Experimental Realization of Type-II Weyl Points and Fermi Arcs in Phononic Crystal

Weyl points (WPs), as the doubly degenerate points in three-dimensional momentum band structures, carry quantized topological charges and give rise to a variety of extraordinary properties, such as robust surface wave and chiral anomaly. Type-II Weyl semimetals, which have conical dispersions in Fermi surfaces and a strongly tilted dispersion with respect to type I, have recently been proposed in condensed-matter systems and photonics. Although the type-II WPs have been theoretically predicted in acoustics, the experimental realization in phononic crystals has not been reported so far. Here, we experimentally realize a type-II Weyl phononic crystal. We demonstrate the topological transitions observed at the WP frequencies and the topological surface acoustic waves between the Weyl frequencies. The experiment results are in good accordance with our theoretical analyses. Due to the violation of the Lorentz symmetry, the type-II WPs only exist in low energy systems. As the analog counterpart in classical waves, the phononic crystal brings a platform for the research of type-II WPs in macroscopic systems.

Figure 1

The Weyl phononic crystal and its unit cell. (a) An image of the experimental sample. (b) Magnified image of the top view. A unit cell is outlined with red hexagon. (c) Geometry of the unit cell. (d) The first bulk BZ of the Weyl phononic crystal. The olive and blue spheres label WPs with opposite charges. The red solid line on the right side shows the Chern number of the 2D band with a fixed $k_z$.

Figure 2

Bulk bands of the two lowest modes. (a)–(e) In planes (a) $k_z=0$, (b) $0.38\pi /h$, (c) $0.58\pi /h$, (d) $0.78\pi /h$, (e) $\pi /h$, and (f) along the $KH$ direction. (g)–(i) The fermi surface at $k_y=0$ for different frequencies. (g) 9036 Hz is set to the lower-frequency WP1. Contact between electron and hole pockets occurs at WP1. (h) 9600 Hz is set to be between the two WPs. The two band pockets are disconnected. WP1 is enclosed by one of the bands. The positions of WP1 and WP2 are denoted by blue and olive spheres. (i) 10 268 Hz is set to the higher-frequency WP2, two band pockets touch again at WP2. The amplitudes represent the strength of the states stimulated in the phononic crystal.

Figure 3

Observation of topological SAWs. SAWs are excited by point sources placed at the center of the surfaces. (a) and (b) The temporal pressure field of (a) $XZ1$ and (b) $YZ1$ surfaces at 9600 Hz. (c) and (d) Fourier transforms of the SAW fields on the (c) $XZ1$ and (d) $YZ1$ surfaces, showing the equifrequency contours in the extended surface BZ at the WP1 frequency 9036 Hz (left), 9600 Hz (middle), and the WP2 frequency 10 268 Hz (right). (e) and (f) Surface band dispersion of $k_z=0.6\pi /h$ for (e) XZ1 and (f) $YZ1$ surfaces. The gray dashed lines represent the outlines of the projected bulk bands. The positions of projected WP1 and WP2 are denoted by blue and olive spheres. The grey regions display the projected bulk bands. The green solid and dashed lines represent the simulated SAWs and the results on opposite surfaces.