Second Chern crystals with inherently non-trivial topology.

Chern insulators have been generalized to many classical wave systems and thereby lead to many potential applications such as robust waveguides, quantum computation and high-performance lasers. However, the band structure of a material can be either topologically trivial or non-trivial, depending on how the crystal structure is designed. Here, we propose a second Chern crystal in a four-dimensional parameter space by introducing two extra synthetic translation dimensions. Since the topology of the bulk bands in the synthetic translation space is intrinsically non-trivial, our proposed four-dimensional crystal is guaranteed to be topologically non-trivial regardless of the crystal's detailed configuration. We derive the topologically protected modes on the lower dimensional boundaries of such a crystal via dimension reduction. Remarkably, we observe the one-dimensional gapless dislocation modes and confirm their robustness in experiments. Our findings provide novel perspectives on topologically non-trivial crystals and may inspire designs of classical wave devices.

Observation of robust edge mode and in-gap corner mode in Kagome surface-wave photonic crystals.

Recent theory has demonstrated that Kagome photonic crystals (PCs) support first-order and second-order topological phenomena. Here, we extend the topological physics of the Kagome lattice to surface electromagnetic waves and experimentally show a Kagome surface-wave PC. Under the protection of first-order and second-order topologies, both robust edge modes and in-gap corner modes are observed. The robust transport of edge modes is demonstrated by high transmission through the waveguide with a sharp bend. The localized corner mode is found at the corner with one isolated rod when a triangle-shaped sample is constructed. Our work not only shows a platform to mimic the topological physics in classical wave systems, but also offers a potential application in designing high-performance photonic devices.

Antichiral surface states in time-reversal-invariant photonic semimetals.

Besides chiral edge states, the hallmark of quantum Hall insulators, antichiral edge states can exhibit unidirectional transport behavior but in topological semimetals. Although such edge states provide more flexibility for molding the flow of light, their realization usually suffers from time-reversal breaking. In this study, we propose the realization of antichiral surface states in a time-reversal-invariant manner and demonstrate our idea with a three-dimensional (3D) photonic metacrystal. Our system is a photonic semimetal possessing two asymmetrically dispersed Dirac nodal lines. Via dimension reduction, the nodal lines are rendered a pair of offset Dirac points. By introducing synthetic gauge flux, each two-dimensional (2D) subsystem with nonzero kz is analogous to a modified Haldane model, yielding a kz-dependent antichiral surface transport. Through microwave experiments, the bulk dispersion with asymmetric nodal lines and associated twisted ribbon surface states are demonstrated in our 3D time-reversal-invariant system. Although our idea is demonstrated in a photonic system, we propose a general approach to realize antichiral edge states in time-reversal-invariant systems. This approach can be easily extended to systems beyond photonics and may pave the way for further applications of antichiral transport.

Direct Observation of Corner States in Second-Order Topological Photonic Crystal Slabs.

Recently, higher-order topological phases that do not obey the usual bulk-edge correspondence principle have been introduced in electronic insulators and brought into classical systems, featuring in-gap corner or hinge states. In this Letter, using near-field scanning measurements, we show the direct observation of corner states in second-order topological photonic crystal slabs consisting of periodic dielectric rods on a perfect electric conductor. Based on the generalized two-dimensional Su-Schrieffer-Heeger model, we show that the emergence of corner states roots in the nonzero edge dipolar polarization instead of the nonzero bulk quadrupole polarization. We demonstrate the topological transition of two-dimensional Zak phases of photonic crystal slabs by tuning intracell distances between two neighboring rods. We also directly observe in-gap one-dimensional edge states and zero-dimensional corner states in the microwave regime. Our work presents that the photonic crystal slab is a powerful platform to directly observe topological states and paves the way to study higher-order photonic topological insulators.