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.

Growth and characterization of Bi(110)/CrTe_(2) heterostructures:Exploring interplay between magnetism and topology

The interplay between topology and magnetism is vital for realizing exotic quantum phenomena,significant examples including quantum anomalous Hall effect,axion insulators,and high-order topological states.These states host great potential for future applications in high-speed and low-consumption electronic devices.Despite being extensively investigated,practical platforms are still scarce.In this work,with molecular beam epitaxy(MBE),we provide the first experimental report on high-quality Bi(110)/CrTe_(2) magnetic heterostructure.By employing in-situ high-resolution scanning tunneling microscopy,we are able to examine the interaction between magnetism and topology.There is a potential edge state at an energy level above the Fermi level,but no edge states observed near the Fermi level The absence of high-order topological corner states near EF highlights the importance of lattice matching and interface engineering in designing high-order topological states.Our study provides key insights into the interplay between two-dimensional magnetic and topological materials and offers an important dimension for engineering magnetic topological states.

Recent progress on valley polarization and valley-polarized topological states in two-dimensional materials

Valleytronics, using valley degree of freedom to encode, process, and store information, may find practical applications in low-power-consumption devices. Recent theoretical and experimental studies have demonstrated that twodimensional(2D) honeycomb lattice systems with inversion symmetry breaking, such as transition-metal dichalcogenides(TMDs), are ideal candidates for realizing valley polarization. In addition to the optical field, lifting the valley degeneracy of TMDs by introducing magnetism is an efficient way to manipulate the valley degree of freedom. In this paper, we first review the recent progress on valley polarization in various TMD-based systems, including magnetically doped TMDs,intrinsic TMDs with both inversion and time-reversal symmetry broken, and magnetic TMD heterostructures. When topologically nontrivial bands are empowered into valley-polarized systems, valley-polarized topological states, namely valleypolarized quantum anomalous Hall effect can be realized. Therefore, we have also reviewed the theoretical proposals for realizing valley-polarized topological states in 2D honeycomb lattices. Our paper can help readers quickly grasp the latest research developments in this field.

Topological photonic states in gyromagnetic photonic crystals:Physics,properties,and applications

Topological photonic states(TPSs)as a new type of waveguide state with one-way transport property can resist backscattering and are impervious to defects,disorders and metallic obstacles.Gyromagnetic photonic crystal(GPC)is the first artificial microstructure to implement TPSs,and it is also one of the most important platforms for generating truly one-way TPSs and exploring their novel physical properties,transport phenomena,and advanced applications.Herein,we present a brief review of the fundamental physics,novel properties,and practical applications of TPSs based on GPCs.We first examine chiral one-way edge states existing in uniformly magnetized GPCs of ordered and disordered lattices,antichiral one-way edge states in cross magnetized GPCs,and robust one-way bulk states in heterogeneously magnetized GPCs.Then,we discuss the strongly coupling effect between two co-propagating(or counter-propagating)TPSs and the resulting physical phenomena and device applications.Finally,we analyze the key issues and prospect the future development trends for TPSs in GPCs.The purpose of this brief review is to provide an overview of the main features of TPSs in GPC systems and offer a useful guidance and motivation for interested scientists and engineers working in related scientific and technological areas.

Identification of Topological Surface State in PdTe2 Superconductor by Angle-Resolved Photoemission Spectroscopy

High-resolution angle-resolved photoemission measurements are carried out on transition metal dichalcogenide PdTe2 that is a superconductor with a Tc at 1.7K. Combined with theoretical calculations, we discover for the first time the existence of topologically nontrivial surface state with Dirac cone in PbTe2 superconductor. It is located at the Brillouin zone center and possesses helical spin texture. Distinct from the usual three-dimensional topological insulators where the Dirac cone of the surface state lies at the Fermi level, the Dirac point of the surface state in PdTe2 lies deeply below the Fermi level at - 1.75 eV binding energy and is well separated from the bulk states. The identification of topological surface state in PdTe2 superconductor deeply below the Fermi level provides a unique system to explore new phenomena and properties and opens a door for finding new topological materials in transition metal ehalcogenides.

