Higher-order topological semimetal in acoustic crystals

Abstract

The notion of higher-order topological insulator has opened up a new avenue toward novel topological states and materials. Particularly, a 3D higher-order topological insulator can host topologically protected 1D hinge states, referred to as the second-order topological insulator, or 0D corner states, referred to as the third-order topological insulator. Similarly, a 3D higher-order topological semimetal can be envisaged, if it hosts states on the 1D hinges or 0D corners. Here, we report the first realization of a second-order topological Weyl semimetal in a 3D phononic crystal, which possesses Weyl points in 3D momentum space, gapped surface states on the 2D surfaces and gapless hinge states on the 1D hinges. The 1D hinge states in a triangle-shaped sample exhibit a dispersion connecting the projections of the Weyl points. Our results extend the concept of the higher-order topology from the insulator to the semimetal, which may play a significant role in topological physics and produce new applications in materials.

Higher-order Dirac sonic crystals

“…Interestingly for a HO Dirac semimetal, its gapped 2D slices may be classified into two HO topologically distinct insulators, for which the transition occurs exactly at the Dirac points 4,5 . Similar topological transitions also emerge in HO Weyl semimetals [12][13][14][15] . Such features lead to the presence of fascinating one-dimensional (1D) hinge modes connecting the projected Dirac or Weyl nodes, a robust manifestation of the HO bulk-hinge correspondence.…”

“…Nontrivial HO topology has been predicted not only in gapped insulators [6][7][8][9][10][11] but also in gapless semimetals 4,5,[12][13][14][15] . These new HO members greatly enrich the already diverse spectrum of topological phases of matter.…”

“…To date there have been extensive studies of various HO topological phases in condensed matter and materials physics [4][5][6][7][8][9][10][11][12][13][14][15][20][21][22][23][24][25][26] , ranging from solid-state materials to ultra-cold atoms, from photonics to acoustics, etc. In particular, the artificial crystals for classical waves have been demonstrated to be exceptional platforms for exploring those otherwise elusive topological phases, benefiting from their macroscopically more controllable structures and less demanding measurements 27,28 .…”

Tunable Topological Surface States of Three-Dimensional Acoustic Crystals

“…Compared to 1D and 2D topological phases, 3D topological phases can efficiently manipulate waves in multiple dimensions [23][24][25][26][27]. Nevertheless, despite many works on 3D acoustic semimetals [28][29][30][31][32][33][34][35][36][37][38], the studies on 3D acoustic topological insulators are insufficient [39,40].…”

Spin-Chern insulator induced by pseudospin-orbit coupling in phononic crystals

“…在电磁波、机械波和声波等经典波系统中, 制备 和操控拓扑态也取得了很多重要进展 [13][14][15][16][17] . 电磁波的 陈数拓扑绝缘体在磁光光子晶体中 [18] 、机械波的陈 数拓扑绝缘体在陀螺超材料中 [19] 、声波的陈数拓扑 绝缘体在具有环形气流的声子晶体中 [20] , 都已分别被 实现.…”