In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete bounda...In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.展开更多
In magnetic topological materials,the interplay between magnetism and nontrivial topology gives rise to exotic quantum transport phenomena,including the anomalous Hall effect and anomalous Nernst effect.Here,we report...In magnetic topological materials,the interplay between magnetism and nontrivial topology gives rise to exotic quantum transport phenomena,including the anomalous Hall effect and anomalous Nernst effect.Here,we report the observation of intrinsic topological Hall and topological Nernst effects below the Néel temperature(T_(N)=25 K)in the antiferromagnetic(AFM)topological insulator Mn Bi_(2)Te_(4).The maximum of topological Hall resistivity reaches approximately 9μΩ·cm at 2 K,while the topological Nernst signal attains a peak value of 0.1μV/K near 10 K.These anomalous transport behaviors originate from the net Berry curvature induced by the non-collinear spin structure in the canted AFM state.Our results suggest a close connection between the topological thermoelectric effect and non-collinear AFM order in AFM topological insulators.展开更多
In this study,we explore a spherically symmetric charged black hole(BH)with a negative cosmological constant under the influence of a Kalb-Ramond field background.We compute the photon sphere and shadow radii,validati...In this study,we explore a spherically symmetric charged black hole(BH)with a negative cosmological constant under the influence of a Kalb-Ramond field background.We compute the photon sphere and shadow radii,validating our findings using observational data from the Event Horizon Telescope,with a particular emphasis on the shadow images of Sagittarius A^(*).Furthermore,we investigate the greybody factors,emission rate,and partial absorption cross section.It is shown that the Lorentz-violating parameter l has an important effect on the absorption cross section.Our analysis also includes an examination of the topological charge,temperature-dependent topology,and generalized free energy.In particular,we regard the AdS charged BH with an antisymmetric tensor background as a topological defect in the thermodynamic space,then the system has the same topological classification to the charged Reissner-Nordström-AdS BH.展开更多
In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This s...In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This study aims to explore the complex evolution of the space debris environment and assess the collision risks associated with spacecraft.First,a space debris environment topological network model is proposed,which incorporates interdisciplinary methods from topological networks,fluid mechanics,and spacecraft dynamics.This model enables a structured representation of the relationships among space objects and provides rapid predictions of the space debris environment.Then,a collision probability algorithm based on the topological network model is introduced.This algorithm inherits the efficiency advantages of the topological network model and has been validated for reliability through comparison with the classical ESA’s DRAMA software.Finally,based on the above models,the collision risks of constellation satellites in Low Earth Orbit(LEO)are analyzed,including both operational and deorbit processes.The study reveals that constellation satellites face a much higher risk of internal collisions with satellites from the same constellation during operations than that with other space objects.Additionally,during the satellite deorbit process,the collision risk peaks when satellites traverse the operational region of Starlink satellites.展开更多
A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable...A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.展开更多
Topological phases are governed by lattice symmetries,yet how different symmetry-breaking paths(SBPs)affect topological transitions remains insufficiently understood.Most existing studies rely on a single SBP,and addr...Topological phases are governed by lattice symmetries,yet how different symmetry-breaking paths(SBPs)affect topological transitions remains insufficiently understood.Most existing studies rely on a single SBP,and address only one bandgap,limiting independent control of multiple gaps.Here,we investigate multiple isolated Dirac points in a trefoil-knot-modified honeycomb lattice,and show that a single SBP generally inverts all relevant Dirac points simultaneously,whereas the tailored combinations of SBPs enable selective and programmable band inversion at targeted gaps.The excitation-dependent responses reveal strong modal selectivity.This capability is exploited to realize independently controllable multi-channel signal splitting,which is unattainable with a single SBP.The results enable SBPs as an effective design degree of freedom for programmable and reconfigurable topological elastic devices.展开更多
Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and ...Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and unstable,making high-quality single-crystal growth,characterization,and measurements difficult,and most do not exhibit superconductivity at ambient pressure.In contrast,La_(3) In stands out for its ambient-pressure superconductivity(T_(C)∼9.4 K)and the availability of high-quality single crystals.Here,we investigate its low-energy electronic structure using angle-resolved photoemission spectroscopy and first-principles calculations.The bands near the Fermi energy(E_(F))are mainly derived from La 5d and In 5p orbitals.A saddle point is directly observed at the Brillouin zone(BZ)boundary,while a three-dimensional Van Hove singularity crosses E_(F) at the BZ corner.First-principles calculations further reveal topological Dirac surface states within the bulk energy gap above E_(F).The coexistence of a high density of states and in-gap topological surface states near𝐸F suggests that La3In offers a promising platform for tuning superconductivity and exploring possible topological superconducting phases through doping or external pressure.展开更多
Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opport...Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opportunities for exploring novel topological phenomena and fascinating applications.Utilizing a low-temperature scanning tunneling microscope,we construct breathing-kagome lattices with Fe adatoms on Ag(111)and investigate their electronic properties.We observe the higher-order topological boundary states in the topological phase but not in the trivial one,which is consistent with the theory.These states are found to be robust against the removal of bulk or edge adatoms.Further,we show the arbitrary positioning of these states either at corner,edge,or bulk sites by slightly modifying their neighbors.Our study not only demonstrates the formation and robustness of the electronic higher-order topological boundary states in real atomic systems but also provides a route for controlling their positions.展开更多
The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,describ...The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,described by the Euler number not the Chern number.The spin textures of a topological Euler insulator in the momentum space is like a Néel-type skyrmion.It is found that the topological edge states exist in the band gap of the topological Euler insulator,and the topological Euler insulator can be transformed into a topological metal without the topological phase transition.展开更多
Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with ...Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with topological quantum chemistry, we investigate bilayer α-In_(2) Se_(3)(2 L-In_(2) Se_(3)) in van der Waals heterostructures with XSe(X = Ga, In, Tl) substrates within space group P 3m1(No. 156). We show that the emergence of ferroelectricity-driven topological phase transitions in these systems is dictated by fundamental symmetry principles rather than material-specific effects. The band bending at the XSe/2 L-In_(2) Se_(3) interface enables topological band inversions, with higher-electron-affinity substrates such as GaSe and TlSe favoring the transition. Remarkably, GaSe/2 L-In_(2) Se_(3) exhibits a reversible transition between topological and trivial insulating phases upon polarization switching, while TlSe/2 L-In_(2) Se_(3) undergoes sequential transitions from a topological insulator to a trivial insulator and eventually to a metallic state. This multistate manipulation highlights a viable route for designing tunable, low-power, multi-functional electronic devices.展开更多
Topological insulators with localized edge or interface states have been extensively studied,particularly in phononic crystals and related fields;however,their application in seismic metamaterials remains largely unex...Topological insulators with localized edge or interface states have been extensively studied,particularly in phononic crystals and related fields;however,their application in seismic metamaterials remains largely unexplored.To address this gap,we designed a topological seismic metamaterial,where the topological interface is formed by joining the ends of two distinct one-dimensional periodic lattices.The first full-scale field experiment confirms the existence of topological interface states,which exhibit pronounced localization characteristics and induce a resonant amplification effect of 7.2 dB on the total energy of seismic surface waves.This study provides the first experimental validation for the implementation of topological principles in the design of seismic metamaterials,enabling novel approaches to high-sensitivity seismic detection and efficient energy localization for wave control.展开更多
Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in ...Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.展开更多
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...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.展开更多
