Ideal type-II Weyl points in topological circuits

Bound-Extended Mode Transition in Type-II Synthetic Photonic Weyl Heterostructures

Photonic structures with Weyl points (WPs), including type I and type II, promise nontrivial surface modes and intriguing light manipulations for their three-dimensional topological bands. While previous studies mainly focus on exploring WPs in a uniform Weyl structure, here we establish Weyl heterostructures (i.e., a nonuniform Weyl lattice) with different rotational orientations in the synthetic dimension by nanostructured photonic waveguides. In this work, we unveil a transition between bound and extended modes on the interface of type-II Weyl heterostructures by tuning their rotational phases, despite the reversed topological order across the interface. This mode transition is also manifested from the total transmission to total reflection at the interface. All of these unconventional effects are attributed to the tilted dispersion of type-II Weyl band structure that can lead to mismatched bands and gaps across the interface. As a comparison, the type-I Weyl heterostructures lack the phase transition due to the untilted band structure. This work establishes a flexible scheme of artificial Weyl heterostructures that opens a new avenue toward high-dimensional topological effects and significantly enhances our capabilities in on-chip light manipulations.

Photonic Weyl Waveguide and Saddle-Chips-like Modes

Topological Weyl semimetals are characterized by open Fermi arcs on their terminal surfaces, these materials not only changed accepted concepts of the Fermi loop but also enabled many exotic phenomena, such as one-way propagation. The key prerequisite is that the two terminal surfaces have to be well separated, i.e., the Fermi arcs are not allowed to couple with each other. Thus, their interaction was overlooked before. Here, we consider coupled Fermi arcs and propose a Weyl planar waveguide, wherein we found a saddle-chips-like hybridized guiding mode. The hybridized modes consist of three components: surface waves from the top and bottom surfaces and bulk modes inside the Weyl semimetal. The contribution of these three components to the hybridized mode appears to be z-position-dependent rather than uniform. Beyond the conventional waveguide framework, those non-trivial surface states, with their arc-type band structures, exhibit strong selectivity in propagation direction, providing an excellent platform for waveguides. Compared with the conventional waveguide, the propagation direction of hybridized modes exhibits high z-position-dependency. For example, when the probe plane shifts from the top interface to the bottom interface, the component propagating horizontally becomes dimmer, while the component propagating vertically becomes brighter. Experimentally, we drilled periodic holes in metal plates to sandwich an ideal Weyl meta-crystal and characterize the topological guiding mode. Our study shows the intriguing behaviors of topological photonic waveguides, which could lead to beam manipulation, position sensing, and even 3D information processing on photonic chip. The Weyl waveguide also provides a platform for studying the coupling and the interaction between surface and bulk states.

Non-Abelian Topological Bound States in the Continuum

Bound states in the continuum (BICs), which are spatially localized states with energies lying in the continuum of extended modes, have been widely investigated in both quantum and classical systems. Recently, the combination of topological band theory with BICs has led to the creation of topological BICs that exhibit extraordinary robustness against disorder. However, the previously proposed topological BICs are only limited in systems with Abelian gauge fields. Whether non-Abelian gauge fields can induce topological BICs and how to experimentally explore these phenomena remains unresolved. Here, we report the theoretical and experimental realization of non-Abelian topological BICs, which are generated by the interplay between two inseparable pseudospins and can coexist in each pseudospin subspace. This unique characteristic necessitates non-Abelian couplings that lack any Abelian counterparts. Furthermore, the non-Abelian couplings can also offer a new avenue for constructing topological subspace-induced BICs at bulk dislocations. Those exotic phenomena are observed by non-Abelian topolectrical circuits. Our results establish the connection between topological BICs and non-Abelian gauge fields, and serve as the catalyst for future investigations on non-Abelian topological BICs across different platforms.

