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We predict novel topological phases with broken time-reversal symmetry supporting the coexistence of opposite chiral edge states, which are fundamentally different from the photonic spin-Hall, valley-Hall, and higher-order topological phases. We find a fine-grained categorization of Chern insulators, their band topologies characterized by identical Chern number are completely different. Furthermore, we prove that different topologies cause zeros in their Bloch wavefunction overlaps, which imprint the band gap closing and appear at the degenerate points of topological phase transition. The Bloch wavefunction overlaps predict the reflection and refraction at a topological time boundary, and the overlap zeros ensure the existence of vanishing revival amplitude at critical times even though different topologies before and after the time boundary have identical Chern number. Our findings create new opportunities for topological metamaterials, uncover the topological feature hidden in the time boundary effect as a probe of topology, and open a venue for the exploration of the rich physics originating from the long-range couplings., Comment: 8 pages, 5 figures

Exceptional point and spectral singularity are two types of singularity that are unique to non-Hermitian systems. Here, we report the high-order spectral singularity as a high-order pole of the scattering matrix for a non-Hermitian scattering system, and the high-order spectral singularity is a unification of the exceptional point and spectral singularity. At the high-order spectral singularity, the scattering coefficients have high-order divergence and the scattering system stimulates high-order lasing. The wave emission intensity is polynomially enhanced, and the order of the growth in the polynomial intensity linearly scales with the order of the spectral singularity. Furthermore, the coherent input controls and alters the order of the spectral singularity. Our findings provide profound insights into the fundamentals and applications of high-order spectral singularities., Comment: 8 pages, 3 figures

Topological edge states are the core of topological photonics. Here we introduce the antihelical edge states of time-reversal symmetric topological metals and propose a photonic realization in an anisotropic square lattice of coupled ring resonators, where the clockwise and counterclockwise modes play the role of pseudospins. The antihelical edge states robustly propagate across the corners toward the diagonal of the square lattice: The same (opposite) pseudospins copropagate in the same (opposite) direction on the parallel lattice boundaries; the different pseudospins separate and converge at the opposite corners. The antihelical edge states in the topological metallic phase alter to the helical edge states in the topological insulating phase under a metal-insulator phase transition. The antihelical edge states provide a unique manner of topologically-protected robust light transport applicable for topological purification. Our findings create new opportunities for topological photonics and metamaterials., Comment: 8 pages, 7 figures

Topological metals possess gapless band structures accompanied with nontrivial edge states. Topological metals are created from the topological insulators by adjusting the magnetic flux. Here we propose the time-reversal symmetry protected topological metal without employing the magnetic flux. Topological metallic phase presents although the Chern number vanishes. In the topologically nontrivial phase, three different cases in the metallic phase are distinguished from the band-touching and in-gap features of the topological edge states. These findings shed light on the time-reversal symmetric topological metals and greatly simplify the realization of topological metals., Comment: 9 pages, 6 figures

We study an anisotropic two-dimensional non-Hermitian Lieb lattice, where the staggered gain and loss present in the horizontal and vertical directions, respectively. The intra-cell nonreciprocal coupling generates magnetic flux enclosed in the unit cell of the Lieb lattice and creates nontrivial topology. The active and dissipative topological edge states are along the horizontal and vertical directions, respectively. The two-dimensional non-Hermitian Lieb lattice also supports passive topological corner state. At appropriate magnetic flux, the non-Hermiticity can alter the corner state from one corner to the opposite corner as the non-Hermiticity increases. The gapless phase of the Lieb lattice is characterized by different configurations of exceptional points in the Brillouin zone. The topology of the anisotropic non-Hermitian Lieb lattices can be verified in many experimental platforms including the optical waveguide lattices, photonic crystals, and electronic circuits., Comment: 11 pages, 9 figures