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Traditional topological insulators often rely on band inversions driven by nonuniform hopping textures and spin-orbit coupling, as exemplified in the Su-Schrieffer-Heeger and Kane-Mele models. We present a novel approach utilizing the spatial nature of sublattice symmetry to induce nontrivial topological insulating properties characterized by second-order corner states without band inversion. To substantiate our proposal, we design a photonic crystal with non primitive translational symmetry, demonstrating unique directional waveguide edge modes and localized corner modes., Comment: 3 pages, 3 figures

The Su-Schrieffer-Heeger (SSH) chain is the reference model of a one-dimensional topological insulator. Its topological nature can be explained by the quantization of the Zak phase, due to reflection symmetry of the unit cell, or of the winding number, due to chiral symmetry. Here, we harness recent graph-theoretical results to construct families of setups whose unit cell features neither of these symmetries, but instead a so-called latent or hidden reflection symmetry. This causes the isospectral reduction -- akin to an effective Hamiltonian -- of the resulting lattice to have the form of an SSH model. As we show, these latent SSH models exhibit features such as multiple topological transitions and edge states, as well as a quantized Zak phase. Relying on a generally applicable discrete framework, we experimentally validate our findings using electric circuits.

Topological states have been widely investigated in different types of systems and lattices. In the present work, we report on topological edge states in double-wave (DW) chains, which can be described by a generalized Aubry-Andr\'e-Harper (AAH) model. For the specific system of a driven-dissipative exciton polariton system we show that in such potential chains, different types of edge states can form. For resonant optical excitation, we further find that the optical nonlinearity leads to a multistability of different edge states. This includes topologically protected edge states evolved directly from individual linear eigenstates as well as additional edge states that originate from nonlinearity-induced localization of bulk states. Extending the system into two dimensions (2D) by stacking horizontal DW chains in the vertical direction, we also create 2D multi-wave lattices. In such 2D lattices multiple Su-Schrieffer-Heeger (SSH) chains appear along the vertical direction. The combination of DW chains in the horizontal and SSH chains in the vertical direction then results in the formation of higher-order topological insulator corner states. Multistable corner states emerge in the nonlinear regime.

Surface waves supported by structured metallic surfaces, i.e. metasurfaces, have drawn wide attention recently. They are promising for various applications ranging from integrated photonic circuits to imaging and bio-sensing in various frequency regimes. In this work, we show that surface states with diverse polarization configurations can be supported by a metasurface consisting of a single layer of bianisotropic metamaterial elements. The structure possesses D2d symmetry, which includes mirror symmetry in the xz and yz plane, and C2 rotational symmetry along y = +-x axis. Due to this unique symmetry, the metasuface supports both transverse electric (TE) and transverse magnetic (TM) waves along kx and ky directions, while a purely longitudinal mode and an elliptically polarized transverse electromagnetic (TEM) mode along ky = +-kx directions. The versatility of the surface modes on the metasurface may lead to new surface wave phenomena and device applications.

There have been considerable efforts devoted to the study of topological phases in certain non-Hermitian systems that possess real eigenfrequencies in the presence of gain and loss. However, it is challenging to experimentally realize such non-Hermitian topological insulators in either quantum or photonic systems, due to the difficulties in introducing controlled gain and loss. On the other hand, the wide choices of active circuit components provide us with unprecedented convenience and flexibility in engineering non-Hermitian topological insulators in electrical circuits. Here, we report experimental realization of a one-dimensional (1D) non-Hermitian topological circuit which exhibits topologically protected edge state purely induced by gain and loss. We show that by tuning the value of the positive/negative resistors in the circuit, our system can switch between different topological phase regions. The topological edge states and interface states are observed at the circuit edge and at the interface between a trivial and nontrivial circuit, which are manifested by a prominent impedance peak at the mid-gap frequency topologically robust to variations of circuit parameters. Our work opens a new gateway towards actively controllable topological systems.

Topological phases of matter are conventionally characterized by the bulk-boundary correspondence in Hermitian systems: The topological invariant of the bulk in $d$ dimensions corresponds to the number of $(d-1)$-dimensional boundary states. By extension, higher-order topological insulators reveal a bulk-edge-corner correspondence, such that $n$-th order topological phases feature $(d-n)$-dimensional boundary states. The advent of non-Hermitian topological systems sheds new light on the emergence of the non-Hermitian skin effect (NHSE) with an extensive number of boundary modes under open boundary conditions. Still, the higher-order NHSE remains largely unexplored, particularly in the experiment. We introduce an unsupervised approach -- physics-graph-informed machine learning (PGIML) -- to enhance the data mining ability of machine learning with limited domain knowledge. Through PGIML, we experimentally demonstrate the second-order NHSE in a two-dimensional non-Hermitian topolectrical circuit. The admittance spectra of the circuit exhibit an extensive number of corner skin modes and extreme sensitivity of the spectral flow to the boundary conditions. The violation of the conventional bulk-boundary correspondence in the second-order NHSE implies that modification of the topological band theory is inevitable in higher dimensional non-Hermitian systems.

