Topological Phase Research Articles

Robust topological rainbow trapping in shamrock-leaf phononic crystal plates

Abstract The topological properties of elastic waves underpin the visions of widespread novel phonon devices such as topological rainbow trapping. In this work, a shamrock-leaf perforated phononic crystal with a graded interface is designed to achieve both the topological edge states (TES) and rainbow effect together. The topological rainbow mechanism activated by varying TES along the gradient interface is uncovered, and spatial trapped waves of different frequencies are presented. Meanwhile, based on the topological rainbow effect, the wave packet behaviors encountering various types of defects at interfaces are observed. Furthermore, deviations from the original trapping position under different disturbance factors are investigated. This work provides a useful handle for piloting applications of topological phononic transports.

Topological transmission and topological corner states combiner in all-dielectric honeycomb valley photonic crystals

Abstract We study the topological states (TSs) of all-dielectric honeycomb valley photonic crystals (VPCs). Breaking the space inversion symmetry of the honeycomb lattice by varying the filling ratio of materials for circular ring dielectric columns in the unit cell, which triggers topological phase transitions and thus achieves topological edge states (TESs) and topological corner states (TCSs). The results demonstrate that this structure has efficient photon transmission characteristics and anti-scattering robustness. In particular, we have found that changing the type of edge splicing between VPCs with different topological properties produces a change in the frequency of TCSs, and then based on this phenomenon, we have used a new method of adjusting only the type of edge splicing of the structure to design a novel TCSs combiner that can integrate four TCSs with different frequencies. This work not only expands the variety and number of unexplored TCSs that may exist in a fixed photonic band gap and can be rationalized to be selectively excited in the fixed configuration. Our study provides a feasible pathway for the design of integrated optical devices in which multiple TSs coexist in a single photonic system.

Harmonic generation with topological edge states and electron-electron interaction

Harmonic generation with topological edge states and electron-electron interaction

Designing Chiral Organometallic Nanosheets with Room-Temperature Multiferroicity and Topological Nodes.

Two-dimensional (2D) room-temperature chiral multiferroic and magnetic topological materials are essential for constructing functional spintronic devices, yet their number is extremely limited. Here, by using the chiral and polar HPP (HPP = 4-(3-hydroxypyridin-4-yl)pyridin-3-ol) as an organic linker and transition metals (TM = Cr, Mo, W) as nodes, we predict a class of 2D TM(HPP)2 organometallic nanosheets that incorporate homochirality, room-temperature magnetism, ferroelectricity, and topological nodes. The homochirality is introduced by chiral HPP linkers, and the change in structural chirality induces a topological phase transition of Weyl phonons. The room-temperature magnetism arises from the strong d-p spin coupling between TM cations and HPP doublet anions. The ferroelectricity is attributed to the breaking of spatial inversion symmetry in the lattice structure. Additionally, by adjusting the type of TMs, these nanosheets show rich and tunable band structures. Notably, all predicted materials are topologically nontrivial, featuring a quadratic nodal point around the Fermi level.

Topological bound states in the continuum in a non-Hermitian photonic system.

Topological insulators and bound states in the continuum represent two fascinating topics in the optical and photonic domain. The exploration of their interconnection and potential applications has emerged as a current research focus. Here, we investigated non-Hermitian photonics based on a parallel cascaded-resonator system, where both direct and indirect coupling between adjacent resonators can be independently manipulated. We observed the emergence of topological Fabry-Pérot bound states in the continuum in this non-Hermitian system, and theoretically validated its robustness. We also observed topological phase transitions and exceptional points in the same system. By elucidating the relationship between topological insulators and bound states in the continuum, this work will enable various applications that harness the advantages of bound states in the continuum, exceptional points, and topology. These applications may include optical delay and storage, highly robust optical devices, high-sensitivity sensing, and chiral mode switching.

Topological phases for extended objects: Semiclassical phase-space approach with tensorial coordinates

It has long been established that certain higher-dimensional topological phases of matter support extended objects like quasistrings and quasimembranes in their bulk states. In this study, we investigate the physics of these topological systems using a phase-space approach in the semiclassical regime, incorporating tensorial coordinates related to the extended objects. Specifically, we explore the semiclassical currents associated to open quasistrings in topological phases in three spatial dimensions, considering the presence of both coordinate-space Kalb-Ramond fields and momentum-space tensor Berry connections. Our results show that the currents associated to the endpoints of open quasistrings on the system’s boundary exhibit a quantum Hall response. This formalism accurately reproduces the boundary response as predicted by an Abelian BF theory proving a novel way to study extended objects in topological matter. Published by the American Physical Society 2025

Origin of Chiral Phase Transition of Polar Vortex in Ferroelectric/Dielectric Superlattices.

