Nontrivial Topological Properties Research Articles

Controllable topological edge mode in an optically excited exciton-polariton lattice

We propose an all-optical scheme of topological lasing and switching based on the Aubry-Andr\'e-Harper (AAH) model of an exciton-polariton chain. We theoretically show that the phase parameter of the optical potential, with a tunable effective quasimomentum, allows the system to exhibit nontrivial topological properties which are attributed to higher dimensions. The topological modes emerging within the bulk band gaps are spatially localized at the edges of the polariton lattice, and their topological properties are characterized by the nonzero Chern numbers of the bulk bands. Polariton lasing in topological edge modes exhibits a higher efficiency and better robustness than in bulk modes, and can be switched between two opposite edges of the lattice by nonresonant excitation, which paves a way for topologically protected optical circuits.

Room temperature quantum anomalous Hall insulator in honeycomb lattice, RuCS3, with large magnetic anisotropy energy

The quantum anomalous Hall (QAH) effect has attracted enormous attention since it can induce topologically protected conducting edge states in an intrinsic insulating material. For practical quantum applications, the main obstacle is the non-existent room temperature QAH systems, especially with both large topological band gap and robust ferromagnetic order. Here, according to first-principles calculations, we predict the realization of the room temperature QAH effect in a two-dimensional (2D) honeycomb lattice, RuCS3 with a non-zero Chern number of C = 1. Especially, the nontrivial topology band gap reaches up to 336 meV for RuCS3. Moreover, we find that RuCS3 has a large magnetic anisotropy energy (2.065 meV) and high Curie temperature (696 K). We further find that the non-trivial topological properties are robust against the biaxial strain. The robust topological and magnetic properties make RuCS3 have great applications in room temperature spintronics and nanoelectronics.

Non-Hermitian topology and exceptional-point geometries

Non-Hermitian theory is a theoretical framework used to describe open systems. It offers a powerful tool in the characterization of both the intrinsic degrees of freedom of a system and the interactions with the external environment. The non-Hermitian framework consists of mathematical structures that are fundamentally different from those of Hermitian theories. These structures not only underpin novel approaches for precisely tailoring non-Hermitian systems for applications but also give rise to topologies not found in Hermitian systems. In this Review, we provide an overview of non-Hermitian topology by establishing its relationship with the behaviours of complex eigenvalues and biorthogonal eigenvectors. Special attention is given to exceptional points — branch-point singularities on the complex eigenvalue manifolds that exhibit nontrivial topological properties. We also discuss recent developments in non-Hermitian band topology, such as the non-Hermitian skin effect and non-Hermitian topological classifications. Non-Hermitian theory consists of mathematical structures that are used to describe open systems, which can give rise to non-Hermitian topology not found in Hermitian systems. This Review provides an overview of non-Hermitian band topology and discusses recent developments, such as the non-Hermitian skin effect and non-Hermitian topological classifications.

Strain-induced two-dimensional topological insulators in monolayer 1T′-RuO2

Because of their unique structure and novel physical properties, two-dimensional (2D) transition metal dichalcogenides (TMDs) have received a lot of attention in recent years. In this paper, we propose a new 2D TMD 1T′-RuO2 with tunable topological properties. Based on first-principles calculations, we demonstrate that it has good dynamics, thermodynamic, energetic stability, and anisotropic mechanical properties. Although 1T′-RuO2 is a typical semiconductor with a direct bandgap, it can be transformed into topological insulator by applying uniaxial tensile strains. The topological phase transition is attributed to the d–d band inversion at Γ point. The nontrivial topological property is further validated by the topological edge states. We predict that monolayer 1T′-RuO2 is an excellent material for future electronic devices with tunable topological properties.

Quantum anomalous Hall effect in M2X3 honeycomb Kagome lattice

The quantum anomalous Hall (QAH) effect has recently drawn great attention in spintronics with extraordinary property of chiral edge states without dissipation in absence of magnetic field. In M2X3 honeycomb Kagome lattice, numerous two-dimensional materials are predicted to be QAH insulators including metal oxides/sulfides and metal organic lattice. In this work, we proposed a general model to explain the mechanism of Dirac half metal with absence of spin orbital coupling and the nontrivial topological property with spin orbital coupling, which could be induced by combination of electron counting rule, crystal field effect and orbitals hybridization. Based on the mechanism, we further predict that triphenyl-metal lattice M2(C6H4)3 (M = V, Nb, Ta) are all QAH insulators with high Curie temperature and large nontrivial band gap for triphenyl-Nb and triphenyl-Ta lattice.

