Institut für Physik, Universität Rostock, Albert-Einstein-Straße 23, 18059 Rostock, Germany.
Interdisciplinary Center for Quantum Information, Zhejiang Province Key Laboratory of Quantum Technology and Device, Department of Physics, Zhejiang University, Hangzhou 310027, Zhejiang Province, China.
Science. 2022 Jun 3;376(6597):1114-1119. doi: 10.1126/science.abm2842. Epub 2022 May 12.
Topological insulators constitute a newly characterized state of matter that contains scatter-free edge states surrounding an insulating bulk. Conventional wisdom regards the insulating bulk as essential, because the invariants that describe the topological properties of the system are defined therein. Here, we study fractal topological insulators based on exact fractals composed exclusively of edge sites. We present experimental proof that, despite the lack of bulk bands, photonic lattices of helical waveguides support topologically protected chiral edge states. We show that light transport in our topological fractal system features increased velocities compared with the corresponding honeycomb lattice. By going beyond the confines of the bulk-boundary correspondence, our findings pave the way toward an expanded perception of topological insulators and open a new chapter of topological fractals.
拓扑绝缘体是一种新的物质状态，它包含围绕绝缘体的无散射边缘态。传统观点认为绝缘体是必不可少的，因为描述系统拓扑性质的不变量是在其中定义的。在这里，我们研究了基于完全由边缘位组成的分形拓扑绝缘体。我们提出了实验证据，证明尽管没有体带，但螺旋波导的光子晶格支持拓扑保护的手性边缘态。我们表明，与相应的蜂窝晶格相比，我们拓扑分形系统中的光传输具有更高的速度。通过超越体边对应关系的限制，我们的发现为拓扑绝缘体的扩展认识铺平了道路，并开辟了拓扑分形的新篇章。
