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Topological singularities, such as Weyl points and Dirac points, can give rise to unidirectional propagation channels known as chiral zero modes (CZMs) when subject to a magnetic field. These CZMs are responsible for intriguing phenomena like the chiral anomaly in quantum systems. The propagation direction of each CZM is determined by both the applied magnetic field and the topological charge of the singularity point. While counter-propagating CZMs have been observed in 2D and 3D systems, the realization of co-propagating CZMs has remained elusive. Here we present the first experimental observation of co-propagating CZMs in magnetic photonic crystals hosting a single pair of ideal Weyl points WPs. By manipulating the crystal's structural configuration, we spatially alter the locations of the WPs, creating pseudo-magnetic fields in opposite directions between them. This arrangement results in a pair of CZMs that possess the same group velocity and co-propagate. Our work opens up new possibilities for topological manipulation of wave propagation and may lead to advancements in optical waveguides, switches, and various other applications., Comment: 6 pages, 5 figures

Tellegen medium has long been a topic of debate, with its existence being contested over several decades. It was first proposed by Tellegen in 1948 and is characterized by a real-valued cross coupling between electric and magnetic responses, distinguishing it from the well-known chiral medium that has imaginary coupling coefficients. Significantly, Tellegen responses are closely linked to axion dynamics, an extensively studied subject in condensed matter physics. Here, we report the realization of Tellegen metamaterials in the microwave region through a judicious combination of subwavelength metallic resonators, gyromagnetic materials, and permanent magnet discs. We observe the key signature of the Tellegen response, i.e. a Kerr rotation for reflected wave, while the polarization remains the same in the transmission direction. The retrieved effective Tellegen parameter is several orders of magnitude greater than that of natural materials. Our work opens door to a variety of nonreciprocal photonic devices and may provide a platform for studying axion physics., Comment: 19 pages, 4 figures

Non-Hermitian physics has received great attention recently. In particular, band structures in non-Hermitian systems can be engineered to exhibit various topological effects. Among them, one of the most intriguing phenomena is the non-Hermitian skin effect (NHSE). Here, we investigate NHSE in systems featuring directed chains or directed graphs, where the arrows denote the directions of the non-reciprocal hopping between neighbouring nodes. We show that the systems exhibit pure skin modes with non-oscillatory wavefunctions, in contrast to previously studied NHSE. Interestingly, the sum of the decay constants along different directions for each skin mode obeys a power partition rule, i.e. their sum is a fixed value and the value of each constant only depends on the ratio between the non-reciprocal hopping parameters and is independent of detailed graph configurations. Such Pure Skin Effect (PSE) can be explained by using a generalized method for solving the Generalized Brillouin-zone with multiple bulk states., Comment: poster in Piers2024

Line excitations in topological phases are a subject of particular interest because their mutual linking structures encode robust topological information of matter. It has been recently shown that the linking and winding of complex eigenenergy strings can classify one-dimensional non-Hermitian topological matter. However, in higher dimensions, bundles of linked strings can emerge such that every string is mutually linked with all the other strings. Interestingly, despite being an unconventional topological structure, a non-Hermitian Hopf bundle has not been experimentally clarified. Here, we make the first attempt to explore the non-Hermitian Hopf bundle by visualizing the global linking structure of spinor strings in the momentum space of a two-dimensional electric circuit. By exploiting the flexibility of reconfigurable couplings between circuit nodes, we can study the non-Hermitian topological phase transition and gain insight into the intricate structure of the Hopf bundle. Furthermore, we find that the emergence of a higher-order skin effect in real space is accompanied by the linking of spinor strings in momentum space, revealing a bulk-boundary correspondence between the two domains. The proposed non-Hermitian Hopf bundle platform and visualization methodology pave the way to design new topologically robust non-Hermitian phases of matter.

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.