Emergent topological states via digital (001) oxide superlattices

Oxide heterostructures exhibit many intriguing properties. Here we provide design principles for inducing multiple topological states in (001) (AMO3)1/(AM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$AM^{\\prime}$$\\end{document}O3)1 oxide superlattices. Aided by first-principles calculations and model analysis, we show that a (SrMO3)1/(SrM′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document}O3)1 superlattice (M = Nb, Ta and M′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$M^{\\prime}$$\\end{document} = Rh, Ir) is a strong topological insulator with Z2 index (1;001). More remarkably, a (SrMoO3)1/(SrIrO3)1 superlattice exhibits multiple coexisting topological insulator (TI) and topological Dirac semi-metal (TDS) states. The TDS state has a pair of type-II Dirac points near the Fermi level and symmetry-protected Dirac node lines. The surface TDS Dirac cone is sandwiched by two surface TI Dirac cones in the energy-momentum space. The non-trivial topological properties arise from the band inversion between d orbitals of two dissimilar transition metal atoms and a particular parity property of (001) superlattice geometry. Our work demonstrates how to induce non-trivial topological states in (001) perovskite oxide heterostructures by rational design.

Topological materials for full-vector elastic waves.

Elastic wave manipulation is important in a wide variety of applications, including information processing in small elastic devices and noise control in large solid structures. The recent emergence of topological materials has opened new avenues for modulating elastic waves in solids. However, because of the full-vector feature and the complicated couplings of the longitudinal and transverse components of elastic waves, manipulating elastic waves is generally difficult compared with manipulating acoustic waves (scalar waves) and electromagnetic waves (vectorial waves but transverse only). To date, topological materials, including insulators and semimetals, have been used for acoustic and electromagnetic waves. Although topological materials with elastic waves have also been reported, the observed topological edge modes lie on the domain wall. A natural question arises: Is there an elastic metamaterial with topological edge modes on its own boundary? Here, we report a 3D metal-printed bilayer metamaterial that topologically insulates elastic waves. By introducing chiral interlayer couplings, the spin-orbit couplings for elastic waves are induced, which give rise to nontrivial topological properties. Helical edge states with vortex features were demonstrated on the boundary of the single topological phase. We further show a heterostructure of the metamaterial that exhibits tunable edge transport. Our findings could be used in devices based on elastic waves in solids.

Evidence for topological features in the electronic and phononic bands of ZGeSb (Z = Hf, Zr, Ti) class of compounds

Nontrivial topological properties in materials have been found in either the electronic or the phononic bands, but they have seldom been shown in both for a compound. With the aid of first-principle calculations, our paper attempts to find topological features in the electron and phonon band structures of ZGeSb (Z = Hf, Zr, Ti) class of compounds. The electron band structure exhibits two nodal rings in each of these compounds. Furthermore, drumhead surface states (DSS) have also been shown. The phonon band structure depicts one nodal ring in each of these compounds. DSS is also seen in the phonon surface states. Layering possibility has also been explored in HfGeSb, which admits a nodal ring each in its electronic and phononic band structure. Finally, these compounds (bulk and mono-layer) possess Dirac points robust to spin–orbit coupling effects, with at least one such Dirac point with its linear dispersion extending to the Fermi energy. Therefore, these compounds fall under the topological nodal line metals class, which is rarely seen in materials. These compounds’ theoretical nontrivial topological nature in their electronic and phononic band structure provides a profound grasp of electronic and phononic nodal-line physics and is a good candidate for experimental verification. The existence of Dirac points close to the Fermi level could also motivate one to look for extreme magnetoresistance in these compounds. Moreover, given their largely metallic nature, these compounds become an excellent arena for novel device applications.

Topological properties of CsCl type superconducting materials

By using the first-principles electronic structure calculation, we have studied electronic band structures and topological properties of CsCl type binary superconductors RuTi and OsTi. Due to the protection of higher crystal symmetry, there are three-dimensional nodal rings around high symmetry points X, Y and Z without spin-orbital coupling (SOC). When SOC is considered, we find the topological phase transition from strong topological insulator phase in RuTi to Dirac semimetal in OsTi. The corresponding surface states are consistent with these nontrivial topologies. We also find strong topological insulator phases near Fermi level in isostructure material MgRh. Based on the topological surface states, the interface of heterostructure of superconductor RuTi (OsTi) and doped topological material MgRh could realize observable topological superconductivity. The nontrivial topological properties in binary superconductors RuTi and OsTi provide us new desirable avenues to study Majorana bound states in vortex cores of topological superconductor.

Nonsymmorphic P21/m‐MoTe2: Novel 2D Topological Materials

Nonsymmorphic symmetries play a significant role in the emergence of topological nontrivial phases in some 2D materials. Herein, a new 2D material P21/m‐MoTe2 with nontrivial topological properties and nonsymmorphic symmetries is proposed. With the help of first‐principles calculations, it is found that it is dynamically stable, and has relatively high energetic stability. When spin–orbit coupling (SOC) is ignored, this material is a semimetal with two intersects appearing on the high‐symmetry line Γ–Y. Detailed symmetry analysis reveal that they are protected by the screw operator . After SOC is turned on, it turns into a topological insulator with a global bandgap of 94 meV. The large gap ensures that the topological nontrivial phase is robust to an external perturbation. The discovery of nonsymmorphic P21/m‐MoTe2 expands the family of transition metal dichalcogenides and provides a new platform to study topological phases in 2D nonsymmorphic materials.