Non-Abelian Inverse Anderson Transitions

Inverse Anderson transitions, where the flat-band localization is destroyed by disorder, have been wildly investigated in quantum and classical systems in the presence of Abelian gauge fields. Here, we report the first investigation on inverse Anderson transitions in the system with non-Abelian gauge fields. It is found that pseudospin-dependent localized and delocalized eigenstates coexist in the disordered non-Abelian Aharonov-Bohm cage, making inverse Anderson transitions depend on the relative phase of two internal pseudospins. Such an exotic phenomenon induced by the interplay between non-Abelian gauge fields and disorder has no Abelian analogy. Furthermore, we theoretically design and experimentally fabricate non-Abelian Aharonov-Bohm topolectrical circuits to observe the non-Abelian inverse Anderson transition. Through the direct measurements of frequency-dependent impedance responses and voltage dynamics, the pseudospin-dependent non-Abelian inverse Anderson transitions are observed. Our results establish the connection between inverse Anderson transitions and non-Abelian gauge fields, and thus comprise a new insight on the fundamental aspects of localization in disordered non-Abelian flat-band systems.

Topological antichiral surface states in a magnetic Weyl photonic crystal

Chiral edge states that propagate oppositely at two parallel strip edges are a hallmark feature of Chern insulators which were first proposed in the celebrated two-dimensional (2D) Haldane model. Subsequently, counterintuitive antichiral edge states that propagate in the same direction at two parallel strip edges were discovered in a 2D modified Haldane model. Recently, chiral surface states, the 2D extension of one-dimensional (1D) chiral edge states, have also been observed in a photonic analogue of a 3D Haldane model. However, despite many recent advances in antichiral edge states and chiral surface states, antichiral surface states, the 2D extension of 1D antichiral edge states, have never been realized in any physical system. Here, we report the experimental observation of antichiral surface states by constructing a 3D modified Haldane model in a magnetic Weyl photonic crystal with two pairs of frequency-shifted Weyl points (WPs). The 3D magnetic Weyl photonic crystal consists of gyromagnetic cylinders with opposite magnetization in different triangular sublattices of a 3D honeycomb lattice. Using microwave field-mapping measurements, unique properties of antichiral surface states have been observed directly, including the antichiral robust propagation, tilted surface dispersion, a single open Fermi arc connecting two projected WPs and a single Fermi loop winding around the surface Brillouin zone (BZ). These results extend the scope of antichiral topological states and enrich the family of magnetic Weyl semimetals.

Acoustic Higher-Order Weyl Semimetal with Bound Hinge States in the Continuum

Higher-order topological phases have raised widespread interest in recent years with the occurrence of the topological boundary states of dimension two or more less than that of the system bulk. The higher-order topological states have been verified in gapped phases, in a wide variety of systems, such as photonic and acoustic systems, and recently also observed in gapless semimetal phase, such as Weyl and Dirac phases, in systems alike. The higher-order topology is signaled by the hinge states emerging in the common band gaps of the bulk states and the surface states. In this Letter, we report our first prediction and observation of a new type of hinge states, the bound hinge states in the continuum (BHICs) bulk band, in a higher-order Weyl semimetal implemented in phononic crystal. In contrast to the hinge state in gap, which is characterized by the bulk polarization, the BHIC is identified by the nontrivial surface polarization. The finding of the topological BHICs broadens our insight to the topological states, and may stimulate similar researches in other systems such as electronic, photonic, and cold atoms systems. Our Letter may pave the way toward high-Q acoustic devices in application.

Square-root higher-order Weyl semimetals

The mathematical foundation of quantum mechanics is built on linear algebra, while the application of nonlinear operators can lead to outstanding discoveries under some circumstances, such as the prediction of positron, a direct outcome of the Dirac equation which stems from the square-root of the Klein-Gordon equation. In this article, we propose a model of square-root higher-order Weyl semimetal (SHOWS) by inheriting features from its parent Hamiltonians. It is found that the SHOWS hosts both “Fermi-arc” surface and hinge states that respectively connect the projection of the Weyl points on the side surface and arris. We theoretically construct and experimentally observe the exotic SHOWS state in three-dimensional (3D) stacked electric circuits with honeycomb-kagome hybridizations and double-helix interlayer couplings. Our results open the door for realizing the square-root topology in 3D solid-state platforms.