Interlayer antiferromagnetic coupling,small magnetic anisotropy,and low air stability of the intrinsic magnetic topological insulator MnBi_(2)Te_(4)have been critical bottlenecks to the future application of the quant...Interlayer antiferromagnetic coupling,small magnetic anisotropy,and low air stability of the intrinsic magnetic topological insulator MnBi_(2)Te_(4)have been critical bottlenecks to the future application of the quantum anomalous Hall efect(QAHE)at zero magnetic feld.In this study,we propose a scheme to utilize capped sliding van der Waals materials to efectively modulate the magnetic and topological properties of MnBi_(2)Te_(4).Our results demonstrate that the h-BN/MnBi_(2)Te_(4)/h-BN heterostructure,constructed by sliding ferroelectric h-BN bilayer and MnBi_(2)Te_(4),not only realizes a transition from interlayer antiferromagnetic to ferromagnetic coupling but also signifcantly enhances the out-of-plane magnetism and air stability of MnBi_(2)Te_(4).Moreover,the above magnetic properties can be further improved by tuning the interlayer distance between h-BN and MnBi_(2)Te_(4).Additionally,the obtained band structures and topological properties clearly support that the h-BN/MnBi_(2)Te_(4)/hBN heterostructure can harbor the QAHE with a Chern number of C=1.This work provides a new and nonvolatile modulation approach to achieve high-temperature and high-precision QAHE at zero magnetic feld.展开更多
This study explores the core characteristics,dynamic progression of the depression-anxiety-stress network among Chinese higher vocational college freshmen and its association with life satisfaction,and identifies key ...This study explores the core characteristics,dynamic progression of the depression-anxiety-stress network among Chinese higher vocational college freshmen and its association with life satisfaction,and identifies key nodes and critical intervention points.Participants were 295 higher vocational college freshmen(male=137;M=18.52,SD=0.69)completing two follow-up surveys(5-month interval).Measures included depression-anxiety-stress symptoms and life satisfaction,analyzed via cross-sectional and binary cross-lagged panel network analysis.The results showed that“Easily agitated”was the central node(strength=1.519,EI=1.967);“Irritable”and“Mouth Dryness”were top predictors(Out-EI=1.101,1.100),with depressive symptoms as the convergence hub.“Easily agitated”had the strongest direct negative impact on life satisfaction(cross-cluster out-predictability=−0.653).This study elucidates depression-anxietystress network mechanisms in higher vocational freshmen,providing a theoretical framework and targeted intervention guidance(e.g.,focusing on somatic and emotional nodes).展开更多
We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(...We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.展开更多
We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrief...We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.展开更多
The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattic...The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.展开更多
Systems hosting flat bands offer a powerful platform for exploring strong correlation physics.Theoretically,topological degeneracy arising in systems with non-trivial topological orders on periodic manifolds of non-ze...Systems hosting flat bands offer a powerful platform for exploring strong correlation physics.Theoretically,topological degeneracy arising in systems with non-trivial topological orders on periodic manifolds of non-zero genus can generate ideal flat bands.However,experimental realization of such geometrically engineered systems is very difficult.In this work,we demonstrate that flat planes with strategically patterned hole defects can engineer ideal flat bands.We construct two families of models:singular flat band systems where degeneracy is stabilized by non-contractible loop excitations tied to hole defects and perfectly nested van Hove systems where degeneracy arises from line excitations in momentum space.These models circumvent the need for exotic manifolds while retaining the essential features of topological flat bands.By directly linking defect engineering to degeneracy mechanisms,our results establish a scalable framework for experimentally accessible flat band design.展开更多
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 stru...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.展开更多
基金supported by the Natural Science Basic Research Program of Shaanxi Province (Grant Nos.2024JC-JCQN-06 and2025JC-QYCX-006)the National Natural Science Foundation of China (Grant No.12474337)Chinese Academy of Sciences Project (Grant Nos.E4BA270100,E4Z127010F,E4Z6270100,and E53327020D)。
文摘In conventional higher-order topological insulators(HOTIs),the emergence of topological states can be explained by using the nonzero bulk polarization index.However,corner states emerge in HOTIs with incomplete boundary unit cells(i.e.,boundary defects)even though the bulk polarization is zero,which challenges the conventional understanding of HOTIs.Here,based on a Kekul´e-distorted honeycomb lattice with incomplete unit cells,we reveal that incomplete unit cells exhibit fractional charges through the analysis of Wannier centers by developing a compensation method and creating the concept of Wannier center domain(WCD)which is the smallest region that one Wannier center occupies.This method compensates for the missing parts of these boundary incomplete unit cells with additional WCDs to make them complete.The compensated WCDs automatically carry the corresponding charge,and this charge together with that of the incomplete unit cell constitutes the total charge of the complete unit cell after compensation.We conclude that the emergence of corner states is attributed to the filling anomaly,which is a fundamental mechanism.Our results refresh the understanding of HOTIs,especially those with structural discontinuities,and provide a novel design for topological states which have application value in producing optical functional devices.