Topological photonic crystals (TPhCs) provide robust manipulation of light with built-in immunity to fabrication tolerances and disorder. Recently, it was shown that TPhCs based on weak topology with a dislocation inherit this robustness and further host topologically protected lower-dimensional localized modes. However, TPhCs with weak topology at optical frequencies have not been demonstrated so far. Here, we use scattering-type scanning near field optical microscopy to verify mid-bandgap zero-dimensional light localization close to 100 THz in a TPhC with nontrivial Zak phase and an edge dislocation. We show that due to the weak topology, differently extended dislocation centers induce similarly strong light localization. The experimental results are supported by full-field simulations. Along with the underlying fundamental physics, our results lay a foundation for the application of TPhCs based on weak topology in active topological nanophotonics, and nonlinear and quantum optic integrated devices due to their strong and robust light localization.

We study the negative couplings amid local resonances of photonic metasurfaces. In our analysis, we discover pseudo-spin-orbit coupled bulk modes leading to lines of circularly polarized radiation eigenstates in two-dimensional momentum space which were considered to exist only in three-dimensions. Our theoretical model is exemplified via a guided resonance dielectric metasurface that possesses Type-II Non-Hermitian diabolical points, from where the circular polarization lines emanate. The designed metasurface carries circular polarized radiation eigenstates in both the 0th and the 1st diffraction orders, allowing spin-selective light deflections. The high quality factor nature and field enhancement of the designed metasurface could lead to applications for spin-selective sensing, beam control and nonlinear optics. Our findings open a gateway for the design of near-field couplings assisted metasurfaces.

Metasurfaces have appeared as a versatile platform for miniaturized functional nonlinear optics due to their design freedom in tailoring wavefronts. The key factor that limits its application in functional devices is the low conversion efficiency. Recently, dielectric metasurfaces governed by either high-quality factor modes (quasi-bound states in the continuum) or Mie modes, enabling strong light-matter interaction, have become a prolific route to achieve high nonlinear efficiency. Here, we demonstrate both numerically and experimentally an effective way of spatial nonlinear phase control by using the Pancharatnam-Berry phase principle with a high third harmonic conversion efficiency of $10^{-4}$ $1/W^2$. We find that the magnetic Mie resonance appears to be the main contributor to the third harmonic response, while the contribution from the quasi-bound states in the continuum is negligible. This is confirmed by a phenomenological model based on coupled anharmonic oscillators. Besides, our metasurface provides experimentally a high diffraction efficiency (80-90%) in both polarization channels. We show a functional application of our approach by experimentally reconstructing an encoded polarization-multiplexed vortex beam array with different topological charges at the third harmonic frequency with high fidelity. Our approach has the potential viability for future on-chip nonlinear signal processing and wavefront control.

Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in momentum space, remain less explored. Here, we explain the theoretical concept of topological nodal lines and review recent and ongoing progress using artificial materials. The review includes recent demonstrations of non-Abelian topological charges of nodal lines in momentum space and examples of nodal lines realized in photonic and other systems. Finally, we will address the challenges involved in both experimental demonstration and theoretical understanding of topological nodal lines., Comment: 21 pages, 11 figures

Thouless pump is a one-dimensional dynamic topological effect that stems from the same topological mechanism as the renowned two-dimensional Chern insulators, with one momentum dimension replaced by a time variant evolution parameter. The underlying physics is abelian, concerning topologies of individual bands. By introducing multi-band non-abelian topology into pumping, much richer physics is expected that goes beyond the abelian counterpart. Here we report the observation of a non-abelian Thouless pump in an acoustic waveguide array with judiciously engineered coupling configurations. The observed non-abelian effect originates from time-evolution of eigen-states in Z_3 pump cycles that traverse across several band degeneracies in the parameter space in a three-band system. Interestingly, the pump of the eigenstates exhibits non-commutativity, i.e. the final state depends critically on the order of the pumping paths. Our study paves ways for exploring and utilizing non-abelian dynamical effects in classical systems., Comment: 9 pages, 5 figures

Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are insensitive to certain types of perturbations, thus naturally enhancing robustness of photonic circuitries. Conventionally, the N-dimensional bulk modes correspond to (N-1)-dimensional boundary states. The higher-order bulk-boundary correspondence relates N-dimensional bulk to boundary states with dimensionality reduced by more than 1. A special interest lies in miniaturization of such higher-order topological states to the nanoscale. Here, we realize nanoscale topological corner states in metasurfaces with C6-symmetric honeycomb lattices. We directly observe nanoscale topology-empowered edge and corner localizations of light and enhancement of light-matter interactions via a nonlinear imaging technique. Control of light at the nanoscale empowered by topology may facilitate miniaturization and on-chip integration of classical and quantum photonic devices., Comment: arXiv admin note: text overlap with arXiv:2011.10164

Weakly supervised object detection (WSOD) aims to classify and locate objects with only image-level supervision. Many WSOD approaches adopt multiple instance learning as the initial model, which is prone to converge to the most discriminative object regions while ignoring the whole object, and therefore reduce the model detection performance. In this paper, a novel cascade attentive dropout strategy is proposed to alleviate the part domination problem, together with an improved global context module. We purposely discard attentive elements in both channel and space dimensions, and capture the inter-pixel and inter-channel dependencies to induce the model to better understand the global context. Extensive experiments have been conducted on the challenging PASCAL VOC 2007 benchmarks, which achieve 49.8% mAP and 66.0% CorLoc, outperforming state-of-the-arts.

