Topological edge and corner states of valley photonic crystals with zipper-like boundary conditions

We present a stable valley photonic crystal(VPC)unit cell with C_(3v)symmetric quasi-ring-shaped dielectric columns and realize its topological phase transition by breaking mirror symmetry.Based on this unit cell structure,topological edge states(TESs)and topological corner states(TCSs)are realized.We obtain a new type of wave transmission mode based on photonic crystal zipper-like boundaries and apply it to a beam splitter assembled from rectangular photonic crystals(PCs).The constructed beam splitter structure is compact and possesses frequency separation functions.In addition,we construct a box-shaped triangular PC structures with zipper-like boundaries and discover phenomena of TCSs in the corners,comparing its corner states with those formed by other boundaries.Based on this,we explore the regularities of the electric field patterns of TESs and TCSs,explain the connection between the characteristic frequencies and locality of TCSs,which helps better control photons and ensures low power consumption of the system.

Topological superconductors with spin-triplet pairings and Majorana Fermi arcs

We construct a three-dimensional topological superconductor Bogoliubov–de Gennes(BdG)Hamiltonian with the normal state being a three-dimensional topological insulator.By introducing inter-orbital spin-triplet pairings term△3,there are topological Majorana nodes in the bulk and they are connected by Majorana Fermi arcs on the surface,similar to the case of Weyl semimetal.Furthermore,by adding an inversion-breaking term to the normal state,momentum-independent pairing terms with different parities can coexist in the Bd G Hamiltonian,which creates more Majorana modes similar to Andreev bound states and a richer phase diagram.

Interacting topological magnons in a checkerboard ferromagnet

This work is devoted to studying the magnon-magnon interaction effect in a two-dimensional checkerboard ferromagnet with the Dzyaloshinskii-Moriya interaction.Using a first-order Green function method,we analyze the influence of magnon-magnon interaction on the magnon band topology.We find that Chern numbers of two renormalized magnon bands are different above and below the critical temperature,which means that the magnon band gap-closing phenomenon is an indicator for one topological phase transition of the checkerboard ferromagnet.Our results show that the checkerboard ferromagnet possesses two topological phases,and its topological phase can be controlled either via the temperature or the applied magnetic field due to magnon-magnon interactions.Interestingly,it is found that the topological phase transition can occur twice with the increase in the temperature,which is different from the results of the honeycomb ferromagnet.

Topological phases and edge modes of an uneven ladder

We investigate the topological properties of a two-chain quantum ladder with uneven legs,i.e.,the two chains differ in their periods by a factor of 2.Such an uneven ladder presents rich band structures classified by the closure of either direct or indirect bandgaps.It also provides opportunities to explore fundamental concepts concerning band topology and edge modes,including the difference of intracellular and intercellular Zak phases,and the role of the inversion symmetry(IS).We calculate the Zak phases of the two kinds and find excellent agreement with the dipole moment and extra charge accumulation.We also find that configurations with IS feature a pair of degenerate two-side edge modes emerging as the closure of the direct bandgap,while configurations without IS feature one-side edge modes emerging as not only the closure of both direct and indirect bandgaps but also within the band continuum.Furthermore,by projecting to the two sublattices,we find that the effective Bloch Hamiltonian corresponds to that of a generalized Su–Schrieffer–Heeger model or the Rice–Mele model whose hopping amplitudes depend on the quasimomentum.In this way,the topological phases can be efficiently extracted through winding numbers.We propose that uneven ladders can be realized by spin-dependent optical lattices and their rich topological characteristics can be examined by near future experiments.

Progress and realization platforms of dynamic topological photonics

Dynamic topological photonics is a novel research field, combining the time-domain optics and topological physics.In this review, the recent progress and realization platforms of dynamic topological photonics have been well introduced.The definition, measurement methods and the evolution process of the dynamic topological photonics are demonstrated to better understand the physical diagram. This review is meant to bring the readers a different perspective on topological photonics, grasp the advanced progress of dynamic topology, and inspire ideas about future prospects.