基金supported in part by the Natural Science Foundation of China(Grant No.U1932155)the Hangzhou Joint Fund of the Zhejiang Provincial Natural Science Foundation of China(Grant No.LHZSZ24A040001)+4 种基金the National Key R&D Program of China(Grant No.2022YFA1602602)the National Key R&D Program of China(Grant Nos.2022YFA1403800 and 20-23YFA1406500)the China Postdoctoral Science Foundation(Grant No.2023-M730011)the National Natural Science Foundation of China(Grant No.12274459)supported by the HZNU Scientific Research and Innovation Team Project(No.TD2025013)。
文摘In magnetic topological materials,the interplay between magnetism and nontrivial topology gives rise to exotic quantum transport phenomena,including the anomalous Hall effect and anomalous Nernst effect.Here,we report the observation of intrinsic topological Hall and topological Nernst effects below the Néel temperature(T_(N)=25 K)in the antiferromagnetic(AFM)topological insulator Mn Bi_(2)Te_(4).The maximum of topological Hall resistivity reaches approximately 9μΩ·cm at 2 K,while the topological Nernst signal attains a peak value of 0.1μV/K near 10 K.These anomalous transport behaviors originate from the net Berry curvature induced by the non-collinear spin structure in the canted AFM state.Our results suggest a close connection between the topological thermoelectric effect and non-collinear AFM order in AFM topological insulators.
基金supported by the Doctoral Foundation of Zunyi Normal University of China (BS [2022] 07)Fundação de Apoio à Pesquisa do Estado da Paraíba (FAPESQ)+5 种基金Conselho Nacional de Desenvolvimento Cientíıfico e Tecnológico (CNPq)-[150891/2023-7] for the financial supportsupported by the Q-CAYLE project, funded by the European Union-Next Generation UE/MICIU/Plan de Recuperacion, Transformacion y Resiliencia/Junta de Castilla y Leon (PRTRC17.11)by project PID2023-148409NB-I00, funded by MICIU/AEI/10.13039/501100011033Financial support of the Department of Education of the Junta de Castilla y LeonFEDER FundsExcellence project Fo S UHK 2203/2025-2026 for the financial support
文摘In this study,we explore a spherically symmetric charged black hole(BH)with a negative cosmological constant under the influence of a Kalb-Ramond field background.We compute the photon sphere and shadow radii,validating our findings using observational data from the Event Horizon Telescope,with a particular emphasis on the shadow images of Sagittarius A^(*).Furthermore,we investigate the greybody factors,emission rate,and partial absorption cross section.It is shown that the Lorentz-violating parameter l has an important effect on the absorption cross section.Our analysis also includes an examination of the topological charge,temperature-dependent topology,and generalized free energy.In particular,we regard the AdS charged BH with an antisymmetric tensor background as a topological defect in the thermodynamic space,then the system has the same topological classification to the charged Reissner-Nordström-AdS BH.
