Acoustic corner states in topological insulators with built-in Zeeman-like fields

The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored first-order topological insulators described by the Z_2 index. However, most recently, a proposal asserts that a significant bridge can be established between the HOTIs and the Z_2 topological insulators. When subject to an in-plane Zeeman field, the corner states, the signature of the HOTIs, can be induced in a Z_2 topological insulator. Such Zeeman field can be produced, for example, by the ferromagnetic proximity effect or magnetic atom doping, which obviously involves the drastically experimental complexity. Here we show that, a phononic crystal, designed as a bilayer of coupled acoustic cavities, hosts exactly the Kane-Mele model with built-in in-plane Zeeman fields. We observe that the helical edge states along the zigzag edges are gapped, and the corner states, localized spatially at the corners of the samples, appear in the gap, confirming the effect induced by the Zeeman field. We further demonstrate the intriguing contrast properties of the corner states at the outer and inner corners in a hexagonal ring-shaped sample.

Chiral Landau levels in Weyl semimetal NbAs with multiple topological carriers

Recently, Weyl semimetals have been experimentally discovered in both inversion-symmetry-breaking and time-reversal-symmetry-breaking crystals. The non-trivial topology in Weyl semimetals can manifest itself with exotic phenomena which have been extensively investigated by photoemission and transport measurements. Despite the numerous experimental efforts on Fermi arcs and chiral anomaly, the existence of unconventional zeroth Landau levels, as a unique hallmark of Weyl fermions which is highly related to chiral anomaly, remains elusive owing to the stringent experimental requirements. Here, we report the magneto-optical study of Landau quantization in Weyl semimetal NbAs. High magnetic fields drive the system towards the quantum limit which leads to the observation of zeroth chiral Landau levels in two inequivalent Weyl nodes. As compared to other Landau levels, the zeroth chiral Landau level exhibits a distinct linear dispersion in z momentum direction and allows the optical transitions without the limitation of zero z momentum or square root of magnetic field evolution. The magnetic field dependence of the zeroth Landau levels further verifies the predicted particle-hole asymmetry of the Weyl cones. Meanwhile, the optical transitions from the normal Landau levels exhibit the coexistence of multiple carriers including an unexpected massive Dirac fermion, pointing to a more complex topological nature in inversion-symmetry-breaking Weyl semimetals. Our results provide insights into the Landau quantization of Weyl fermions and demonstrate an effective tool for studying complex topological systems.

Experimental discovery of nodal chains

Three-dimensional (3D) topological nodal points, such as Weyl and Dirac nodes have attracted wide-spread interest across multiple disciplines and diverse material systems. Unlike nodal points that contain little structural variations, nodal lines can have numerous topological configurations in the momentum space, forming nodal rings, nodal chains and potentially nodal links and nodal knots. However, nodal lines have much less development for the lack of ideal material platforms. In condensed matter for example, nodal lines are often fragile to spin-orbit-coupling, locating off the Fermi level, coexisting with energy-degenerate trivial bands and dispersing strongly in energy of the line degeneracy. Here, overcoming all above difficulties, we theoretically predict and experimentally observe nodal chains in a metallic-mesh photonic crystal having frequency-isolated linear bandtouching rings chained across the entire Brillouin zone (BZ). These nodal chains are protected by mirror symmetries and have a frequency variation less than 1%. We used angle-resolved transmission (ART) to probe the projected bulk dispersions and performed Fourier-transformed field scan (FTFS) to map out the surface dispersions, which is a quadratic touching between two drumhead surface bands. Our results established an ideal nodal-line material for further studies of topological line-degeneracies with nontrivial connectivities, as well as the consequent wave dynamics richer than 2D Dirac and 3D Weyl materials.