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We introduce the notion of topological electronic states on random lattices in non-integer dimensions. By considering a class $D$ model on critical percolation clusters embedded in two dimensions, we demonstrate that these topological…
Quantum entanglement, as the strictly non-classical phenomena, is the kernel of quantum computing and quantum simulation, and has been widely applied ranging from fundamental tests of quantum physics to quantum information processing. The…
Topological quantum phases underpin many concepts of modern physics. While the existence of disorder-immune topological edge states of electrons usually requires magnetic fields, direct effects of magnetic field on light are very weak. As a…
We report the entanglement of topological features, namely, isolated, linked optical vortex loops in the light from spontaneous parametric down-conversion (SPDC). In three dimensions, optical vortices are lines of phase singularity and…
Photonic topological systems, the electromagnetic analog of the topological materials in condensed matter physics, create many opportunities to design optical devices with novel properties. We present an experimental realization of the…
Topological phonics has emerged as a novel approach to engineer the flow of light and provides unprecedented means for developing diverse photonic elements, including robust optical waveguides immune to structural imperfections. However,…
Recent discoveries in topological physics hold a promise for disorder-robust quantum systems and technologies. Topological states provide the crucial ingredient of such systems featuring increased robustness to disorder and imperfections.…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…
The proposition that band geometry alone can protect optical states against disorder has proven not merely theoretically elegant but experimentally incontrovertible. A key attribute of photonic topological systems is their capacity to…
The introduction of topological concepts to the design of photonic crystal cavities holds great promise for applications in integrated photonics due to the prospect of topological protection. This study examines the signatures of…
The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at…
Quadrupole topological phases, exhibiting protected boundary states that are themselves topological insulators of lower dimensions, have recently been of great interest. Extensions of these ideas from current tight binding models to…
We introduce topological defect to a square lattice of elliptical cylinders. Despite the broken translational symmetry, the long-range positional order of the cylinders leads to residual photonic bandgap in the density of optical states.…
Topological defects (TDs) in crystal lattices are elementary lattice imperfections that cannot be removed by local perturbations, due to their real space topology. We show that adding TDs into a valley photonic crystal generates a lattice…
Harnessing high-dimensional entangled states of light presents a frontier for advancing quantum information technologies, from fundamental tests of quantum mechanics to enhanced computation and communication protocols. In this context, the…
Topological phases usually are unreachable in molecular solids, which are characteristic of weakly dispersed energy bands with a large gap, in contrast to topological materials. In this work, however, we propose that nontrivial electronic…
Two-dimensional photonic crystals made of six air holes on a core-shell dielectric material has been proposed to study the newly emerged photonic quantum spin Hall insulator. Specifically, radii modification of the air holes and core-shell…
Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…
Two-dimensional (2D) noble-metal dichalcogenides have emerged as a new platform for the realization of versatile flat optics with a considerable degree of miniaturization. However, light field manipulation at the atomic scale is widely…