基金supported by the National Level Project of China(No.KJSP2023020201)the Foundation of Science and Technology on Aerospace Flight Dynamics Laboratory of China(No.kjw6142210240202)+1 种基金the Beijing Institute of Technology Research Fund Program for Young Scholars of Chinathe Fundamental Research Funds for Central Universities of China。
文摘In recent years,the rapid development of mega-constellations has significantly exacerbated the deterioration of the space debris environment,posing substantial and escalating threats to the safety of spacecraft.This study aims to explore the complex evolution of the space debris environment and assess the collision risks associated with spacecraft.First,a space debris environment topological network model is proposed,which incorporates interdisciplinary methods from topological networks,fluid mechanics,and spacecraft dynamics.This model enables a structured representation of the relationships among space objects and provides rapid predictions of the space debris environment.Then,a collision probability algorithm based on the topological network model is introduced.This algorithm inherits the efficiency advantages of the topological network model and has been validated for reliability through comparison with the classical ESA’s DRAMA software.Finally,based on the above models,the collision risks of constellation satellites in Low Earth Orbit(LEO)are analyzed,including both operational and deorbit processes.The study reveals that constellation satellites face a much higher risk of internal collisions with satellites from the same constellation during operations than that with other space objects.Additionally,during the satellite deorbit process,the collision risk peaks when satellites traverse the operational region of Starlink satellites.
基金supported by Fujian Provincial Natural Science Foundation of China(2024J02022)the NSFC(11571158)+1 种基金supported by the NSFC(12071199)supported by the Young and middle-aged project in Fujian Province(JAT190397)。
文摘A discrete subset S of a topological gyrogroup G with the identity 0 is said to be a suitable set for G if it generates a dense subgyrogroup of G and S∪{0}is closed in G.In this paper,it is proved that each countable Hausdorff topological gyrogroup has a suitable set;moreover,it is shown that each separable metrizable strongly topological gyrogroup has a suitable set.
基金Project supported by the National Natural Science Foundation of China(Nos.12232015 and12572106)the National Key R&D Program of China(Nos.2024YFB3408700,2024YFB3408701,2024YFB3408703)the Natural Science Foundation of Shaanxi Province of China(No.2023-JC-YB-073)。
文摘Topological phases are governed by lattice symmetries,yet how different symmetry-breaking paths(SBPs)affect topological transitions remains insufficiently understood.Most existing studies rely on a single SBP,and address only one bandgap,limiting independent control of multiple gaps.Here,we investigate multiple isolated Dirac points in a trefoil-knot-modified honeycomb lattice,and show that a single SBP generally inverts all relevant Dirac points simultaneously,whereas the tailored combinations of SBPs enable selective and programmable band inversion at targeted gaps.The excitation-dependent responses reveal strong modal selectivity.This capability is exploited to realize independently controllable multi-channel signal splitting,which is unattainable with a single SBP.The results enable SBPs as an effective design degree of freedom for programmable and reconfigurable topological elastic devices.
基金supported by the National Natural Science Foundation of China(Grant Nos.12222413,12174443,12274459,and 12404266)the National Key R&D Program of China(Grant Nos.2023YFA1406500,2022YFA1403800,and 2022YFA1403103)+3 种基金the Natural Science Foundation of Shanghai (Grant No.23ZR1482200)the Natural Science Foundation of Ningbo (Grant No.2024J019)the Science Research Project of Hebei Education Department (Grant No.BJ2025060)the funding of Ningbo Yongjiang Talent Program。
文摘Superconducting elect rides have attracted growing attention for their potential to achieve high superconducting transition temperatures(T_(C))under pressure.However,many known elect rides are chemically reactive and unstable,making high-quality single-crystal growth,characterization,and measurements difficult,and most do not exhibit superconductivity at ambient pressure.In contrast,La_(3) In stands out for its ambient-pressure superconductivity(T_(C)∼9.4 K)and the availability of high-quality single crystals.Here,we investigate its low-energy electronic structure using angle-resolved photoemission spectroscopy and first-principles calculations.The bands near the Fermi energy(E_(F))are mainly derived from La 5d and In 5p orbitals.A saddle point is directly observed at the Brillouin zone(BZ)boundary,while a three-dimensional Van Hove singularity crosses E_(F) at the BZ corner.First-principles calculations further reveal topological Dirac surface states within the bulk energy gap above E_(F).The coexistence of a high density of states and in-gap topological surface states near𝐸F suggests that La3In offers a promising platform for tuning superconductivity and exploring possible topological superconducting phases through doping or external pressure.