Floquet-Engineering Topological Phase Transition in Graphene Nanoribbons by Light

Quasi-one-dimensional(1D)graphene nanoribbons(GNRs)play a crucial role in advancement of nextgeneration devices.Recent studies have suggested their potential to exhibit unique symmetry-protected topological phases defined by a𝑍2 invariant.By employing both the tight-binding model and the Floquet theory,our investigation demonstrates the effective control of the topological phase within quasi-1D armchair GNRs(AGNRs)using elliptically polarized light,unveiling rich topological phase diagrams.Specifically,we observe that varying the amplitude of the light can induce transitions in the band gap(𝐸g)of AGNRs,leading to multiple changes in the system’s𝑍2 invariant.Furthermore,for heterojunctions composed of different AGNR segments,the junction state can be either created or eliminated by the application of elliptically polarized light.

Magnetic Topological Dirac Semimetal Transition Driven by SOC in EuMg_(2)Bi_(2)

Magnetic topological semimetals have been at the forefront of condensed matter physics due to their ability to exhibit exotic transport phenomena.Investigating the interplay between magnetic and topological orders in systems with broken time-reversal symmetry is crucial for realizing non-trivial quantum effects.We delve into the electronic structure of the rare-earth-based antiferromagnetic Dirac semimetal EuMg_(2)Bi_(2) using first-principles calculations and angle-resolved photoemission spectroscopy.Our calculations reveal that the spin-orbit coupling(SOC)in EuMg_(2)Bi_(2) prompts an insulator to topological semimetal transition,with the Dirac bands protected by crystal symmetries.The linearly dispersive states near the Fermi level,primarily originating from Bi 6p orbitals,are observed on both the(001)and(100)surfaces,confirming that EuMg_(2)Bi_(2) is a three-dimensional topological Dirac semimetal.This research offers pivotal insights into the interplay between magnetism,SOC and topological phase transitions in spintronics applications.

Different topological phase transitions in the Su–Schrieffer–Heeger model under different disorder structures

We investigate the topological phase transition in the Su–Schrieffer–Heeger model with the long-range hopping and quasi-periodic modulation.By numerically calculating the real-space winding number,we obtain topological phase diagrams for different disordered structures.These diagrams suggest that topological phase transitions are different by selecting the specific disordered structure.When quasi-periodic modulation is applied to intracell hopping,the resulting disorder induces topological Anderson insulator(TAI)phase with high winding number(W=2),but the topological states are destroyed as the disorder increases.Conversely,when intercell hoppings are modulated quasi-periodically,both TAI phase and the process of destruction and restoration of topological zero modes can be induced by disorder.These topological states remain robust even under strong disorder conditions.Our work demonstrates that disorder effects do not always disrupt topological states;rather,with a judicious selection of disordered structures,topological properties can be preserved.

Observation of Giant Topological Hall Effect in Room-Temperature Ferromagnet Cr_(0.82)Te

Novel magnetic materials with non-trivial magnetic structures have led to exotic magnetic transport properties and significantly promoted the development of spintronics in recent years.Among them is the Crx Tey family,the magnetism of which can persist above room temperature,thus providing an ideal system for potential spintronic applications.Here we report the synthesis of a new compound,Cr_(0.82)Te,which demonstrates a record-high topological Hall effect at room temperature in this family.Cr_(0.82)Te displays soft ferromagnetism below the Curie temperature of 340 K.The magnetic measurement shows an obvious magneto-crystalline anisotropy with the easy axis located in the ab plane.The anomalous Hall effect can be well explained by a dominating skew scattering mechanism.Intriguing,after removing the normal Hall effect and anomalous Hall effect,a topological Hall effect can be observed up to 300 K and reaches up to 1.14μΩ·cm at 10 K,which is superior to most topological magnetic structural materials.This giant topological Hall effect possibly originates from the noncoplanar spin configuration during the spin flop process.Our work extends a new Cr_(x)Te_(y) system with topological non-trivial magnetic structure and broad prospects for spintronics applications in the future.

Hybrid Skin-Topological Effect Induced by Eight-Site Cells and Arbitrary Adjustment of the Localization of Topological Edge States

Hybrid skin-topological effect(HSTE)in non-Hermitian systems exhibits both the skin effect and topological protection,offering a novel mechanism for localization of topological edge states(TESs)in electrons,circuits,and photons.However,it remains unclear whether the HSTE can be realized in quasicrystals.

Nontrivial Topological Phases in Ternary Borides M_(2)XB_(2)(M=W,Mo;X=Co,Ni)

The nontrivial band topologies protected by certain symmetries have attracted significant interest in condensed matter physics.The discoveries of nontrivial topological phases in real materials provide a series of archetype materials to further explore the topological physics.

