近日，上海交通大学的贾金锋及其研究小组与荷兰乌得勒支大学的C. Morais Smith等人合作并取得一项新进展。经过不懈努力，他们揭示铋分形纳米结构中的拓扑边缘和角态。相关研究成果已于2024年7月1日在国际知名学术期刊《自然—物理学》上发表。

该研究团队证明了在锑化铟衬底上沉积薄层铋形成的分形中出现拓扑边缘和角模式。扫描隧道显微镜结果和理论计算揭示了Sierpiński三角形角上接近零能量模式的外观和稳定性，以及更高能量下外部和内部边缘模式的形成。这项工作为在具有鲁棒和受保护的拓扑状态的非整数维度上，扩展电子器件在实际材料中的应用开辟了前景。

据悉，在绝缘体中承载以整量子化电导率为特征的金属边缘的拓扑材料，彻底改变了人们对物质输运的理解。这些边缘状态的拓扑保护是基于对称性和维数的。虽然整数维对拓扑性质的影响已经被广泛研究，但拓扑和分形的相互作用可能具有非整数维，仍然在很大程度上未被探索。

附：英文原文

Title: Topological edge and corner states in bismuth fractal nanostructures

Author: Canyellas, R., Liu, Chen, Arouca, R., Eek, L., Wang, Guanyong, Yin, Yin, Guan, Dandan, Li, Yaoyi, Wang, Shiyong, Zheng, Hao, Liu, Canhua, Jia, Jinfeng, Morais Smith, C.

Issue&Volume: 2024-07-01

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. While integer-dimensional effects on topological properties have been studied extensively, the interplay of topology and fractals, which may have a non-integer dimension, remains largely unexplored. Here we demonstrate that topological edge and corner modes arise in fractals formed upon depositing thin layers of bismuth on an indium antimonide substrate. Our scanning tunnelling microscopy results and theoretical calculations reveal the appearance and stability 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. This work opens the perspective to extend electronic device applications in real materials at non-integer dimensions with robust and protected topological states.

DOI: 10.1038/s41567-024-02551-8

Source: https://www.nature.com/articles/s41567-024-02551-8