[论文解读] Topological edge and corner states in Bi fractals on InSb

Canyellas, R., Chen Liu+11 more|arXiv (Cornell University)|Sep 18, 2023

Topological Materials and PhenomenaPhysics and Astronomy被引用 3

一句话总结

本研究展示了在铋沉积于InSb衬底上形成的自相似分形Sierpiński三角形中，拓扑边缘态和角态的出现。通过扫描隧道显微镜和理论建模，作者观察到在较高能量下具有鲁棒性的零能角模式和边缘态，且在Rashba自旋轨道耦合和无序条件下仍保持拓扑保护，为非整数维系统中的拓扑物理提供了新平台。

ABSTRACT

Topological materials hosting metallic edges characterized by integer quantized conductivity in an insulating bulk have revolutionized our understanding of transport in matter. The topological protection of these edge states is based on symmetries and dimensionality. However, only integer-dimensional models have been classified, and the interplay of topology and fractals, which may have a non-integer dimension, remained largely unexplored. Quantum fractals have recently been engineered in metamaterials, but up to present no topological states were unveiled in fractals realized in real materials. Here, we show theoretically and experimentally that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Scanning tunneling microscopy reveals the appearance of (nearly) zero-energy modes at the corners of Sierpiński triangles, as well as the formation of outer and inner edge modes at higher energies. Unexpectedly, a robust and sharp depleted mode appears at the outer and inner edges of the samples at negative bias voltages. The experimental findings are corroborated by theoretical calculations in the framework of a continuum muffin-tin and a lattice tight-binding model. The stability of the topological features to the introduction of a Rashba spin-orbit coupling and disorder is discussed. This work opens the perspective to novel electronics in real materials at non-integer dimensions with robust and protected topological states.

研究动机与目标

• 探索真实材料中非整数维性下拓扑与分形几何的相互作用。
• 研究在由铋在InSb上形成的工程化量子分形中，拓扑边缘态和角态是否能够出现。
• 确定这些拓扑态在Rashba自旋轨道耦合和无序条件下的稳定性。
• 弥合拓扑相理论模型与其在非整数维系统中实现之间的鸿沟。

提出的方法

• 通过在InSb(111)衬底上外延生长铋，制备Sierpiński三角形分形结构。
• 利用扫描隧道显微镜（STM）探测局域态密度，识别零能角模式和边缘态。
• 采用连续Muffin-tin势和晶格紧束缚模型进行理论建模，模拟电子结构。
• 通过分析对称性保护和拓扑不变量，确认拓扑相的存在。
• 通过数值模拟研究Rashba自旋轨道耦合和无序下的鲁棒性。
• 将实验STM数据与理论预测进行对比，验证拓扑态的存在。

实验结果

研究问题

• RQ1 是否可以在具有分形几何和非整数维性的实际材料中实现拓扑边缘态和角态？
• RQ2 对称性和维度在分形晶格中稳定拓扑态方面起什么作用？
• RQ3 Rashba自旋轨道耦合和无序如何影响分形系统中拓扑模式的稳定性？
• RQ4 观测到的零能角模式是否具有拓扑保护性，其空间分布如何？
• RQ5 是否能明确地在分形纳米结构中识别出拓扑态的实验特征？

主要发现

• 扫描隧道显微镜揭示了Sierpiński三角形分形角落处近乎零能的局域模式，表明存在拓扑角态。
• 在外围和内围边缘处观测到较高能量的边缘模式，与分形几何中的拓扑边缘态一致。
• 在负偏压下，外边缘和内边缘均出现鲁棒且尖锐的耗尽模式，表明强局域化和拓扑保护。
• 连续Muffin-tin模型和晶格紧束缚模型的理论计算重现了实验观测结果，证实了这些态的拓扑起源。
• 在引入Rashba自旋轨道耦合和无序后，拓扑特征依然保持稳定，表现出鲁棒性。
• 本工作首次在具有非整数维性的实际材料中实现了拓扑态，为拓扑电子学开辟了新途径。