Tuning Second Chern Number in a Four-Dimensional Topological Insulator by High-Frequency Time-Periodic Driving

Floquet engineering has attracted considerable attention as a promising approach for tuning topological phase transitions.We investigate the effects of high-frequency time-periodic driving in a four-dimensional(4D)topological insulator,focusing on topological phase transitions at the off-resonant quasienergy gap.The 4D topological insulator hosts gapless three-dimensional boundary states,characterized by the second Chern number C_(2).We demonstrate that the second Chern number of 4D topological insulators can be modulated by tuning the amplitude of time-periodic driving.This includes transitions from a topological phase with C_(2)=±3 to another topological phase with C_(2)=±1,or to a topological phase with an even second Chern number C_(2)=±2,which is absent in the 4D static system.Finally,the approximation theory in the high-frequency limit further confirms the numerical conclusions.

From Topological Nodal-Line Semimetals to Quantum Spin Hall Insulators in Tetragonal SnX Monolayers(X=F,Cl,Br,I)

Two-dimensional(2D)topological materials have recently garnered significant interest due to their profound physical properties and promising applications for future quantum nanoelectronics.Achieving various topological states within one type of materials is,however,seldom reported.Based on first-principles calculations and tightbinding models,we investigate topological electronic states in a novel family of 2D halogenated tetragonal stanene(T-SnX,X=F,Cl,Br,I).All the four monolayers are found to be unusual topological nodal-line semimetals(NLSs),protected by a glide mirror symmetry.When spin-orbit coupling(SOC)is turned on,T-SnF and TSnCl are still ascertained as topological NLSs due to the remaining band inversion,primarily composed of Sn pxy orbitals,while T-Sn Br and T-SnI become quantum spin Hall insulators.The phase transition is ascribed to moving up in energy of Sn s orbitals and increasing of SOC strengths.The topology origin in the materials is uniformly rationalized through elementary band representations.The robust and diverse topological states found in the 2D T-SnX monolayers position them as an excellent material platform for development of innovative topological electronics.

Rydberg-Induced Topological Solitons in Three-Dimensional Rotation Spin–Orbit-Coupled Bose–Einstein Condensates

We present a novel approach for generating stable three-dimensional(3D)spatiotemporal solitons(SSs)within a rotating Bose–Einstein condensate,incorporating spin–orbit coupling(SOC),a weakly anharmonic potential and cold Rydberg atoms.This intricate system facilitates the emergence of quasi-stable 3D SSs with topological charges|m|≤3 in two spinor components,potentially exhibiting diverse spatial configurations.Our findings reveal that the Rydberg long-range interaction,spin–orbit coupling,and rotational angular frequency exert significant influence on the domains of existence and stability of these solitons.Notably,the Rydberg interaction contributes to a reduction in the norm of topological solitons,while the SOC plays a key role in stabilizing the SSs with finite topological charges.This research of SSs exhibits potential applications in precision measurement,quantum information processing,and other advanced technologies.

New approach to measuring topological phase transitions utilizing Floquet technology

The Floquet technique provides a novel anomalous topological phase for non-equilibrium phase transitions.Based on the high symmetry of the quantum anomalous Hall model,the findings suggest a one-to-one correspondence between the average spin texture and the Floquet quasi-energy spectrum.A new approach is proposed to directly measure the quasienergy spectrum,replacing previous measurements of the average spin texture.Finally,we proposed a reliable experimental scheme based on ion trap platforms.This scheme markedly reduces the measurement workload,improves the measurement fidelity,and is applicable to multiple platforms such as cold atoms and nuclear magnetic resonance.

Dzyaloshinskii–Moriya interaction and field-free sub-10 nm topological magnetism in Fe/bismuth oxychalcogenides heterostructures

Topological magnetism with strong robustness,nanoscale dimensions and ultralow driving current density(106 A/m^(2))is promising for applications in information sensing,storage,and processing,and thus sparking widespread research interest.Exploring candidate material systems with nanoscale size and easily tunable properties is a key for realizing practical topological magnetism-based spintronic devices.Here,we propose a class of ultrathin heterostructures,Fe/Bi_(2)O_(2)X(X=S,Se,Te)by deposing metal Fe on quasi-two-dimensional(2D)bismuth oxychalcogenides Bi_(2)O_(2)X(X=S,Se,Te)with excellent ferroelectric/ferroelastic properties.Large Dzyaloshinskii–Moriya interaction(DMI)and topological magnetism can be realized.Our atomistic spin dynamics simulations demonstrate that field-free vortex–antivortex loops and sub-10 nm skyrmions exist in Fe/Bi_(2)O_(2)S and Fe/Bi_(2)O_(2)Se interfaces,respectively.These results provide a possible strategy to tailor topological magnetism in ultrathin magnets/2D materials interfaces,which is extremely vital for spintronics applications.

