论文标题
在声学分形晶格中的高阶拓扑阶段
Higher-order topological phase in an acoustic fractal lattice
论文作者
论文摘要
与一阶拓扑绝缘子相比，支持低维拓扑边界状态的高阶拓扑绝缘子在整数维系统中得到了深入研究。在这里，我们通过在分形维系统中在实验上展示一个高阶拓扑阶段来提供新的范式。通过将Benalcazar，Bernevig和Hughes模型应用于Sierpinski地毯分形晶格，我们发现了一个挤压的高阶高阶相图，其中包含零维外角状态和1.89维内角状态，这些角度由零维的角状态组成。结果，编成率现在为1.89，我们的模型可以分为分数拓扑绝缘子。外部/内部角处的非零分数电荷表明分形系统中的所有角状态在拓扑上确实是非平凡的。最后，在制作的声学分形晶格中，我们通过局部声学测量值观察了外部/内角状态。我们的工作证明了在声学分形晶格中的高阶拓扑阶段，并可能为分数阶拓扑绝缘子铺平道路。
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new paradigm by presenting experimentally a higher-order topological phase in a fractal-dimensional system. Through applying the Benalcazar, Bernevig, and Hughes model into a Sierpinski carpet fractal lattice, we uncover a squeezed higher-order phase diagram featuring the abundant corner states, which consist of zero-dimensional outer corner states and 1.89-dimensional inner corner states. As a result, the codimension is now 1.89 and our model can be classified into the fractional-order topological insulators. The non-zero fractional charges at the outer/inner corners indicate that all corner states in the fractal system are indeed topologically nontrivial. Finally, in a fabricated acoustic fractal lattice, we experimentally observe the outer/inner corner states with local acoustic measurements. Our work demonstrates a higher-order topological phase in an acoustic fractal lattice and may pave the way to the fractional-order topological insulators.