Valley-dependent topological edge states in plasma photonic crystals

Plasma photonic crystals designed in this paper are composed of gas discharge tubes to control the flow of electromagnetic waves.The band structures calculated by the finite element method are consistent with the experimental results which have two distinct attenuation peaks in the ranges of 1-2.5 GHz and 5-6 GHz.Electromagnetic parameters of the plasma are extracted by the Nicolson-Ross-Weir method and effective medium theory.The measured electron density is between 1×1011 cm-3 and1×1012 cm-3,which verifies the correctness of the parameter used in the simulation,and the collision frequency is near 1.5×1010 Hz.As the band structures are corroborated by the measured scattering parameters,we introduce the concept of photonic topological insulator based on the quantum Valley Hall effect into the plasma photonic crystal.A valley-dependent plasma photonic crystal with hexagonal lattice is constructed,and the phase transition of the valley K(K’)occurs by breaking the spatial inversion symmetry.Valley-spin locked topological edge states are generated and excited by chiral sources.The frequency of the non-bulk state can be dynamically regulated by the electron density.This concept paves the way for novel,tunable topological edge states.More interestingly,the Dirac cone is broken when the electron density increases to 3.1×1012 cm-3,which distinguishes from the methods of applying a magnetic field and changing the symmetry of the point group.

High-fidelity topological quantum state transfers in a cavity-magnon system

We propose a scheme for realizing high-fidelity topological state transfer via the topological edge states in a onedimensional cavity-magnon system.It is found that the cavity-magnon system can be mapped analytically into the generalized Su-Schrieffer-Heeger model with tunable cavity-magnon coupling.It is shown that the edge state can be served as a quantum channel to realize the photonic and magnonic state transfers by adjusting the coupling strength between adjacent cavity modes.Further,our scheme can realize the quantum state transfer between photonic state and magnonic state by changing the cavity-magnon coupling strength.With the numerical simulation,we quantitatively show that the photonic,magnonic and magnon-to-photon state transfers can be achieved with high fidelity in the cavity-magnon system.Spectacularly,three different types of quantum state transfer schemes can be even transformed into each other in a controllable fashion.The Su-Schrieffer-Heeger model based on the cavity-magnon system provides us a tunable platform to engineer the transport of photon and magnon,which may have potential applications in topological quantum processing.

Engineering topological state transfer in four-period Su–Schrieffer–Heeger chain

An extended Su–Schrieffer–Heeger(SSH) model containing four periods of the hopping coefficients, called SSH4 model, is constructed to explore robust quantum state transfer. The gap state protected by the energy gap plays the role of the topological channel where the particle initially located at the last lattice site has the probability to arise at the first and all even lattice sites equally. Serving those sites as ports, a multi-port router can be realized naturally, and the fidelity reaches unity in a wide range of parameters under the long chain and random disorder. Further, when we reduce the third intracell hopping to a small value, the occupancy probability of the second lattice site in every unit cell will reduce to zero, by which a new topological router can be induced. In addition, our SSH4 model can work as a 1/3 beam splitter. Namely, the particle initially occupies the first lattice site and finally appears with equal probability at three lattice sites. We can also realize a 1/2 beam splitter. Our four-period SSH model provides a novel way for topological quantum information processing and can engineer two kinds of quantum optical devices.

Solid-state quantum computation station

Solid-state quantum computation station belongs to the group 2 of manipulation of quantum state in the Synergetic Extreme Condition User Facility. Here we will first outline the research background, aspects, and objectives of the station, followed by a discussion of the recent scientific as well as technological progress in this field based on similar experimental facilities to be constructed in the station. Finally, a brief summary and research perspective will be presented.

High-performance chiral all-optical OR logic gate based on topological edge states of valley photonic crystal

For all-optical communication and information processing,it is necessary to develop all-optical logic gates based on photonic structures that can directly perform logic operations.All-optical logic gates have been demonstrated based on conventional waveguides and interferometry,as well as photonic crystal structures.Nonetheless,any defects in those structures will introduce high scattering loss,which compromises the fidelity and contrast ratio of the information process.Based on the spin-valley locking effect that can achieve defect-immune unidirectional transmission of topological edge states in valley photonic crystals(VPCs),we propose a high-performance all-optical logic OR gate based on a VPC structure.By tuning the working bandwidth of the two input channels,we prevent interference between the two channels to achieve a stable and high-fidelity output.The transmittance of both channels is higher than 0.8,and a high contrast ratio of 28.8 dB is achieved.Moreover,the chirality of the logic gate originated from the spin-valley locking effect allows using different circularly polarized light as inputs,representing“1”or“0”,which is highly desired in quantum computing.The device’s footprint is 18μm×12μm,allowing high-density on-chip integration.In addition,this design can be experimentally fabricated using current nanofabrication techniques and will have potential applications in optical communication,information processing,and quantum computing.