Chiral vortices and their phase transition in ferroelectric/dielectric heterostructures have drawn significant attention in the field of condensed matter. However, the dynamical origin of the chiral phase transition from achiral to chiral polar vortices has remained elusive. Here, we develop a phase-field perturbation model and discover the softening of out-of-plane vibration mode of polar vortices in [(PbTiO3)m/(SrTiO3)m]n superlattices at a critical epitaxial strain or temperature. The softening of the mode leads to the appearance of the axial polarization at vortex cores, resulting in chiral phase transition. It is found that the local negative permittivity plays a crucial role in the enhanced oscillation of axial polarization near the phase transition. Our findings not only reveal the origin of the chiral phase transition of polar vortices but also provide considerable new insight into the dynamics of topological structures and topological phase transitions in ferroelectric systems.

Strain manipulation of spin-polarized topological phase in WSe2/CrI3 heterostructure

Here, based on first-principles calculations and topological analysis, we show that the spin-polarized topological phase is present in a van der Waals (vdW) heterostructure WSe2/CrI3. We reveal that magnetism induced by proximity effects in the heterostructure breaks the time-reversal symmetry (TRS) and thus induces gapped topological edge states, exhibiting the TRS-breaking quantum spin Hall (QSH) effect. By applying a stress field, the WSe2/CrI3 heterostructure manifests enhanced spin polarization, Rashba splitting, and tunable bandgap. The TRS-breaking QSH effect observed in the WSe2/CrI3 heterostructure exhibits remarkable robustness against interlayer shearing. The distinct anisotropy associated with in-plane strain provides precise manipulation strategies for bandgap engineering. Notably, in-plane tensile strain can significantly increase the nontrivial bandgap by up to 98 meV, suggesting the magnetic WSe2/CrI3 heterostructure represents an outstanding platform for achieving the TRS-breaking QSH effect at room temperature. Our findings provide a theoretical foundation for the development of low-dissipation spintronic nanodevices.

Topology of far-field signals for photonic crystal slabs

The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high-order corner states. However, this work investigated the polarization distribution of radiated fields for photonic crystal slabs to get their far-field properties of band topology. We introduced a topological invariant—the winding number of far-field polarization around the Brillouin zone boundary and confirmed a robust correspondence between it and the Chern number of energy bands from the perspective of symmetry, which can be used to analyze the process of topological phase transition. It is found that changes in the winding number and Chern number, associated with the exchange of far-field polarization singularities, especially for bound states in the continuum, will emerge during phase transition. These findings offer insights for further understanding the intriguing properties of topological materials.

Plasmonic resonances of metallic moiré superlattices in the infrared range.

The recent surge of interest in moiré photonics arises from the possibility of exploring many groundbreaking physical phenomena in photonics. These phenomena include photonic topological states and magic-angle lasing, which offer an attractive platform for manipulating the flow and confinement of light from remarkably simple device geometries. In this work, we fabricate a series of metallic moiré superlattices supporting moiré plasmon polaritons and explore the moiré-potential induced plasmonic resonances. We demonstrate that two-dimensional moiré plasmonic superlattices exhibit transmittance and polarization-dependent responses because of the localized plasmonic resonances in the infrared range, whose modes have a near-flat dispersion band. Our findings hold the potential for the understanding of localized plasmonic resonances within moiré superlattices.

