Topological protection of bound states against the hybridization

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

Non-Abelian Topological Bound States in the Continuum

Bound states in the continuum (BICs), which are spatially localized states with energies lying in the continuum of extended modes, have been widely investigated in both quantum and classical systems. Recently, the combination of topological band theory with BICs has led to the creation of topological BICs that exhibit extraordinary robustness against disorder. However, the previously proposed topological BICs are only limited in systems with Abelian gauge fields. Whether non-Abelian gauge fields can induce topological BICs and how to experimentally explore these phenomena remains unresolved. Here, we report the theoretical and experimental realization of non-Abelian topological BICs, which are generated by the interplay between two inseparable pseudospins and can coexist in each pseudospin subspace. This unique characteristic necessitates non-Abelian couplings that lack any Abelian counterparts. Furthermore, the non-Abelian couplings can also offer a new avenue for constructing topological subspace-induced BICs at bulk dislocations. Those exotic phenomena are observed by non-Abelian topolectrical circuits. Our results establish the connection between topological BICs and non-Abelian gauge fields, and serve as the catalyst for future investigations on non-Abelian topological BICs across different platforms.

Structure, Merits, Gel Formation, Gel Preparation and Functions of Konjac Glucomannan and Its Application in Aquatic Food Preservation

Konjac glucomannan (KGM) is a natural polysaccharide extracted from konjac tubers that has a topological structure composed of glucose and mannose. KGM can be used as a gel carrier to load active molecules in food preservation. The three-dimensional gel network structure based on KGM provides good protection for the loaded active molecules and allows for sustained release, thus enhancing the antioxidant and antimicrobial activities of these molecules. KGM loaded with various active molecules has been used in aquatic foods preservation, with great potential for different food preservation applications. This review summarizes recent advances in KGM, including: (i) structural characterization, (ii) the formation mechanism, (iii) preparation methods, (iv) functional properties and (v) the preservation of aquatic food.

Universal Mirror-Stacking Approach for Constructing Topological Bound States in the Continuum

Bound states in the continuum (BICs) are counterintuitive localized states with eigenvalues embedded in the continuum of extended states. Recently, nontrivial band topology is exploited to enrich the BIC physics, resulting in topological BICs (TBICs) with extraordinary robustness against perturbations or disorders. Here, we propose a simple but universal mirror-stacking approach to turn nontrivial bound states of any topological monolayer model into TBICs. Physically, the mirror-stacked bilayer Hamiltonian can be decoupled into two independent subspaces of opposite mirror parities, each of which directly inherits the energy spectrum information and band topology of the original monolayer. By tuning the interlayer couplings, the topological bound state of one subspace can move into and out of the continuum of the other subspace continuously without hybridization. As representative examples, we construct one-dimensional first-order and two-dimensional higher-order TBICs, and demonstrate them unambiguously by acoustic experiments. Our findings will expand the research implications of both topological materials and BICs.

Lanthanide Ion Resonance-Driven Rayleigh Scattering of Nanoparticles for Dual-Modality Interferometric Scattering Microscopy

Light scattering from nanoparticles is significant in nanoscale imaging, photon confinement. and biosensing. However, engineering the scattering spectrum, traditionally by modifying the geometric feature of particles, requires synthesis and fabrication with nanometre accuracy. Here it is reported that doping lanthanide ions can engineer the scattering properties of low-refractive-index nanoparticles. When the excitation wavelength matches the ion resonance frequency of lanthanide ions, the polarizability and the resulted scattering cross-section of nanoparticles are dramatically enhanced. It is demonstrated that these purposely engineered nanoparticles can be used for interferometric scattering (iSCAT) microscopy. Conceptually, a dual-modality iSCAT microscopy is further developed to identify different nanoparticle types in living HeLa cells. The work provides insight into engineering the scattering features by doping elements in nanomaterials, further inspiring exploration of the geometry-independent scattering modulation strategy.

Frequency conversion in nano-waveguides using bound-state-in-continuum

Optical frequency conversion in semiconductor nanophotonic devices usually imposes stringent requirements on fabrication accuracy and etch surface roughness. Here, we adopt the concept of bound-state-in-continuum (BIC) for waveguide frequency converter design, which obviates the limitations in nonlinear material nano-fabrication and requires to pattern only a low-refractive-index strip on the nonlinear slab. Taking gallium phosphide (GaP) as an example, we study second-harmonic generation using horizontally polarized pump light at 1.55 µm phase matching to vertically polarized BIC modes. A theoretical normalized frequency conversion efficiency of 1.1×10⁴ % W ^-1 c m ^-2 is obtained using the fundamental BIC mode, which is comparable to that of conventional GaP waveguides.

