Observation of chiral edge states in gapped nanomechanical graphene

Parity-Frequency-Space Elastic Spin Control of Wave Routing in Topological Phononic Circuits

Topological phononic cavities, such as ring resonators with topological whispering gallery modes (TWGMs), offer a flexible platform for the realization of robust phononic circuits. However, the chiral mechanism governing TWGMs and their selective routing in integrated phononic circuits remain unclear. This work reveals, both experimentally and theoretically, that at a phononic topological interface, the elastic spin texture is intricately linked to, and can be explained through a knowledge of, the phonon eigenmodes inside each unit cell. Furthermore, for paired, counterpropagating TWGMs based on such interfaces in a waveguide resonator, this study demonstrates that the elastic spin exhibits locking at discrete frequencies. Backed up by theory, experiments on kHz TWGMs in thin honeycomb-lattice aluminum plates bored with clover-leaf shaped holes show that together with this spin-texture related angular-momentum locking mechanism at a single topological interface, there are triplicate parity-frequency-space selective wave routing mechanisms. In the future, these mechanisms can be harnessed for the versatile manipulation of elastic-spin based routing in phononic topological insulators.

Observation of Free-Boundary-Induced Chiral Anomaly Bulk States in Elastic Twisted Kagome Metamaterials

Chiral anomaly bulk states (CABSs) can be realized by choosing appropriate boundary conditions in a finite-size waveguide composed of two-dimensional Dirac semimetals, which have unidirectional and robust transport similar to that of valley edge states. CABSs use almost all available guiding space, which greatly improves the utilization of metamaterials. Here, free-boundary-induced CABSs in elastic twisted kagome metamaterials with C_{3v} symmetry are experimentally confirmed. The robust valley-locked transport and complete valley state conversion are experimentally observed. Importantly, the sign of the group velocity near the K and K^{'} points can be reversed by suspending masses at the boundary to manipulate the onsite potential. Moreover, CABSs are demonstrated in nanoelectromechanical phononic crystals by constructing an impedance-mismatched hard boundary. These results open new possibilities for designing more compact, space-efficient, and robust elastic wave macro- and microfunctional devices.

Engineering Gapless Edge States from Antiferromagnetic Chern Homobilayer

We put forward that stacked Chern insulators with opposite chiralities offer a strategy to achieve gapless helical edge states in two dimensions. We employ the square lattice as an example and elucidate that the gapless chiral and helical edge states emerge in the monolayer and antiferromagnetically stacked bilayer, characterized by Chern number C = - 1 and spin Chern number C S = - 1 , respectively. Particularly, for a topological phase transition to the normal insulator in the stacked bilayer, a band gap closing and reopening procedure takes place accompanied by helical edge states disappearing, where the Chern insulating phase in the monolayer vanishes at the same time. Moreover, EuO is revealed as a suitable candidate for material realization. This work is not only valuable to the research of the quantum anomalous Hall effect but also offers a favorable platform to realize magnetic topologically insulating materials for spintronics applications.

Dynamic topological domain walls driven by lithium intercalation in graphene

Stacking engineering in van der Waals (vdW) materials is a powerful method to control topological electronic phases for quantum device applications. Atomic intercalation into the vdW material can modulate the stacking structure at the atomic scale without a highly technical protocol. Here we report that lithium intercalation in a topologically structured graphene/buffer system on SiC(0001) drives dynamic topological domain wall (TDW) motions associated with stacking order change by using an in situ aberration-corrected low-energy electron microscope in combination with theoretical modelling. We observe sequential and selective lithium intercalation that starts at topological crossing points (AA stacking) and then selectively extends to AB stacking domains. Lithium intercalation locally changes the domain stacking order to AA and in turn alters the neighbouring TDW stacking orders, and continuous intercalation drives the evolution of the whole topological structure network. Our work reveals moving TDWs protected by the topology of stacking and lays the foundation for controlling the stacking structure via atomic intercalation. These findings open up new avenues to realize intercalation-driven vdW electronic devices.

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.

Experimental realization of chiral Landau levels in two-dimensional Dirac cone systems with inhomogeneous effective mass

Chiral zeroth Landau levels are topologically protected bulk states. In particle physics and condensed matter physics, the chiral zeroth Landau level plays a significant role in breaking chiral symmetry and gives rise to the chiral anomaly. Previous experimental works on such chiral Landau levels are mainly based on three-dimensional Weyl degeneracies coupled with axial magnetic fields. Their realizations using two-dimensional Dirac point systems, being more promising for future applications, were never experimentally realized before. Here we propose an experimental scheme for realizing chiral Landau levels in a two-dimensional photonic system. By introducing an inhomogeneous effective mass through breaking local parity-inversion symmetries, a synthetic in-plane magnetic field is generated and coupled with the Dirac quasi-particles. Consequently, the zeroth-order chiral Landau levels can be induced, and the one-way propagation characteristics are experimentally observed. In addition, the robust transport of the chiral zeroth mode against defects in the system is also experimentally tested. Our system provides a new pathway for the realization of chiral Landau levels in two-dimensional Dirac cone systems, and may potentially be applied in device designs utilizing the chiral response and transport robustness.

Wide-Field and Real-Time Super-Resolution Optical Imaging By Titanium Dioxide Nanoparticle-Assembled Solid Immersion Lens

Super-resolution optical imaging techniques can break the optical diffraction limit, thus providing unique opportunities to visualize the microscopic world at the nanoscale. Although near-field optical microscopy techniques have been proven to achieve significantly improved imaging resolution, most near-field approaches still suffer from a narrow field of view (FOV) or difficulty in obtaining wide-field images in real time, which may limit their widespread and diverse applications. Here, the authors experimentally demonstrate an optical microscope magnification and image enhancement approach by using a submillimeter-sized solid immersion lens (SIL) assembled by densely-packed 15 nm TiO₂ nanoparticles through a silicone oil two-step dehydration method. This TiO₂ nanoparticle-assembled SIL can achieve both high transparency and high refractive index, as well as sufficient mechanical strength and easy-to-handle size, thus providing a fast, wide-field, real-time, non-destructive, and low-cost solution for improving the quality of optical microscopic observation of a variety of samples, including nanomaterials, cancer cells, and living cells or bacteria under conventional optical microscopes. This study provides an attractive alternative to simplify the fabrication and applications of high-performance SILs.