The topological properties of square-root Weyl semimetals are derived from the square of the Hamiltonian. Here, the authors propose a tight-binding model for a square-root higher-order Weyl semimetal hosting both Fermi-arc surface and hinge states.

Fully integrated topological electronics

Topological insulators (TIs) have attracted significant attention in photonics and acoustics due to their unique physical properties and promising applications. Electronics has recently emerged as an exciting arena to study various topological phenomena because of its advantages in building complex topological structures. Here, we explore TIs on an integrated circuit (IC) platform with a standard complementary metal-oxide-semiconductor technology. Based on the Su–Schrieffer–Heeger model, we design a fully integrated topological circuit chain using multiple capacitively-coupled inductor–capacitor resonators. We perform comprehensive post-layout simulations on its physical layout to observe and evaluate the salient topological features. Our results demonstrate the existence of the topological edge state and the remarkable robustness of the edge state against various defects. Our work shows the feasibility and promise of studying TIs with IC technology, paving the way for future explorations of large-scale topological electronics on the scalable IC platform.

Experimental Realization of Two-Dimensional Weak Topological Insulators

We report the experimental realization of a two-dimensional (2D) weak topological insulator (WTI) in spinless Su-Schrieffer-Heeger circuits with parity-time and chiral symmetries. Strong and weak Z2 topological indexes are adopted to explain the experimental findings that a Dirac semimetal (DSM) phase and four WTI phases emerge in turn when we modulate the centrosymmetric circuit deformations. In the DSM phase, it is found that the Dirac cone is highly anisotropic and that it is not pinned to any high-symmetry points but can widely move within the Brillouin zone, which eventually leads to the phase transition between WTIs. In addition, we observe a pair of flat-band domain wall states by designing spatially inhomogeneous node connections. Our work provides the first experimental evidence for 2D WTIs, which significantly advances our understanding of the strong and weak nature of topological insulators, the robustness of flat bands, and the itinerant and anisotropic features of Dirac cones.

Ideal type-II Weyl points in twisted one-dimensional dielectric photonic crystals

We proposed an one-dimensional layer-stacked photonic crystal using anisotropic materials to realize ideal type-II Weyl points. The topological transition from Dirac to Weyl points can be clearly observed by tuning the twist angle between layers. Also, on the interface between the photonic type-II Weyl material and air, gapless surface states have been demonstrated in an incomplete bulk bandgap. By breaking parameter symmetry, these ideal type-II Weyl points would transform into the non-ideal ones, exhibiting topological surface states with single group velocity. Our work may provide a new idea for the realization of photonic semimetal phases by utilizing naturally anisotropic materials.

Valley Hall edge solitons in a photonic graphene

We predict the existence and study properties of the valley Hall edge solitons in a composite photonic graphene with a domain wall between two honeycomb lattices with broken inversion symmetry. Inversion symmetry in our system is broken due to detuning introduced into constituent sublattices of the honeycomb structure. We show that nonlinear valley Hall edge states with sufficiently high amplitude bifurcating from the linear valley Hall edge state supported by the domain wall, can split into sets of bright spots due to development of the modulational instability, and that such an instability is a precursor for the formation of topological bright valley Hall edge solitons localized due to nonlinear self-action and travelling along the domain wall over large distances. Topological protection of the valley Hall edge solitons is demonstrated by modeling their passage through sharp corners of the Ω-shaped domain wall.

Dynamic Observation of Topological Soliton States in a Programmable Nanomechanical Lattice

Topological soliton states, existing in the topological structures with edge defect or interface defect, are usually studied under steady state. Here, we experimentally observe the dynamic processes of the generation and the extinction of such soliton states in the Su-Schrieffer-Heeger model. The different topological structures are implemented on a programmable nanomechanical lattice, consisting of eight adjacent string resonators which are parametrically coupled by manipulation voltages. Moreover, the beating and localization behaviors at different topological interfaces are also observed in the same device. These results explicitly exhibit the dynamic processes of topological soliton states, which reveal real potential toward integrated multifunctional topological materials.