Phase transitions, Dirac and Weyl semimetal states in Mn1−xGexBi2Te4

Using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT), an experimental and theoretical study of changes in the electronic structure (dispersion dependencies) and corresponding modification of the energy band gap at the Dirac point (DP) for topological insulator (TI) have been carried out with gradual replacement of magnetic Mn atoms by non-magnetic Ge atoms when concentration of the latter was varied from 10% to 75%. It was shown that when Ge concentration increases, the bulk band gap decreases and reaches zero plateau in the concentration range of 45–60% while trivial surface states (TrSS) are present and exhibit an energy splitting of 100 and 70 meV in different types of measurements. It was also shown that TSS disappear from the measured band dispersions at a Ge concentration of about 40%. DFT calculations of band structure were carried out to identify the nature of observed band dispersion features and to analyze the possibility of magnetic Weyl semimetal state formation in this system. These calculations were performed for both antiferromagnetic (AFM) and ferromagnetic (FM) ordering types while the spin-orbit coupling (SOC) strength was varied or a strain (compression or tension) along the c-axis was applied. Calculations show that two different series of topological phase transitions (TPTs) may be implemented in this system, depending on the magnetic ordering. In the case of AFM ordering, the transition between TI and the trivial insulator phase passes through the Dirac semimetal state, whereas for FM phase such route admits three intermediate states instead of one (TI—Dirac semimetal—Weyl semimetal—Dirac semimetal—trivial insulator). Weyl points that form in the FM system along the direction annihilate when either the SOC strength decreases or a sufficient tensile strain is applied, which is accompanied by the corresponding TPTs. Model calculations of the influence of local magnetic ordering in AFM were carried out by alternating Mn layers with Ge-doped layers and showed that the magnetic Weyl semimetal state in this system is reachable at a Ge concentration of approximately 40% without application of any external magnetic fields.

Singular topological edge states in locally resonant metamaterials.

Band topology has emerged as a novel tool for material design across various domains, including photonic and phononic systems, and metamaterials. A prominent model for band topology is the Su-Schrieffer-Heeger (SSH) chain, which reveals topological in-gap states within Bragg-type gaps (BG) formed by periodic modification. Apart from classical BGs, another mechanism for bandgap formation in metamaterials involves strong coupling between local resonances and propagating waves, resulting in a local resonance-induced bandgap (LRG). Previous studies have shown the challenge of topological edge state emergence within the LRG. Here, we reveal that topological edge states can emerge within an LRG by achieving both topological phase and bandgap transitions simultaneously. We describe this using a model of inversion-symmetric extended SSH chains for locally resonant metamaterials. Notably, this topological state can lead to highly localized modes, comparable to a subwavelength unit cell, when it emerges within the LRG. We experimentally demonstrate distinct differences in topologically protected modes-highlighted by wave localization-between the BG and the LRG using locally resonant granule-based metamaterials. Our findings suggest the scope of topological metamaterials may be extended via their bandgap nature.

Replica wormholes and entanglement islands in the Karch-Randall braneworld

The Karch-Randall braneworld provides a natural set-up to study the Hawking radiation from a black hole using holographic tools. Such a black hole lives on a brane and is highly quantum yet has a holographic dual as a higher dimensional classical theory that lives in the ambient space. Moreover, such a black hole is coupled to a nongravitational bath which is absorbing its Hawking radiation. This allows us to compute the entropy of the Hawking radiation by studying the bath using the quantum extremal surface prescription. The quantum extremal surface geometrizes into a Ryu-Takayanagi surface in the ambient space. The topological phase transition of the Ryu-Takayanagi surface in time from connecting different portions of the bath to the one connecting the bath and the brane gives the Page curve of the Hawking radiation that is consistent with unitarity. Nevertheless, there doesn’t exit a derivation of the quantum extremal surface prescription and its geometrization in the Karch-Randall braneworld. In this paper, we fill this gap. We mainly focus on the case that the ambient space is (2+1)-dimensional for which explicit computations can be done in each description of the set-up. We show that the topological phase transition of the Ryu-Takayanagi surface corresponds to the formation of the replica wormhole on the Karch-Randall brane as the dominant contribution to the replica path integral. For higher dimensional situations, we show that the geometry of the brane satisfies Einstein’s equation coupled with conformal matter. We comment on possible implications to the general rule of gravitational path integral from this equation.

Photonic axion insulator.

Axions, hypothetical elementary particles that remain undetectable in nature, can arise as quasiparticles in three-dimensional crystals known as axion insulators. Previous implementations of axion insulators have largely been limited to two-dimensional systems, leaving their topological properties in three dimensions unexplored in experiment. Here, we realize an axion insulator in a three-dimensional photonic crystal and probe its topological properties. Demonstrated features include half-quantized Chern numbers on each surface that resembles a fractional Chern insulator, unidirectional chiral hinge states forming topological transport in three dimensions, and arithmetic operations between fractional and integer Chern numbers. Our work experimentally establishes the axion insulator as a three-dimensional topological phase of matter and enables chiral states to form complex, unidirectional three-dimensional networks through braiding.

Correspondence between Euler charges and nodal-line topology in Euler semimetals.

