Recently, the topological physics in artificial crystals for classical waves has become an emerging research area. In this Letter, we propose a unique bilayer design of sonic crystals that are constructed by two layers of coupled hexagonal array of triangular scatterers. Assisted by the additional layer degree of freedom, a rich topological phase diagram is achieved by simply rotating scatterers in both layers. Under a unified theoretical framework, two kinds of valley-projected topological acoustic insulators are distinguished analytically, i.e., the layer-mixed and layer-polarized topological valley Hall phases, respectively. The theory is evidently confirmed by our numerical and experimental observations of the nontrivial edge states that propagate along the interfaces separating different topological phases. Various applications such as sound communications in integrated devices can be anticipated by the intriguing acoustic edge states enriched by the layer information.

Understanding fragile topology: Exploiting topological features in materials is being pursued as a route to build in robustness of particular properties. Stemming from crystalline symmetries, such topological protection renders the properties robust against defects and provides a platform of rich physics to be studied. Recent developments have revealed the existence of so-called fragile topological phases, where the means of classification due to symmetry is unclear. Z.-D. Song et al. and Peri et al. present a combined theoretical and experimental approach to identify, classify, and measure the properties of fragile topological phases. By invoking twisted boundary conditions, they are able to describe the properties of fragile topological states and verify the expected experimental signature in an acoustic crystal. Understanding how fragile topology arises could be used to develop new materials with exotic properties. Science , this issue p. 794 , p. 797

Exceptional points and skin effect, as the two distinct hallmark features unique to the non-Hermitian physics, have each attracted enormous interests. Recent theoretical works reveal that the topologically nontrivial exceptional points can guarantee the non-Hermitian skin effect, which is geometry-dependent, relating these two unique phenomena. However, such novel relation remains to be confirmed by experiments. Here, we realize a non-Hermitian phononic crystal with exceptional points, which exhibits the geometry-dependent skin effect. The exceptional points connected by the bulk Fermi arcs, and the skin effects with the geometry dependence, are evidenced in simulations and experiments. Our work, building an experimental bridge between the exceptional points and skin effect and uncovering the unconventional geometry-dependent skin effect, expands a horizon in non-Hermitian physics.

The asymmetric electron dispersion in type-II Weyl semimetal theoretically hosts anisotropic transport properties. Here, we observe the significant anisotropic Adler-Bell-Jackiw (ABJ) anomaly in the Fermi-level delicately adjusted ${\mathrm{WTe}}_{1.98}$ crystals. Quantitatively, $C_W$, a coefficient representing the intensity of the ABJ anomaly along the $a$ and $b$ axis of ${\mathrm{WTe}}_{1.98}$ are 0.030 and $0.051{\mathrm{T}}^{-2}$ at 2 K, respectively. We found that the temperature-sensitive ABJ anomaly is attributed to a topological phase transition from a type-II Weyl semimetal to a trivial semimetal, which is verified by a first-principles calculation using experimentally determined lattice parameters at different temperatures. Theoretical electrical transport study reveals that the observation of an anisotropic ABJ along both the $a$ and $b$ axes in ${\mathrm{WTe}}_{1.98}$ is attributed to electrical transport in the quasiclassical regime. Our work may suggest that electron-doped ${\mathrm{WTe}}_2$ is an ideal playground to explore the novel properties in type-II Weyl semimetals.