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

A topological pump enables robust transport of quantized particles when the system parameters are varied in a cyclic process. In previous studies, topological pump was achieved inhomogeneous systems guaranteed by a topological invariant of the bulk band structure when time is included as an additional synthetic dimension. Recently, bulk-boundary correspondence has been generalized to the bulk-disclination correspondence, describing the emergence of topological bounded states in the crystallographic defects protected by the bulk topology. Here we show the topological pumping can happen between different disclination states with different chiralities in an inhomogeneous structure. Based on a generalized understanding of the charge pumping process, we explain the topological disclination pump by tracing the motion of Wannier centers in each unit cell. Besides, by constructing two disclination structures and introducing a symmetry-breaking perturbation, we achieve a topological pumping between different dislocation cores. Our result opens a route to study the topological pumping in inhomogeneous topological crystalline systems and provides a flexible platform for robust energy transport., Comment: 6 pages, 4 figures

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

In crystals, two bands may cross each other and form degeneracies along a closed loop in the three-dimensional momentum space, which is called nodal line. Nodal line degeneracy can be designed to exhibit various configurations such as nodal rings, chains, links and knots. Very recently, non-Abelian band topology was proposed in nodal link systems, where the nodal lines formed by consecutive pairs of bands exhibit interesting braiding structures and the underlying topological charges are described by quaternions. Here, we experimentally demonstrate non-Abelian nodal links in a biaxial hyperbolic metamaterial. The linked nodal lines threading through each other are formed by the crossings between three adjacent bands. Based on the non-Abelian charges, we further analyze various admissible nodal link configurations for the three-band system. On the interface between the metamaterial and air, surface bound states in the continuum (BICs) are observed, which serves as the symmetry-enforced derivative of drumhead surface states from the linked nodal lines. Our work serves as a direct observation of the global topological structures of nodal links, and provides a platform for studying non-Abelian topological charge in the momentum space., Comment: 18 pages, 4 figures

Topological phases arise from the elegant mathematical structures imposed by the interplay between symmetry and topology1-5. From gapped topological insulators to gapless semimetals, topological materials in both quantum and classical systems, have grown rapidly in the last decade. Among them, three-dimensional Dirac semimetal lies at the topological phase transition point between various topological phases. It shares multiple exotic topological features with other topological materials, such as Fermi arcs and chiral anomaly with Weyl semimetals30, spin-dependent surface states with topological insulators29. In spite of the important role it plays in topological physics, no experimental observation of three-dimension Dirac points has been reported in classical systems so far. Here, we experimentally demonstrate three-dimension photonic Dirac points in an elaborately designed photonic metamaterial, in which two symmetrically placed Dirac points are stabilized by electromagnetic duality symmetry31. Spin-polarized surface arcs (counterparts of Fermi arcs in electronic systems) are demonstrated, which paves the way towards spin-multiplexed topological surface wave propagation. Closely linked to other exotic states through topological phase transitions, our system offers an effective medium platform for topological photonics., Comment: 18 pages, 4 figures

Cascaded optical field enhancement (CFE) can be realized in some specially designed multiscale plasmonic nanostructures, where the generation of extremely strong field at nanoscale volume is crucial for many applications, for example, surface enhanced Raman spectroscopy (SERS). Here, we propose a strategy of realizing a high-quality plasmonic nanoparticle-in-cavity (PIC) nanoantenna array, where strong coupling between a nanoparticle dark mode with a high order nanocavity bright mode can produce Fano resonance at a target wavelength. The Fano resonance can effectively boost the CFE in the PIC, with a field enhancement factor up to 5X10^2. A cost-effective and reliable nanofabrication method is developed with room temperature nanoimprinting lithography to manufacture high-quality PIC arrays. This technique guarantees the generation of only one gold nanoparticle at the bottom of each nanocavity, which is crucial for the generation of the expected CFE. As a demonstration of the performance and application of the PIC array, it is used as active SERS substrate for detecting 4-aminothiophenol molecules. The SERS enhancement factor up to 2X10^7 is obtained experimentally, verifying the field enhancement and potential of this device., Comment: 19 pages and 4 figures