Topological states of light represent counterintuitive optical modes localized at boundaries of finite-size optical structures that originate from the properties of the bulk. Being defined by bulk properties, such boundary states are insensitive to certain types of perturbations, thus naturally enhancing robustness of photonic circuitries. Conventionally, the N-dimensional bulk modes correspond to (N-1)-dimensional boundary states. The higher-order bulk-boundary correspondence relates N-dimensional bulk to boundary states with dimensionality reduced by more than 1. A special interest lies in miniaturization of such higher-order topological states to the nanoscale. Here, we realize nanoscale topological corner states in metasurfaces with C6-symmetric honeycomb lattices. We directly observe nanoscale topology-empowered edge and corner localizations of light and enhancement of light-matter interactions via a nonlinear imaging technique. Control of light at the nanoscale empowered by topology may facilitate miniaturization and on-chip integration of classical and quantum photonic devices.

Second-order topological insulators (SOTIs) are the topological phases of matter in d dimensions that manifest (d-2)-dimensional localized modes at the intersection of the edges. We show that SOTIs can be designed via stacked Chern insulators with opposite chiralities connected by interlayer coupling. To characterize the bulk-corner correspondence, we establish a Jacobian-transformed nested Wilson loop method and an edge theory that are applicable to a wider class of higher-order topological systems. The corresponding topological invariant admits a filling anomaly of the corner modes with fractional charges. The system manifests a fragile topological phase characterized by the absence of a Wannier gap in the Wilson loop spectrum. Furthermore, we argue that the proposed approach can be generalized to multilayers. Our work offers perspectives for exploring and understanding higher-order topological phenomena., Comment: 5 pages, 4 figures

Weyl particles exhibit chiral transport property under external curved space-time geometry. This effect is called chiral gravitational effect, which plays an important role in quantum field theory. However, the absence of real Weyl particles in nature hinders the observation of such interesting phenomena. In this paper, we show that chiral gravitational effect can be manifested in Weyl metamaterials with spatially controlled nonlocality. This inhomogeneous modulation results in a spatially dependent group velocity in the Weyl cone dispersion, which is equivalent to introducing a curved background space-time (or gravitational field) for Weyl pseudo-spinors. The synthetic gravitational field leads to the quantization of energy levels, including chiral zeroth order energy modes (or simply chiral zero modes) that determine the chiral transport property of pseudo-spinors. The inhomogeneous Weyl metamaterial provides an experimentally realizable platform for investigating the interaction between Weyl particles and gravitational field, allowing for observation of chiral gravitational effect in table-top experiments.

Scatterings and transport in Weyl semimetals have caught growing attention in condensed matter physics, with observables including chiral zero modes and the associated magnetoresistance and chiral magnetic effects. Measurement of electrical conductance is usually performed in these studies, which, however, cannot resolve the momentum of electrons, preventing direct observation of the phase singularities in scattering matrix associated with Weyl point. Here we experimentally demonstrate a helical phase distribution in the angle (momentum) resolved scattering matrix of electromagnetic waves in a photonic Weyl metamaterial. It further leads to spiraling Fermi arcs in an air gap sandwiched between a Weyl metamaterial and a metal plate. Benefiting from the alignment-free feature of angular vortical reflection, our findings establish a new platform in manipulating optical angular momenta with photonic Weyl systems., Comment: 14 pages, 3 figures

Metamaterials, artificially engineered materials consisting of subwavelength unit cell, have shown potentials in light manipulation with their extraordinary optical properties. Especially, topological metamaterials possessing topologically protected surface states enable extremely robust control of light. Here, we demonstrate extremely broadband topological phase in a photonic topological metamaterials with double helix structure. In particular topological surface states are observed for all the frequencies below a certain cut-off, originating from a double Weyl point at zero frequency. The extreme bandwidth and robustness of the photonic topological metamaterial are beneficial for practical applications such as one-way waveguide and photonic integrated systems but also advantageous in design and fabrication since the only necessary condition is to satisfy the effective hyperbolic and chiral properties, without entailing strict periodic arrangement.

Weyl points, serving as monopoles in the momentum space and laying the foundation of topological gapless phases, have recently been experimentally demonstrated in various physical systems. However, none of the observed Weyl degeneracies are ideal: they either offset in energy or coexist with trivial dispersions at other momenta. The lack of an ideal Weyl system sets a serious limit to the further development of Weyl physics and potential applications. Here, by constructing a photonic metamaterial, we experimentally observe an ideal Weyl system, whose nodal frequencies are pinned by symmetries to exactly the same value. Benefitting from the ideal Weyl nodes, we are able to map out the complete evolution of the helicoid surface states spinning around the projections of each Weyl nodes. Our discovery provides an ideal photonic platform for Weyl systems and novel topological devices.