Random-Gate-Voltage Induced Al'tshuler–Aronov–Spivak Effect in Topological Edge States

Helical edge states are the hallmark of the quantum spin Hall insulator. Recently, several experiments have observed transport signatures contributed by trivial edge states, making it difficult to distinguish between the topologically trivial and nontrivial phases. Here, we show that helical edge states can be identified by the randomgate-voltage induced Φ_(0)/2-period oscillation of the averaged electron return probability in the interferometer constructed by the edge states. The random gate voltage can highlight the Φ_(0)/2-period Al'tshuler–Aronov–Spivak oscillation proportional to sin^(2)(2πΦ/Φ_(0)) by quenching the Φ_(0)-period Aharonov–Bohm oscillation. It is found that the helical spin texture induced π Berry phase is key to such weak antilocalization behavior with zero return probability at Φ = 0. In contrast, the oscillation for the trivial edge states may exhibit either weak localization or antilocalization depending on the strength of the spin-orbit coupling, which has finite return probability at Φ = 0. Our results provide an effective way for the identification of the helical edge states. The predicted signature is stabilized by the time-reversal symmetry so that it is robust against disorder and does not require any fine adjustment of system.

Tunable topological interface states and resonance states of surface waves based on the shape memory alloy

Topological interface state(TIS)of elastic wave has attracted significant research interest due to its potential prospects in strengthening acoustic energy and enhancing the signal accuracy of damage identification and quantification.However,previous implementations on the interface modes of surface waves are limited to the non-adjustable frequency band and unalterable mode width.Here,we demonstrate the tunable TIS and topological resonance state(TRS)of Rayleigh wave by using a shape memory alloy(SMA)stubbed semi-infinite one-dimensional(1D)solid phononic crystals(PnCs),which simultaneously possesses the adjustable mode width.The mechanism of tunability stems from the phase transformation of the SMA between the martensite at low temperature and the austenite at high temperature.The tunable TIS of Rayleigh wave is realized by combining two bandgap-opened PnCs with different Zak phases.The TRS with adjustable mode width is achieved in the heterostructures by adding PnCs with Dirac point to the middle of two bandgap-opened PnCs with different Zak phases,which exhibits the extraordinary robustness in contrast to the ordinary Fabry–Perot resonance state.This research provides new possibilities for the highly adjustable Rayleigh wave manipulation and find promising applications such as tunable energy harvesters,wide-mode filters,and high-sensitivity Rayleigh wave detectors.

Tailoring topological corner states in photonic crystals by near-and far-field coupling effects

We explore the behaviors of optically coupled topological corner states in supercell arrays composed of photonic crystal rods,where each supercell is a second-order topological insulator.Our findings indicate that the coupled corner states possess nondegenerate eigenfrequencies at theΓpoint,with coupled dipole corner states excited resonantly by incident plane waves and displaying a polarization-independent characteristic.The resonance properties of coupled dipole corner states can be effectively modulated via evanescently near-field coupling,while multipole decomposition shows that they are primarily dominated by electric quadrupole moment and magnetic dipole moment.Furthermore,we demonstrate that these coupled corner states can form surface lattice resonances driven by diffractively far-field coupling,leading to a dramatic increase in the quality factor.This work introduces more optical approaches to tailoring photonic topological states,and holds potential applications in mid-infrared topological micro-nano devices.

Topological phases and type-II edge state in two-leg-coupled Su-Schrieffer-Heeger chains

Topological quantum states have attracted great attention both theoretically and experimentally.Here,we show that the momentum-space lattice allows us to couple two Su-Schrieffer-Heeger(SSH)chains with opposite dimerizations and staggered interleg hoppings.The coupled SSH chain is a four-band model which has sublattice symmetry similar to the SSH4.Interestingly,the topological edge states occupy two sublattices at the same time,which can be regarded as a one-dimension analogue of the type-II corner state.The analytical expressions of the edge states are also obtained by solving the eigenequations.Finally,we provide a possible experimental scheme to detect the topological winding number and corresponding edge states.

Dual-channel tunable near-infrared absorption enhancement with graphene induced by coupled modes of topological interface states

The dual-channel nearly perfect absorption is realized by the coupled modes of topological interface states(TIS) in the near-infrared range. An all-dielectric layered heterostructure composed of photonic crystals(Ph C)/graphene/Ph C/graphene/Ph C on Ga As substrate is proposed to excite the TIS at the interface of adjacent Ph C with opposite topological properties. Based on finite element method(FEM) and transfer matrix method(TMM), the dualchannel absorption can be modulated by the periodic number of middle Ph C, Fermi level of graphene, and angle of incident light(TE and TM polarizations). Especially, by fine-tuning the Fermi level of graphene around 0.4 e V, the absorption of both channels can be switched rapidly and synchronously. This design is hopefully integrated into silicon-based chips to control light.

