Observation of Free-Boundary-Induced Chiral Anomaly Bulk States in Elastic Twisted Kagome Metamaterials

Chiral anomaly bulk states (CABSs) can be realized by choosing appropriate boundary conditions in a finite-size waveguide composed of two-dimensional Dirac semimetals, which have unidirectional and robust transport similar to that of valley edge states. CABSs use almost all available guiding space, which greatly improves the utilization of metamaterials. Here, free-boundary-induced CABSs in elastic twisted kagome metamaterials with $C_{3v}$ symmetry are experimentally confirmed. The robust valley-locked transport and complete valley state conversion are experimentally observed. Importantly, the sign of the group velocity near the $K$ and $K^{\prime }$ points can be reversed by suspending masses at the boundary to manipulate the onsite potential. Moreover, CABSs are demonstrated in nanoelectromechanical phononic crystals by constructing an impedance-mismatched hard boundary. These results open new possibilities for designing more compact, space-efficient, and robust elastic wave macro- and microfunctional devices.

Figure 1

(a) Schematic diagram to implement CABSs in a continuous elastic body. The red boxes are two types of unit cells. (b) Upper panel: the first Brillouin zone of the PnCs. Lower panel: the twist angle. (c) Band diagram of an out-of-plane elastic wave. The inset images show the eigenstates, where the color bar is out-of-plane displacements ($w$). The blue band and the red band correspond to an even mode and an odd mode with a mirror-$y$ parity, respectively. (d) Projected band of the PnCs waveguides, which is a free boundary in the $y$ direction, and periodic boundary condition in the $x$ direction. The pseudogap (shadow region) is caused by the finite width of the PnC waveguide. The PnCs waveguides have 10 layers, and the thickness of each layer is $(\sqrt{6}/2)a$. (e) $w$ field of CABSs. Arrows show energy flux fields. (f) The bandwidth of CABS varies with the number of layers in PnCs waveguide. Because CABS exists in the entire pseudogap, the pseudogap bandwidth is equivalent to the operating bandwidth of CABS.

Figure 2

(a) Experimental sample of the 10-layer unmodified waveguides, waveguides with suspended masses on both sides and waveguides with a suspended mass on one side from left to right, respectively. Inset: partially enlarged view of the structure. (b) $w$ distributions at 34.2 kHz excited by a point source (yellow star). (c),(d) Fourier spectra for the 10-layer waveguides and waveguides with suspended masses on both sides, respectively, which are obtained by $w$ in the dotted box in (a). (e)–(g) Experimentally tested projected bands correspond to the three waveguides in (a), which are obtained by a Fourier transformation of the measured field distribution interval with a lattice period along the yellow dotted line in (a). The solid line in figure is the calculated band curve.

Figure 3

(a) Photo of the PnCs waveguides with a 120° bend. (b) Simulated $w$ distributions at 34.2 kHz for a point source (yellow star) on the 120°-bend waveguides. (c) Experimental $w$ distributions at 34.2 kHz for a point source on the 120°-bend waveguides. (d) Photo of the disordered waveguides (left panel) and $w$ distributions (34.2 kHz) on the disordered waveguides (right panel). The distortion is marked in the red dotted box. (e) Photo of the defective waveguides (left panel) and $w$ distributions (34.2 kHz) on the defective waveguides (right panel). (f) Transmission curves of the 120-degree-bend waveguides and the disordered waveguides are compared with those of the waveguide with no defects. Inset picture of (b), (c), and (e): Corresponding Fourier spectra in the dashed rectangle.

Figure 4

(a) Schematic diagram of the implementation of CABSs in nanoelectromechanical systems, which incorporate a dual 120°-bend waveguide. Its lattice constant $a_n$ is $6\sqrt{3}$ um, the circular rods’ diameter $r_n$ is 4 um, and the micropillar height $h_n$ is 200 nm. (b) Band diagram. The inset images are the eigenstates. (c) Projected band of the PnCs waveguides. $w$ of the CABSs (right panel). The PnCs waveguides have six layers. (d) $w$ of the triangular waveguide resonator at 72.457 MHz.