Higher-order And High-charge Weyl Points In Phononic Crystals

Since the discovery of the quantum Hall effect,exploring new topological phases has become an important topic in condensed matter physics.In recent years,similar explorations have been made in classical waves,and new topological phases have been obtained in optical and acoustic systems.Phononic crystals are becoming one of the hot topics in topological physics research due to their macroscopic tunability.The dimension of the conventional topological boundary state is usually only one dimension lower than the bulk dimension,which is called the first-order topological phase.Recently,it has been found that the dimension difference between the topological boundary states and the bulk states can be greater than one,and such states are collectively referred to as higher-order topological phases.Higher-order topological phases can appear not only in topological insulators,but also in topological semimetals.We studied higher-order topological phases in Weyl phononic crystals,examining their bulk topology and boundary transport properties derived from bulk-boundary correspondences.Weyl phononic crystals not only possess higher-order topological states,but also the Weyl points that constitute their bulk dispersion can have different topological charges.Previous studies have focused on double degenerate Weyl points with topological charges 1 or2.Recent theoretical work found that double degenerate Weyl points with the highest topological charge 4 can exist in nature.However,such high-charge Weyl points have not yet been discovered experimentally.We realize the high-charge Weyl point in phononic crystal and investigate its topological bands and related topological transport phenomena.In addition,we studied the higher-order square-root topological phases.The specific contents are as follows:1.Bulk topology in higher-order Weyl phononic crystal.The higher-order Weyl tightbinding model of the uniaxial helical structure was constructed by theoretical analysis.By analyzing the topological invariants of the model,it was found that there were not only conventional Weyl points with topological charge 1,but also Weyl points with topological charge 2 and higher-order Weyl points.Based on the tight-binding model,a chiral phononic crystal with quadruple helical symmetry in the z-axis was designed.The bulk dispersion and the corresponding higher-order Weyl points in higher-order Weyl phononic crystal were clearly observed experimentally,confirming the existence of higher-order Weyl phononic crystals.2.Bulk-boundary correspondence in higher-order Weyl phononic crystal.According to the bulk-boundary correspondence,the coexistence of topologically protected 2D surface states and 1D hinge states was experimentally observed.In momentum space,these topological boundary states connected projections of Weyl points in different dimensions and directions.Due to the characteristic of topological protection,such 1D hinge states could resist structural disorder and possessed robustness.This research provided a new method for the study of higherorder topological physics in Weyl semimetals,and a new realization method for the directional transmission of acoustic waves.3.High-charge Weyl point in phononic crystal.By simultaneously introducing chiral coupling in the three directions of x,y and z,a phononic crystal with high-charge Weyl point was constructed,which hosted various types of Weyl points,especially the high-charge Weyl point with topological charge 4.Through the measurement of projected bulk dispersion in experiment,high-charge Weyl point and many other different types of Weyl points were observed.In particular,the quadruple helicoid surface states generated by the high-charge Weyl point were clearly observed,and the topological charge of the high-charge Weyl point was verified by the connection of the Fermi arcs of the surface states.High-charge Weyl point and their surface states enriched the study of Weyl phononic crystals.4.Higher-order square-root topological states in phononic crystals.First-and higher-order square-root topological insulators of phononic crystals were realized based on the acoustic lattice model.A variety of acoustic modes were observed in phononic crystals in the frequency range of two different band gaps.Further stacking lattices,we obtained 3D acoustic higherorder square-root Weyl semimetal and observed higher-order topological boundary states in higher-order square-root Weyl semimetal,which provide a new idea for the construction of square-root topological states.