Higher-order topological phase in an acoustic fractal lattice

声学分形晶格中的高阶拓扑相

Higher-order topological insulators(HOTIs)are a newly devel-oped topological phase which hosts higher-codimensional topolog-ical states with lower dimensionality localized at the“boundaries of boundaries”[1,2].There are various methods to induce a higher-order topological phase.A quintessential example is the quadrupole insulator based on the Benalcazar,Bernevig,and Hughes(BBH)model[1],which has vanishing dipole polarization but a quantized quadrupole moment.Due to the extended higher-order bulk-boundary correspondence principle,a tWo-dimensional(2D)quadrupole insulator supports 0D in-gap corner states and 1D gapped edge states.Another canonical approach is to directly generalize the 1D SSH model to higher dimensions.

高阶拓扑绝缘体支持比一阶拓扑绝缘体更低维的拓扑边界态,其在整数维系统中得到了深入的研究.本文通过实验展示了声学分形晶格中的高阶拓扑相,为高阶拓扑绝缘体提供了一个新的范式.通过将分形引入到方形晶格中,作者发现了一个压缩的高阶相图,其具有丰富的角态,包括零维的外角态和1.89维的内角态.因此,分形晶格的余维数为1.89,分形模型可以被归类为分数阶的拓扑绝缘体.此外,外角/内角的分数电荷表明,分形系统中的所有角态都是拓扑非平庸的.最后,在一个人工制造的声学分形晶格中,作者通过声学测量,实验观察到了外角/内角态.本研究证明了声学分形晶格中存在高阶拓扑相,并可能为低阶拓扑绝缘体提供新的思路.