Terahertz topological photonic crystals with dual edge states for efficient routing

Topological photonic crystals with robust pseudo-spin and valley edge states have shown promising and wide applications in topological waveguides, lasers, and antennas. However, the limited bandwidth and intrinsic coupling properties of a single pseudo-spin or valley edge state have imposed restrictions on their multifunctional applications in integrated photonic circuits. Here, we propose a topological photonic crystal that can support pseudo-spin and valley edge states simultaneously in a single waveguiding channel, which effectively broadens the bandwidth and enables a multipath routing solution for terahertz information processing and broadcasting. We show that distorted Kekulé lattices can open two types of bandgaps with different topological properties simultaneously by molding the inter- and intra-unit cell coupling of the tight-binding model. The distinct topological origins of the edge states provide versatile signal routing paths toward free space radiation or on-chip self-localized edge modes by virtue of their intrinsic coupling properties. Such a powerful platform could function as an integrated photonic chip with capabilities of broadband on-chip signal processing and distributions that will especially benefit terahertz wireless communications.

Observation of boundary induced chiral anomaly bulk states and their transport properties

The most useful property of topological materials is perhaps the robust transport of topological edge modes, whose existence depends on bulk topological invariants. This means that we need to make volumetric changes to many atoms in the bulk to control the transport properties of the edges in a sample. We suggest here that we can do the reverse in some cases: the properties of the edge can be used to induce chiral transport phenomena in some bulk modes. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hard-wall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap due to finite size effect. We experimentally observed robust valley-selected transport, complete valley state conversion, and valley focusing of the chiral anomaly bulk states (CABSs) in such phononic crystal waveguides. The same concept also applies to electromagnetics.

Boundary configured chiral edge states in valley topological photonic crystal

Chiral edge states (CESs) have been demonstrated at the external boundary of a valley photonic crystal (VPC), with flexibly tunable group velocity and frequency range by adjusting the boundary structure. In this work, we show parallel and antiparallel CESs located at two opposite VPC-air boundaries, which contain wave components belonging to opposite valleys or the same valley. In addition, we design a meta-structure with four types of air-contacted boundary that support CESs in different frequency ranges. The structure also has an internal interface channel supporting the valley edge state that bridges the top and bottom boundaries. We show that the CESs, while excited at a given port, can be exclusively guided to the other three ports, depending on the operating frequency. Our work provides an alternative way to design compact topological devices for optical waveguides and wave splitters.

Tracking Valley Topology with Synthetic Weyl Paths

Inspired by the newly emergent valleytronics, great interest has been attracted to the topological valley transport in classical metacrystals. The presence of nontrivial domain-wall states is interpreted with a concept of valley Chern number, which is well defined only in the limit of small band gap. Here, we propose a new visual angle to track the intricate valley topology in classical systems. Benefiting from the controllability of our acoustic metacrystals, we construct Weyl points in synthetic three-dimensional momentum space through introducing an extra structural parameter (rotation angle here). As such, the two-dimensional valley-projected band topology can be tracked with the strictly quantized topological charge in three-dimensional Weyl crystal, which features open surface arcs connecting the synthetic Weyl points and gapless chiral surface states along specific Weyl paths. All theoretical predictions are conclusively identified by our acoustic experiments. Our findings may promote the development of topological valley physics, which is less well defined yet under hot debate in multiple physical disciplines.

Nonreciprocal Single-Photon Band Structure

We study a single-photon band structure in a one-dimensional coupled-resonator optical waveguide that chirally couples to an array of two-level quantum emitters (QEs). The chiral interaction between the resonator mode and the QE can break the time-reversal symmetry without the magneto-optical effect and an external or synthetic magnetic field. As a result, nonreciprocal single-photon edge states, band gaps, and flat bands appear. By using such a chiral QE coupled-resonator optical waveguide system, including a finite number of unit cells and working in the nonreciprocal band gap, we achieve frequency-multiplexed single-photon circulators with high fidelity and low insertion loss. The chiral QE-light interaction can also protect one-way propagation of single photons against backscattering. Our work opens a new door for studying unconventional photonic band structures without electronic counterparts in condensed matter and exploring its applications in the quantum regime.

Extended topological valley-locked surface acoustic waves

Stable and efficient guided waves are essential for information transmission and processing. Recently, topological valley-contrasting materials in condensed matter systems have been revealed as promising infrastructures for guiding classical waves, for they can provide broadband, non-dispersive and reflection-free electromagnetic/mechanical wave transport with a high degree of freedom. In this work, by designing and manufacturing miniaturized phononic crystals on a semi-infinite substrate, we experimentally realized a valley-locked edge transport for surface acoustic waves (SAWs). Critically, original one-dimensional edge transports could be extended to quasi-two-dimensional ones by doping SAW Dirac “semimetal” layers at the boundaries. We demonstrate that SAWs in the extended topological valley-locked edges are robust against bending and wavelength-scaled defects. Also, this mechanism is configurable and robust depending on the doping, offering various on-chip acoustic manipulation, e.g., SAW routing, focusing, splitting, and converging, all flexible and high-flow. This work may promote future hybrid phononic circuits for acoustic information processing, sensing, and manipulation.