Robust boundary states epitomize how deep physics can give rise to concrete experimental signatures with technological promise. Of late, much attention has focused on two distinct mechanisms for boundary robustness—topological protection, as well as the non-Hermitian skin effect. In this work, we report the experimental realizations of hybrid higher-order skin-topological effect, in which the skin effect selectively acts only on the topological boundary modes, not the bulk modes. Our experiments, which are performed on specially designed non-reciprocal 2D and 3D topolectrical circuit lattices, showcases how non-reciprocal pumping and topological localization dynamically interplays to form various states like 2D skin-topological, 3D skin-topological-topological hybrid states, as well as 2D and 3D higher-order non-Hermitian skin states. Realized through our highly versatile and scalable circuit platform, theses states have no Hermitian nor lower-dimensional analog, and pave the way for applications in topological switching and sensing through the simultaneous non-trivial interplay of skin and topological boundary localizations.

Topological lasers are immune to imperfections and disorder. They have been recently demonstrated based on many kinds of robust edge states, which are mostly at the microscale. The realization of 2D on-chip topological nanolasers with a small footprint, a low threshold and high energy efficiency has yet to be explored. Here, we report the first experimental demonstration of a topological nanolaser with high performance in a 2D photonic crystal slab. A topological nanocavity is formed utilizing the Wannier-type 0D corner state. Lasing behaviour with a low threshold of approximately 1 µW and a high spontaneous emission coupling factor of 0.25 is observed with quantum dots as the active material. Such performance is much better than that of topological edge lasers and comparable to that of conventional photonic crystal nanolasers. Our experimental demonstration of a low-threshold topological nanolaser will be of great significance to the development of topological nanophotonic circuitry for the manipulation of photons in classical and quantum regimes.

Recently, a new family of symmetry-protected higher-order topological insulators has been proposed and was shown to host lower-dimensional boundary states. However, with the existence of the strong disorder in the bulk, the crystal symmetry is broken, and the associated corner states are disappeared. It is well known that the emergence of robust edge states and quantized transport can be induced by adding sufficient disorders into a topologically trivial insulator, that is the so-called topological Anderson insulator. The question is whether disorders can also cause the higher-order topological phase. This is not known so far, because interactions between disorders and the higher-order topological phases are completely different from those with the first-order topological system. Here, we demonstrate theoretically that the disorder-induced higher-order topological corner state and quantized fraction corner charge can appear in a modified Haldane model. In experiments, we construct the classical analog of such higher-order topological Anderson insulators using electric circuits and observe the disorder-induced corner state through the voltage measurement. Our work defies the conventional view that the disorder is detrimental to the higher-order topological phase, and offers a feasible platform to investigate the interaction between disorders and higher-order topological phases.

Recent theoretical studies have extended the Berry phase framework to account for higher electric multipole moments; quadrupole and octupole topological phases have been proposed. Although the two-dimensional quantized quadrupole insulators have been demonstrated experimentally, octupole topological phases have not previously been observed experimentally. Here we report on the experimental realization of a classical analog of the octupole topological insulator in the electric circuit system. Three-dimensional topolectrical circuits for realizing such topological phases are constructed experimentally. We observe octupole topological states protected by the topology of the bulk, which are localized at the corners. Our results provide conclusive evidence of a form of robustness against disorder and deformation, which is characteristic of octupole topological insulators. Our study opens a route toward higher-order topological phenomena in three dimensions and paves the way for employing topolectrical circuitry to study complex topological phenomena.

The discovery of novel topological states has served as a major branch in physics and material sciences. To date, most of the established topological states have been employed in Euclidean systems. Recently, the experimental realization of the hyperbolic lattice, which is the regular tessellation in non-Euclidean space with a constant negative curvature, has attracted much attention. Here, we demonstrate both in theory and experiment that exotic topological states can exist in engineered hyperbolic lattices with unique properties compared to their Euclidean counterparts. Based on the extended Haldane model, the boundary-dominated first-order Chern edge state with a nontrivial real-space Chern number is achieved. Furthermore, we show that the fractal-like midgap higher-order zero modes appear in deformed hyperbolic lattices, and the number of zero modes increases exponentially with the lattice size. These novel topological states are observed in designed hyperbolic circuit networks by measuring site-resolved impedance responses and dynamics of voltage packets. Our findings suggest a useful platform to study topological phases beyond Euclidean space, and may have potential applications in the field of high-efficient topological devices, such as topological lasers, with enhanced edge responses.

The novel physics of twisted bilayer graphene has motivated extensive studies of magic-angle flat bands hosted by moiré structures in electronic, photonic, and acoustic systems. On the other hand, bound states in the continuum (BICs) have also attracted great attention in recent years because of their potential applications in the field of designing superior optical devices. Here, we combine these two independent concepts to construct a new optical state in a twisted bilayer photonic crystal slab, which is called as moiré quasi-BIC, and numerically demonstrate that such an exotic optical state possesses dual characteristics of moiré flat bands and quasi-BICs. To illustrate the mechanism for the formation of moiré flat bands, we develop an effective model at the center of the Brillouin zone and show that moiré flat bands could be fulfilled by balancing the interlayer coupling strength and the twist angle around the band edge above the light line. Moreover, by decreasing the twist angle of moiré photonic crystal slabs with flat bands, it is shown that the moiré flat-band mode at the Brillouin center gradually approaches a perfect BIC, where the total radiation loss from all diffraction channels is significantly suppressed. To clarify the advantage of moiré quasi-BICs, enhanced second-harmonic generation (SHG) is numerically proven with a wide-angle optical source. The efficiency of SHG assisted by designed moiré quasi-BICs can be greatly improved compared with that based on dispersive quasi-BICs with similar quality factors.