Photonic Floquet topological insulators in a fractal lattice

We present Floquet fractal topological insulators:photonic topological insulators in a fractal-dimensional lattice consisting of helical waveguides.The helical modulation induces an artificial gauge field and leads to a trivial-totopological phase transition.The quasi-energy spectrum shows the existence of topological edge states corresponding to real-space Chern number 1.We study the propagation of light along the outer edges of the fractal lattice and find that wavepackets move along the edges without penetrating into the bulk or backscattering even in the presence of disorder.In a similar vein,we find that the inner edges of the fractal lattice also exhibit robust transport when the fractal is of sufficiently high generation.Finally,we find topological edge states that span the circumference of a hybrid half-fractal,half-honeycomb lattice,passing from the edge of the honeycomb lattice to the edge of the fractal structure virtually without scattering,despite the transition from two dimensions to a fractal dimension.Our system offers a realizable experimental platform to study topological fractals and provides new directions for exploring topological physics.

Higher-order topological phase in an acoustic fractal lattice

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.