Real multi-bandgap systems have non-abelian topological charges, with Euler semimetals being a prominent example characterized by real triple degeneracies (RTDs) in momentum space. These RTDs serve as "Weyl points" for real topological phases. Despite theoretical interest, experimental observations of RTDs have been lacking, and studies mainly focus on individual RTDs. Here, we experimentally demonstrate physical systems with multiple RTDs in crystals, analyzing the distribution of Euler charges and their global connectivity. Through Euler curvature fields, we reveal that type I RTDs have quantized point Euler charges, while type II RTDs show continuously distributed Euler charges along nodal lines. We discover a correspondence between the Euler number of RTDs and the abelian/non-abelian topological charges of nodal lines, extending the Poincaré-Hopf index theorem to Bloch fiber bundles and ensuring nodal line connectivity. In addition, we propose a "no-go" theorem for RTD systems, mandating the balance of positive and negative Euler charges within the Brillouin zone.

Electrically Switchable Multi-Stable Topological States Enabled by Surface-Induced Frustration in Nematic Liquid Crystal Cells.

In liquid crystal (LC) cells, the surface patterning directs the self-assembly of the uniaxial building blocks in the bulk, enabling the design of stimuli-response optical devices with various functionalities. The combination of different anchoring patterns at both substrates can lead to surface induced frustration, preventing a purely planar and defect-free configuration. In cells with crossed assembly of rotating anchoring patterns, elastic deformations allow to obtain a defect-free bulk configuration, but an electrical stimulus can induce disclination lines. The disclination network is preserved without applied voltage. Depending on the electric field treatment and geometrical parameters, different multi-stable states with and without disclinations are obtained. This is demonstrated with the help of dual-frequency LCs, for which the frequency dependent dielectric properties allow repeatable switching between multi-stable states. Topological protection and the associated energy barrier between different states explains the observed metastability. The obtained configurations are retrieved with Q-tensor simulations and the validity is confirmed by matching optical simulations with experimentally obtained microscopy images. The realized multi-stable topological states interact differently with light, resulting in distinct optical properties. Optimization allows to switch between a highly transparent state and an opaque state, opening up opportunities for smart windows with low energy consumption.

Magnetic-proximity-induced anomalous Hall effect at the EuO/Sb2Te3 interface

Time-reversal symmetry breaking of a topological insulator phase generates zero-field edge modes which are the hallmark of the quantum anomalous Hall effect (QAHE) and of possible value for dissipation-free switching or non-reciprocal microwave devices. But present material systems exhibiting the QAHE, such as magnetically doped bismuth telluride and twisted bilayer graphene, are intrinsically unstable, limiting their scalability. A pristine magnetic oxide at the surface of a TI would leave the TI structure intact and stabilize the TI surface, but epitaxy of an oxide on the lower-melting-point chalcogenide presents a particular challenge. Here we utilize pulsed laser deposition to grow (111)-oriented EuO on vacuum cleaved and annealed Sb2Te3(0001) surfaces. Under suitable growth conditions, we obtain a pristine interface and surface, as evidenced by x-ray reflectivity and scanning tunneling microscopy, respectively. Despite bulk transport in the thick (2 mm) Sb2Te3layers, devices prepared for transport studies show a strong AHE, the necessary precursor to the QAHE. Our demonstration of EuO-Sb2Te3epitaxy presents a scalable thin film approach to realize QAHE devices with radically improved chemical stability as compared to competing approaches.

Topological Cavity Chains via Shifted Photonic Crystal Interfaces

Recent advances in topological photonics provide unprecedented opportunities to realize a photonic cavity. A recent work shows that the electromagnetic wave can be effectively trapped via the shifted photonic crystal interfaces (SPCIs), which offers an alternative approach to realizing the photonic cavity. Here, we proposed one-dimensional topological insulators based on an SPCIs-induced cavity chain, which is analogous to the Su–Schrieffer–Hegger model and is compatible with the silicon-on-insulator platform. Owing to the asymmetry feature of SPCIs-induced cavities, the topological cavity chains can be either realized by alternating the cavity modes or by tuning the distance between two cavities. The nontrivial band topology of SPCIs-induced cavity chains is further confirmed by observing topological end states, which exhibit robustness against geometrical imperfections. Our work holds promises for designing robust photonic devices, which may find potential applications in future integrated photonics.

Topological order in spin nematics from the quantum melting of a disclination lattice

Topological order in spin nematics from the quantum melting of a disclination lattice

Design and analysis of high-performance cascaded microring resonator and highly sensitive temperature sensor using photonic crystal–based topological edge state

Design and analysis of high-performance cascaded microring resonator and highly sensitive temperature sensor using photonic crystal–based topological edge state