Quantum transport signatures of non-trivial topological edge states in a ring-shaped Su–Schrieffer–Heeger double-chain system

In the ring-shaped Su–Schrieffer–Heeger(SSH)double-chain,the quantum interference between the two different electron tunneling paths of the upper and lower chains has an important influence on the electron transport properties of non-trivial topological edge states.Here,we have studied the electron transport signatures of non-trivial topological edge states in a ring-shaped SSH double-chain system based on the wave-guide theory and transfer-matrix method.In the ringshaped SSH double-chain with the upper chain being different from the lower one,it is demonstrated that the electron transmission probability displays the four and two resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes,respectively.Whereas in the case of the upper chain being the same as the lower one,the two transmission resonance peaks associated with the non-trivial topological edge states in the weak coupling regime are only found,and that in the strong coupling regime disappear that originated from the destructive interference between the two different electron tunneling paths of the upper and lower chains.Consequently,the variation of the number of transmission resonance peaks associated with the non-trivial topological edge states in the weak and strong coupling regimes suggests that an alternative scheme for detecting non-trivial topological edge states in the ring-shaped SSH doublechain system.

Surface states modulated exchange interaction in Bi2Se3/thulium iron garnet heterostructures

We investigate the modulation of magnetic anisotropy of thulium iron garnet(TmIG)films by interfaced Bi2Se3 thin films.High quality epitaxial growth of Bi2Se3 films has been achieved by molecular beam epitaxy on TmIG films.By the method of ferromagnetic resonance,we find that the perpendicular magnetic anisotropy(PMA)of TmIG can be greatly strengthened by the adjacent Bi2Se3 layer.Moreover,the competition between topological surface states and thickness dependent bulk states of Bi2Se3 gives rise to the modulation of PMA of the Bi2Se3/TmIG heterostructures.The interfacial interaction can be attributed to the enhanced exchange coupling between Fe^3+ions of TmIG mediated by topological surface electrons of Bi2Se3.

Single- and Few-Electron States in Deformed Topological Insulator Quantum Dots

We theoretically investigate the single- and few-electron states in deformed HgTe quantum dots （QDs） with an inverted band structure using the full configuration interaction method. For the circular and deformed QD, it is found that the energy of edge states is robust against the shape from the circular QD in various elliptic ones. For the few electron states, electrons will firstly fill the edge states localized at the short axis, then the states localized at the long axis of the QD before filling the bulk states. The filling of the edge states can be controlled by tuning the dot size or the deformation of the geometry of the HgTe QD, respectively.

Thermoelectric Transport by Surface States in Bi2Se3-Based Topological Insulator Thin Films

We develop a tractable theoretical model to investigate the thermoelectric （TE） transport properties of surface states in topological insulator thin films （TITFs） of Bi2Sea at room temperature. The hybridization between top and bottom surface states in the TITF plays a significant role. With the increasing hybridization-induced surface gap, the electrical conductivity and electron thermal conductivity decrease while the Seebeck coefficient increases. This is due to the metal-semiconductor transition induced by the surface-state hybridization. Based on these TE transport coefficients, the TE figure-of-merit ZT is evaluated. It is shown that ZT can be greatly improved by the surface-state hybridization. Our theoretical results are pertinent to the exploration of the TE transport properties of surface states in TITFs and to the potential application of Bi2Sea-based TITFs as high-performance TE materials and devices.

Competition of Quantum Anomalous Hall States and Charge Density Wave in a Correlated Topological Model

We investigate the topological phase transition driven by non-local electronic correlations in a realistic quantum anomalous Hall model consisting of d_(xy)–d_(x^(2)-y^(2)) orbitals. Three topologically distinct phases defined in the noninteracting limit evolve to different charge density wave phases under correlations. Two conspicuous conclusions were obtained: The topological phase transition does not involve gap-closing and the dynamical fluctuations significantly suppress the charge order favored by the next nearest neighbor interaction. Our study sheds light on the stability of topological phase under electronic correlations, and we demonstrate a positive role played by dynamical fluctuations that is distinct to all previous studies on correlated topological states.