Nodal links are special configurations of band degeneracies in the momentum space, where nodal line branches encircle each other. In $PT$ symmetric systems, nodal lines can be topologically characterized using the eigenvector frame rotations along an encircling loop and the linking structure can be described with non-Abelian frame charges involving adjacent bands. While the commutation rules between the frame charges are well established, the underlying relationship between distant band gap closing nodes remains to be explored. In this Letter, we present a photonic multiple nodal links system, where the nodal lines of nonadjacent bands are investigated with symmetry constraints on frame charges. Through an orthogonal nodal chain, the nodal line from the lower two bands predicts the existence of nodal lines formed between the higher bands. We designed and fabricated a metamaterial, with which the multiple nodal links and the topological connection between nonadjacent nodal lines are experimentally demonstrated.
Here we present an experimental observation of the self-organization effect of the polystyrene particles formed by acoustically-induced interaction forces. Two types of stable configurations are observed experimentally: one is mechanically equilibrium and featured by nonzero inter-particle separations, and the other corresponds to a close-packed assembly, which is formed by strong attractions among the aggregated particles. For the former case involving two or three particles, the most probable inter-particle separations (counted for numerous independent initial arrangements) agree well with the theoretical predictions. For the latter case, the number of the final stable configurations grows with the particle number, and the occurrence probability of each configuration is interpreted by a simple geometric model.
In this work, we study the acoustically mediated interaction forces among multiple well-separated spherical particles trapped in the same node or antinode plane of a standing wave. An analytical expression of the acoustic interaction force is derived, which is accurate even for the particles beyond the Rayleigh limit. Interestingly, the multi-particle system can be decomposed into a series of independent two-particle systems described by pairwise interactions. Each pairwise interaction is a long-range interaction, as characterized by a soft oscillatory attenuation (at the power exponent of n = −1 or −2). The vector additivity of the acoustic interaction force, which is not well expected considering the nonlinear nature of the acoustic radiation force, is greatly useful for exploring a system consisting of a large number of particles. The capability of self-organizing a big particle cluster can be anticipated through such acoustically controllable long-range interaction.
The robust transport of edge modes is perhaps the most useful property of topological materials. The existence of edge modes is guaranteed by the bulk-edge correspondence, which states that the number of topological edge modes is determined by the bulk topological invariants. To obtain robust transport on the edge, we need to make volumetric changes to many bulk atoms to control the properties of a few edge atoms in a lower dimension. We suggest here that we can do the reverse in some cases: the properties of the edge can guarantee chiral transport phenomena in some bulk modes, achieving phenomena that are essentially the same as those observed in topological valley-Hall systems. Specifically, we show that a topologically trivial 2D hexagonal phononic crystal slab (waveguide) bounded by hardwall boundaries guarantees the existence of bulk modes with chiral anomaly inside a pseudogap. 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.
Electromagnetic wave propagation in three-dimensional space typically suffers omnidirectional scattering when encountering obstacles. In this study, we employed Chern vectors to construct a topological heterostructure, where large-volume non-reciprocal topological transport in three-dimension is achieved. The shape of the cross-section in the heterostructure can be arbitrary designed, and we experimentally observed the distinctive cross-shaped field pattern transport, non-reciprocal energy harvesting, and most importantly, the remarkable ability of electromagnetic wave to traverse obstacles and abrupt structure changes without encountering reflections in 3D space.
Recently, a photonic alloy with non-trivial topological properties has been proposed, based on the random mixing of Yttrium Iron Garnet (YIG) and magnetized YIG rods. When the doping concentration of magnetized YIG rods is less than one, a chiral edge state (CES) of the topological photonic alloy appears in the frequency range of the non-trivial topological gap of the magnetized YIG crystal. In this work, we surprisingly find that by randomly mixing the Perfect Electric Conductor (PEC) and magnetized YIG rods in a square lattice, the photonic alloy system with appropriate doping concentrations can present CES in special frequency intervals even when both components support the propagation of bulk states. Analyzing the band structure of two components, we noticed a shift between the first trivial bandgap for PEC and the first topological bandgap for magnetized YIG. When calculating the transmission spectrum of the photonic alloy, we discovered that the frequency range for the topological gap gradually opens from the lower limit frequency of the bandgap for PEC to the bandgap for the magnetized YIG rods. The topological gap opening occurs as the doping concentration of magnetized YIG rods increases, creating an effective band alignment effect. Moreover, the topological gap for the photonic alloy is confirmed by calculating the reflection phase winding with the scattering method. Lastly, the gradual appearance of the CES is identified by applying Fourier transformation to real-space electromagnetic fields. Our work broadens the possibilities for flexible topological gap engineering in the photonic alloy system.