基金supported by the National Key R&D Program of China(Grant Nos.2024YFA140850,2022YFA1403601,and 2023YFC2410501)the National Natural Science Foundation of China(Grants Nos.12241402,12474059,12274203,12374113,and 12274204)。
文摘Higher-order topological insulators,which host topologically protected states at boundaries that are at least two dimensions lower than the bulk,are an emerging class of topological materials.They provide great opportunities for exploring novel topological phenomena and fascinating applications.Utilizing a low-temperature scanning tunneling microscope,we construct breathing-kagome lattices with Fe adatoms on Ag(111)and investigate their electronic properties.We observe the higher-order topological boundary states in the topological phase but not in the trivial one,which is consistent with the theory.These states are found to be robust against the removal of bulk or edge adatoms.Further,we show the arbitrary positioning of these states either at corner,edge,or bulk sites by slightly modifying their neighbors.Our study not only demonstrates the formation and robustness of the electronic higher-order topological boundary states in real atomic systems but also provides a route for controlling their positions.
基金supported by the National Natural Science Foundation of China(Grants Nos.12174288 and 12274326)the National Key R&D Program of China(Grant No.2021YFA1400602)。
文摘The topological phases and edge states of a topological Euler insulator on a triangular lattice is studied.Differently from two-band Chern insulators,a topological Euler insulator is a kind of three-band model,described by the Euler number not the Chern number.The spin textures of a topological Euler insulator in the momentum space is like a Néel-type skyrmion.It is found that the topological edge states exist in the band gap of the topological Euler insulator,and the topological Euler insulator can be transformed into a topological metal without the topological phase transition.
基金supported by the National Natural Science Foundation of China (Grant Nos.11874141,12174059,and 11604134)。
文摘Ferroelectric topological insulators realized in heterostructures of two topologically trivial two-dimensional materials have recently attracted significant interest. Using first-principles calculations combined with topological quantum chemistry, we investigate bilayer α-In_(2) Se_(3)(2 L-In_(2) Se_(3)) in van der Waals heterostructures with XSe(X = Ga, In, Tl) substrates within space group P 3m1(No. 156). We show that the emergence of ferroelectricity-driven topological phase transitions in these systems is dictated by fundamental symmetry principles rather than material-specific effects. The band bending at the XSe/2 L-In_(2) Se_(3) interface enables topological band inversions, with higher-electron-affinity substrates such as GaSe and TlSe favoring the transition. Remarkably, GaSe/2 L-In_(2) Se_(3) exhibits a reversible transition between topological and trivial insulating phases upon polarization switching, while TlSe/2 L-In_(2) Se_(3) undergoes sequential transitions from a topological insulator to a trivial insulator and eventually to a metallic state. This multistate manipulation highlights a viable route for designing tunable, low-power, multi-functional electronic devices.
基金supported by the National Natural Science Foundation of China(Grant No.11974044)。
文摘Topological insulators with localized edge or interface states have been extensively studied,particularly in phononic crystals and related fields;however,their application in seismic metamaterials remains largely unexplored.To address this gap,we designed a topological seismic metamaterial,where the topological interface is formed by joining the ends of two distinct one-dimensional periodic lattices.The first full-scale field experiment confirms the existence of topological interface states,which exhibit pronounced localization characteristics and induce a resonant amplification effect of 7.2 dB on the total energy of seismic surface waves.This study provides the first experimental validation for the implementation of topological principles in the design of seismic metamaterials,enabling novel approaches to high-sensitivity seismic detection and efficient energy localization for wave control.
