an Aperiodic Monotile with Graphene-like Features, Chirality, and Zero Modes.
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DOI：
10.1103/physrevlett.132.086402
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发表时间：
2023-07
影响因子：
8.6
通讯作者：
Justin Schirmann;S. Franca;F. Flicker;A. Grushin
中科院分区：
文献类型：
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作者：
Justin Schirmann;S. Franca;F. Flicker;A. Grushin
帽子的发现，一个非周期的monotile，揭示了新的数学方面的非周期平铺。然而，粒子在这样的环境中传播的物理学仍然没有被探索。在这项工作中，我们研究了定义在帽子上的紧束缚模型的光谱和输运性质。我们发现：（i）光谱函数显示出与石墨烯惊人的相似之处，包括六重对称性和Dirac样特征;（ii）与石墨烯不同，monotile光谱函数是手性的，其两种对映体不同;（iii）光谱在零能量处具有宏观数量的简并态;（iv）当每个元胞的磁通量（μ）是磁通量量子的一半时，零模被发现局限于反射的“反帽”周围;以及（v）它的Hofstadter谱在μ中是周期性的，不像其他准晶。我们的工作作为一个基础，研究波和电子的传播在可能的实验实现的帽子，我们建议。
The discovery of the Hat, an aperiodic monotile, has revealed novel mathematical aspects of aperiodic tilings. However, the physics of particles propagating in such a setting remains unexplored. In this work we study spectral and transport properties of a tight-binding model defined on the Hat. We find that (i) the spectral function displays striking similarities to that of graphene, including sixfold symmetry and Dirac-like features; (ii) unlike graphene, the monotile spectral function is chiral, differing for its two enantiomers; (iii) the spectrum has a macroscopic number of degenerate states at zero energy; (iv) when the magnetic flux per plaquette (ϕ) is half of the flux quantum, zero modes are found localized around the reflected "anti-hats"; and (v) its Hofstadter spectrum is periodic in ϕ, unlike for other quasicrystals. Our work serves as a basis to study wave and electron propagation in possible experimental realizations of the Hat, which we suggest.