Chiral zeroth Landau levels are topologically protected bulk states that give rise to chiral anomaly. Previous discussions on such chiral Landau levels are based on three-dimensional Weyl degeneracies. Their realizations using two-dimensional Dirac point systems, being more promising for future applications, were never reported before. Here we propose a theoretical and experimental scheme for realizing chiral Landau levels in a photonic system. By introducing an inhomogeneous effective mass through breaking local parity inversion symmetries, the zeroth-order chiral Landau levels with one-way propagation characteristics are experimentally observed. In addition, the robust transport of the chiral zeroth mode against defects in the system is experimentally tested. Our system provides a new pathway for the realization of chiral Landau levels in two-dimensional Dirac systems, and may potentially be applied in device designs utilizing the transport robustness.
The conservation of CPT is considered applicable to all physical laws, but more and more research has discovered the possibility of CPT violation. This paper attempts to find a more complex and essential conservation than CPT conservation. This paper uses the method of theoretical structural analysis to discover the relationship between C, P, T symmetry, phase rotation symmetry, space rotation symmetry, and time translation symmetry, and prove the relationship between CPT symmetry, charge conservation, angular momentum conservation and energy conservation by studying the transformation modes of phase space, space, and time. Then the composition rules of uncertainty relationships and the fact that charge, weak isospin, and color charge are all related to the internal symmetry of matter are used to provide evidence for the inherent connection between charge, weak isospin rotation, and color charge demonstrating the similarity among these three. Finally, the joint conservation of CPT, weak isospin, and color charge are proposed.
We examine the optimal proportion of employee stocks in two kinds of duopoly markets: The first market includes two mixed‐ownership state‐owned enterprises (SOEs), and the second market includes one mixed‐ownership SOE and one private enterprise. We introduce the particularities of employee stock ownership plans in SOEs in China to the subjective function and cost function. We find that partial holding, full holding, or non‐holding can be optimal, and the optimal proportion depends on the types of rival firms, the efficiency gap in different kinds of shares, and employee behavioral tendencies. Moreover, the optimal proportion of employee stocks is subject to external institutional environment.
Photonic double-zero-index media, distinguished by concurrently zero-valued permittivity and permeability, exhibit extraordinary properties not found in nature. Remarkably, the notion of zero-index can be substantially expanded by generalizing the constitutive parameters from null scalars to nonreciprocal tensors with nonzero matrix elements but zero determinants. Here, we experimentally realize such a new class of gyromagnetic double-zero-index metamaterials possessing both double-zero-index features and nonreciprocal hallmarks. As an intrinsic property, this metamaterial always emerges at a spin-1/2 Dirac point of a topological phase transition. We discover and rigorously prove that a spatiotemporal reflection vortex singularity is always anchored to the metamaterial's Dirac point, with the vortex charge being determined by the topological invariant leap across the phase transition. This establishes a unique bulk-spatiotemporal vortex correspondence that extends the protected boundary effects into the time domain and exclusively characterizes topological phase transition points, setting it apart from any pre-existing bulk-boundary correspondence. Based on this correspondence, we propose and experimentally demonstrate a mechanism to deterministically generate optical spatiotemporal vortex pulses with firmly fixed central frequency and momentum, hence showing unparalleled robustness. Our findings uncover deep connections between zero-refractive-index photonics, topological photonics, and singular optics, opening the avenue for the manipulation of space-time topological light fields via the inherent topology of extreme-parameter metamaterials.
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