Dirac points and the transition towards Weyl points in three-dimensional sonic crystals

Abstract

A four-fold-degenerate three-dimensional (3D) Dirac point, represents a degenerate pair of Weyl points carrying opposite chiralities. Moreover, 3D Dirac crystals have shown many exotic features different from those of Weyl crystals. How these features evolve from 3D Dirac to Weyl crystals is important in research on 3D topological matter. Here, we realized a pair of 3D acoustic Dirac points from band inversion in a hexagonal sonic crystal and observed the surface states and helical interface states connecting the Dirac points. Furthermore, each Dirac point can transition into a pair of Weyl points with the introduction of chiral hopping. The exotic features of the surface states and interface states are inherited by the resulting Weyl crystal. Our work may serve as an ideal platform for exploring exotic physical phenomena in 3D topological semimetals.

A Review of Topological Semimetal Phases in Photonic Artificial Microstructures

“…Upon symmetry breaking, the band structure can transit into the Z 2 nodal ring, Weyl dipole, and topological bandgap supporting gapless surface states [74] or hinge states [75]. Recently, the transition from the 3D Dirac point to Weyl dipole is experimentally demonstrated in acoustics [76].…”

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].…”

Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals

“…Specifially, Dirac/Weyl semimetals have been demonstrated to exhibit several peculiar phenomena, such as Fermi arcs and chiral anomaly [1,11], while for type-II Weyl points, the unique features including tilted cone dispersion and the surface states existed in an incomplete bandgap would bring more exotic effects [10]. In classical systems, the analogues of various topological semimetals have also been achieved in photonics [12][13][14][15][16][17][18][19][20][21][22][23][24][25], acoustics [26][27][28][29][30][31],circuits [32] and magnetic systems [33,34]. Type-I Weyl points and the arc surface states have been theoretically [12] and experimentally [13,14,27] verified in 3D photonic/phononic crystals and metamaterials, and also been found recently that the Weyl semimetals can sustain higher-order topological hinge states [35][36][37][38].…”

“…However, it is shown that in bosonic system these Weyl semimetals are usually realized using 3D artificial periodical structures with complicated structure designs, and the ideal type-II Wely points is still beyond realization in photonic system. Besides, for the topological transition from Dirac points to Weyl points in classical semimetals, previous works usually achieved this effect in two artificial structures with different symmetries or couplings [18,31], which is very inflexible and untunable.…”