基金supported by the National Natural Science Foundation of China(Grant Nos.12275260 and 11905211)the Fundamental Research Funds for the Central Universities(Grant No.202364008)the Young Talents Project of Ocean University of China。
文摘Non-Abelian topological insulators are characterized by matrix-valued,non-commuting topological charges with regard to more than one energy gap.Their descriptions go beyond the conventional topological band theory,in which an additive integer like the winding or Chern number is endowed separately with each(degenerate group of)energy band(s).In this work,we reveal that Floquet(time-periodic)driving could not only enrich the topology and phase transitions of non-Abelian topological matter,but also induce bulk-edge correspondence unique to nonequilibrium setups.Using a one-dimensional,three-band model as an illustrative example,we demonstrate that Floquet driving could reshuffle the phase diagram of the non-driven system,yielding both gapped and gapless Floquet band structures with non-Abelian topological charges.Moreover,by dynamically tuning the anomalous Floquet π-quasienergy gap,non-Abelian topological transitions inaccessible to static systems could arise,leading to much more complicated relations between non-Abelian topological charges and Floquet edge states.These discoveries put forth periodic driving as a powerful scheme of engineering non-Abelian topological phases and incubating unique non-Abelian band topology beyond equilibrium.
文摘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.
基金supported by the National Key R&D Program of China(Grant No.2024YFA1408103)National Natural Science Foundation of China(Grants No.11974098,12474158,12234017 and 12488101)+3 种基金Innovation Program for Quantum Science and Technology(Grant No.2021ZD0302800)Natural Science Foundation of Hebei Province(Grant No.A202305017)Anhui Initiative in Quantum Information Technologies(Grant No.AHY170000)Fundamental Research Funds for the Central Universities(Grant No.WK2340000082)。
文摘Interlayer antiferromagnetic coupling,small magnetic anisotropy,and low air stability of the intrinsic magnetic topological insulator MnBi_(2)Te_(4)have been critical bottlenecks to the future application of the quantum anomalous Hall efect(QAHE)at zero magnetic feld.In this study,we propose a scheme to utilize capped sliding van der Waals materials to efectively modulate the magnetic and topological properties of MnBi_(2)Te_(4).Our results demonstrate that the h-BN/MnBi_(2)Te_(4)/h-BN heterostructure,constructed by sliding ferroelectric h-BN bilayer and MnBi_(2)Te_(4),not only realizes a transition from interlayer antiferromagnetic to ferromagnetic coupling but also signifcantly enhances the out-of-plane magnetism and air stability of MnBi_(2)Te_(4).Moreover,the above magnetic properties can be further improved by tuning the interlayer distance between h-BN and MnBi_(2)Te_(4).Additionally,the obtained band structures and topological properties clearly support that the h-BN/MnBi_(2)Te_(4)/hBN heterostructure can harbor the QAHE with a Chern number of C=1.This work provides a new and nonvolatile modulation approach to achieve high-temperature and high-precision QAHE at zero magnetic feld.
基金supported by the Anhui Philosophical and Social Science Fund for University Research:The Application of Painting Psychological Analysis in College Students’Mental Health Education Courses(Grant#:2023AH052874),which has provided essential financial support for data collection.
文摘This study explores the core characteristics,dynamic progression of the depression-anxiety-stress network among Chinese higher vocational college freshmen and its association with life satisfaction,and identifies key nodes and critical intervention points.Participants were 295 higher vocational college freshmen(male=137;M=18.52,SD=0.69)completing two follow-up surveys(5-month interval).Measures included depression-anxiety-stress symptoms and life satisfaction,analyzed via cross-sectional and binary cross-lagged panel network analysis.The results showed that“Easily agitated”was the central node(strength=1.519,EI=1.967);“Irritable”and“Mouth Dryness”were top predictors(Out-EI=1.101,1.100),with depressive symptoms as the convergence hub.“Easily agitated”had the strongest direct negative impact on life satisfaction(cross-cluster out-predictability=−0.653).This study elucidates depression-anxietystress network mechanisms in higher vocational freshmen,providing a theoretical framework and targeted intervention guidance(e.g.,focusing on somatic and emotional nodes).
基金supported by Research Grants Council(RGC),University Grants Committee(UGC)of Hong Kong(ECS No.24304722)。
文摘We classify condensable𝐸E_(2)-algebras in a modular tensor category C up to 2-Morita equivalence.Physically,this classification provides an explicit criterion to determine when distinct condensable𝐸E_(2)-algebras yield the same condensed topological phase under a two-dimensional anyon condensation process.The relations between different condensable algebras can be translated into their module categories,interpreted physically as gapped domain walls in topological orders.As concrete examples,we interpret the categories of quantum doubles of finite groups and examples beyond group symmetries.Our framework fully elucidates the interplay among condensable𝐸E_(1)-algebras in C,condensable𝐸E_(2)-algebras in C up to 2-Morita equivalence,and Lagrangian algebras in C⊠C.