From 0D to 3D:Hierarchical structured high-performance free-standing silicon anodes based on binder-induced topological network architecture

Free-standing silicon anodes with high proportion of active materials have aroused great attention;however,the mechanical stability and electrochemical performance are severely suppressed.Herein,to resolve the appeal issues,a free-standing anode with a"corrugated paper"shape on micro-scale and a topological crosslinking network on the submicron and nano-scale is designed.Essentially,an integrated three-dimensional electrode structure is constructed based on robust carbon nanotubes network with firmly anchored SiNPs via forming interlocking junctions.In which,the hierarchical interlocking structure is achieved by directional induction of the binder,which ensures well integration during cycling so that significantly enhances mechanical stability as well as electronic and ionic conductivity of electrodes.Benefiting from it,this anode exhibits outsta nding performance under harsh service conditions including high Si loading,ultrahigh areal capacity(33.2 mA h cm^(-2)),and high/low temperatures(-15-60℃),which significantly extends its practical prospect.Furthermore,the optimization mechanism of this electrode is explored to verify the crack-healing and structure-integration maintaining along cycling via a unique self-stabilization process.Thus,from both the fundamental and engineering views,this strategy offers a promising path to produce high-performance free-standing electrodes for flexible device applications especially facing volume effect challenges.

Ultra-broadband and wide-angle reflective terahertz polarization conversion metasurface based on topological optimization

Terahertz polarization conversion devices have significant potential applications in various fields such as terahertzimaging and spectroscopy.In this paper,we utilize genetic algorithms to topologically optimize the metasurface unit cellsand design a reflective linear polarization conversion metasurface with ultra-broadband and wide-angle characteristics.By partitioning the metallic pattern layer into quadrants,the encoding length is effectively reduced,resulting in a shorteroptimization time.The research results indicate that the converter possesses a polarization conversion efficiency ratio higherthan 90%and a relative bandwidth ratio of 125%in a range of 0.231-0.995 THz.Meanwhile,it can maintain excellentpolarization conversion properties when the incident angle of terahertz waves is less than 45°and the polarization angle isless than 15°,demonstrating excellent practicality.New insights are provided for the design of terahertz wide-angle ultrawidebandpolarization conversion devices,and the proposed metasurfce has potential applications in terahertz polarizationimaging,spectroscopy and communication fields.

Higher-order topological Anderson insulator on the Sierpiński lattice

Disorder effects on topological materials in integer dimensions have been extensively explored in recent years. However, its influence on topological systems in fractional dimensions remains unclear. Here, we investigate the disorder effects on a fractal system constructed on the Sierpiński lattice in fractional dimensions. The system supports the second-order topological insulator phase characterized by a quantized quadrupole moment and the normal insulator phase. We find that the second-order topological insulator phase on the Sierpiński lattice is robust against weak disorder but suppressed by strong disorder. Most interestingly, we find that disorder can transform the normal insulator phase to the second-order topological insulator phase with an emergent quantized quadrupole moment. Finally, the disorder-induced phase is further confirmed by calculating the energy spectrum and the corresponding probability distributions.

Topological phase transition in compressed van der Waals superlattice heterostructure BiTeCl/HfTe_(2)

Based on first-principles calculations,we investigate the electronic band structures and topological properties of heterostructure BiTeCl/HfTe_(2) under c-direction strain.In the primitive structure,this material undergoes a phase transition from an insulator with a narrow indirect gap to a metal by strong spin-orbital coupling.When strain effect is considered,band inversion at time-reversal invariant point Z is responsible for the topological phase transition.These nontrivial topologies are caused by two different types of band crossings.The observable topological surface states in(110)surface also support that this material experiences topological phase transition twice.The layered heterostructure with van der Waals force provides us with a new desirable platform upon which to control topological phase transition and construct topological superconductors.