Observation of Polarization Vortices in Momentum Space

The vortex, a fundamental topological excitation featuring the in-plane winding of a vector field, is important in various areas such as fluid dynamics, liquid crystals, and superconductors. Although commonly existing in nature, vortices were observed exclusively in real space. Here, we experimentally observed momentum-space vortices as the winding of far-field polarization vectors in the first Brillouin zone of periodic plasmonic structures. Using homemade polarization-resolved momentum-space imaging spectroscopy, we mapped out the dispersion, lifetime, and polarization of all radiative states at the visible wavelengths. The momentum-space vortices were experimentally identified by their winding patterns in the polarization-resolved isofrequency contours and their diverging radiative quality factors. Such polarization vortices can exist robustly on any periodic systems of vectorial fields, while they are not captured by the existing topological band theory developed for scalar fields. Our work provides a new way for designing high-Q plasmonic resonances, generating vector beams, and studying topological photonics in the momentum space.

A band of bound states in the continuum induced by disorder

Bound states in the continuum usually refer to the phenomenon of a single or a few discrete bound states embedded in a continuous spectrum of extended states. Here we propose a simple mechanism to achieve a band of bound states in the continuum in a class of disordered quasi-1D and quasi-2D systems, where the bound states and extended states overlap completely in a spectral range. The systems are partially disordered in a way that a band of extended states always exists, not affected by the randomness, whereas the states in all other bands become localized and cover the entire spectrum of extended states. We demonstrate such disordered-induced bound states in the continuum in disordered multi-chain and multi-layer systems.

Formation mechanism of guided resonances and bound states in the continuum in photonic crystal slabs

We develop a formalism, based on the mode expansion method, to describe the guided resonances and bound states in the continuum (BICs) in photonic crystal slabs with one-dimensional periodicity. This approach provides analytic insights to the formation mechanisms of these states: the guided resonances arise from the transverse Fabry–Pérot condition, and the divergence of the resonance lifetimes at the BICs is explained by a destructive interference of radiation from different propagating components inside the slab. We show BICs at the center and on the edge of the Brillouin zone protected by symmetry, BICs at generic wave vectors not protected by symmetry, and the annihilation of BICs at low-symmetry wave vectors.

Observation of surface states with algebraic localization

We introduce and experimentally demonstrate a class of surface bound states with algebraic decay in a one-dimensional tight-binding lattice. Such states have an energy embedded in the spectrum of scattered states and are structurally stable against perturbations of lattice parameters. Experimental demonstration of surface states with algebraic localization is presented in an array of evanescently coupled optical waveguides with tailored coupling rates.

Floquet bound states in the continuum

Quantum mechanics predicts that certain stationary potentials can sustain bound states with an energy buried in the continuous spectrum of scattered states, the so-called bound states in the continuum (BIC). Originally regarded as mathematical curiosities, BIC have found an increasing interest in recent years, particularly in quantum and classical transport of matter and optical waves in mesoscopic and photonic systems where the underlying potential can be judiciously tailored. Most of our knowledge of BIC is so far restricted to static potentials. Here we introduce a new kind of BIC, referred to as Floquet BIC, which corresponds to a normalizable Floquet state of a time-periodic Hamiltonian with a quasienergy embedded into the spectrum of Floquet scattered states. We discuss the appearance of Floquet BIC states in a tight-binding lattice model driven by an ac field in the proximity of the dynamic localization regime.

Tamm-Hubbard surface states in the continuum

In the framework of the Bose-Hubbard model, we show that two-particle surface bound states embedded in the continuum (BIC) can be sustained at the edge of a semi-infinite one-dimensional tight-binding lattice for any infinitesimally-small impurity potential V at the lattice boundary. Such thresholdless surface states, which can be referred to as Tamm-Hubbard BIC states, exist provided that the impurity potential V is attractive (repulsive) and the particle-particle Hubbard interaction U is repulsive (attractive), i.e. for UV < 0.