基金supported by the National Natural Science Foundation of China(Grant Nos.12175315 and 12205385)。
文摘We propose a novel approach to generate and manipulate topological Floquet bound states in the continuum(BICs)via a class of systems constructed by coupling two identical periodically driven one-dimensional Su-Schrieffer-Heeger chains.The formation of topological Floquet BICs can be adjusted only by tuning the driving amplitude or frequency,regardless of whether the static system has BICs or not.The interchain bias can only change the localization property of topological Floquet BICs,and a bigger bias can lead to transforming topological Floquet BICs into bound states out of the continuum(BOCs).But it does not change the topological properties of these topological Floquet states.Based on the repulsion effect of edge states,we propose to detect occurrence of topological Floquet BICs and transition point between topological Floquet BICs and BOCs using quantum walk.Our work provided a convenient and realistic approach for the experimental realization and manipulation of BICs in a single-particle quantum system.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 12074101 and 11604081)sponsored by the Natural Science Foundation of Henan Province, China (Grant No. 212300410040)。
文摘The topological states of the two-leg and three-leg ladders formed by two trivial quantum wires with different lattice constants are theoretically investigated. Firstly, we take two trivial quantum wires with a lattice constant ratio of 1:2 as an example. For the symmetric nearest-neighbor intra-chain hopping two-leg ladder, the inversion symmetry protected topological insulator phase with two degenerate topological edge states appears. When the inversion symmetry is broken, the topological insulators with one or two topological edge states of different energies and topological metals with edge states embedded in the bulk states could emerge depending on the filling factor. The topological origin of these topological states in the two-leg ladders is the topological properties of the Chern insulators and Chern metals. According to the arrangement of two trivial quantum wires, we construct two types of three-leg ladders. Each type of the three-leg ladder could be divided into one trivial subspace and one topological nontrivial subspace by unitary transformation. The topological nontrivial subspace corresponds to the effective two-leg ladder model. As the filling factor changes, the system could be in topological insulators or topological metals phases. When the two-leg ladder is constructed by two trivial quantum wires with a lattice constant ratio of 1:3 and 2:3, the system could also realize rich topological states such as the topological insulators and topological metals with the topological edge states. These rich topological states in the two-leg and three-leg ladders could be confirmed by current experimental techniques.
基金supported by the Ministry of Science and Technology(Grant No.2022YFA1403901)the National Natural Science Foundation of China(Grant Nos.12494594,11888101,12174428,and 12504192)+2 种基金the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB28000000)the New Cornerstone Investigator Program,the Chinese Academy of Sciences through the Youth Innovation Promotion Association(Grant No.2022YSBR-048)the Shanghai Science and Technology Innovation Action Plan(Grant No.24LZ1400800).
文摘Systems hosting flat bands offer a powerful platform for exploring strong correlation physics.Theoretically,topological degeneracy arising in systems with non-trivial topological orders on periodic manifolds of non-zero genus can generate ideal flat bands.However,experimental realization of such geometrically engineered systems is very difficult.In this work,we demonstrate that flat planes with strategically patterned hole defects can engineer ideal flat bands.We construct two families of models:singular flat band systems where degeneracy is stabilized by non-contractible loop excitations tied to hole defects and perfectly nested van Hove systems where degeneracy arises from line excitations in momentum space.These models circumvent the need for exotic manifolds while retaining the essential features of topological flat bands.By directly linking defect engineering to degeneracy mechanisms,our results establish a scalable framework for experimentally accessible flat band design.
基金Project supported by the Suzhou Basic Research Project (Grant No.SJC2023003)Suzhou City University National Project Pre-research Project (Grant No.2023SGY014)。
文摘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.