Topological edge states of quasiperiodic elastic metasurfaces

In this work, we investigate the dynamic behavior and the topological properties of quasiperiodic elastic metasurfaces, namely arrays of mechanical oscillators arranged over the free surface of a semi-infinite elastic medium according to a quasiperiodic spatial distribution. An ad-hoc multiple scattering formulation is developed to describe the dynamic interaction between Rayleigh waves and a generic array of surface resonators. The approach allows to calculate the spectrum of natural frequencies of the quasiperiodic metasurface which reveals a fractal distribution of the frequency gaps reminiscent of the Hofstadter butterfly. These gaps have nontrivial topological properties and can host Rayleigh-like edge modes. We demonstrate that such topologically protected edge modes can be driven from one boundary to the opposite of the array by a smooth variation of the phason, a parameter which modulates the geometry of the array. The proposed analytical framework could pave the way towards the design of devices for surface wave localization with applications in vibration mitigation and energy harvesting technologies.

Realization of topological superlattices and the associated interface states in one-dimensional plasmonic crystals

In analogous to the Su-Schrieffer-Heeger (SSH) model, one-dimensional (1D) electromagnetic (EM) crystals can exhibit nontrivial topological properties. In particular, when a nontrivial EM crystal is in contact with its trivial counterpart, a topologically protected interface state is formed. While much attention has been focused on single interface state, multiple interface states can interact collectively when under suitable conditions, giving rise to trivial or nontrivial band topologies resembling to the standard SSH model. Here, we study the topological properties of 1D metallic superlattices that support multiple interface states. We first demonstrate single interface state exists at the boundary between two topologically distinct metallic arrays that carry Bloch-like surface plasmon polaritons. Such interface state is then used as the building block for further constructing the superlattices. By exploiting the separation between two dimerized interface states and the distinct inter- and intra-interface configurations to facilitate different intracell and intercell interactions, we vary the band topology of the superlattices. More importantly, new superlattice interface state is formed when trivial and nontrivial superlattices are brought together. The superlattice interface state is found to have smaller angular divergence and longer localization length than its single counterpart, thus is desired for robust signal transmission and high finesse cavity.

Dirac Fermions in the Boron Nitride Monolayer with a Tetragon.

Two-dimensional (2D) boron nitride (BN) is a promising candidate for aerospace materials due to its excellent mechanical and thermal stability properties. However, its unusually prominent band gap limits its application prospects. In this work, we report a gapless monolayer BN, t-BN, which has four anisotropic Dirac cones in the first Brillouin zone exactly at the Fermi level. To further confirm the semimetallic character, the nontrivial topological properties are proven through the topologically protected edge states and the invariant non-zero Z2. Additionally, the Young's modulus and Poisson ratio characterize the strong mechanical strength of t-BN. Our theoretical predictions provide more possibilities for exploring the Dirac cone in BN, which will enhance the 2D boron derivative materials.

Self-assembly of magnetic Co atoms on stanene

We have investigated magnetic Co atoms self-assembled on ultraflat stanene on Cu(111) substrate by utilizing scanning tunneling microscopy/spectroscopy (STM/STS) in conjunction with density functional theory (DFT). By means of depositing Co onto the stanene/Cu(111) held at 80 K, Co atoms have developed into monomer, dimer, and trimer structures containing one, two, and three Co atoms, respectively. As per atomically resolved topographic images and bias-dependent apparent heights, the atomic structure models based on Sn atoms substituted by Co atoms have been deduced, which are in agreement with both self-consistent DFT calculations and STM simulations. Apart from that, the projected density of states has revealed a maximum at around $\ensuremath{-}0.5$ eV from the Co-3${d}_{3{z}^{2}\ensuremath{-}{r}^{2}}$ minority band, which contributes predominately to the peak feature at about $\ensuremath{-}0.3$ eV in tunneling conductance $(dI/dU)$ spectra taken at the Co atomic sites. As a result of the exchange splitting between the $\mathrm{Co}\text{\ensuremath{-}}3d$ majority and minority bands, there are nonzero magnetic moments, including about $0.60{\ensuremath{\mu}}_{B}$ in monomer, $0.56{\ensuremath{\mu}}_{B}$ in dimer, and $0.29{\ensuremath{\mu}}_{B}$ in trimer of the Co-atom assembly on the stanene. Such a magnetic Co-atom assembly, therefore, could provide the vital building blocks to stabilize the local magnetism on two-dimensional stanene with nontrivial topological properties.

Tailoring higher-order topological phases via orbital hybridization

Higher-order topological insulators (HOTIs) have attracted much attention in photonics due to the tightly localized disorder-robust corner and hinge states. Here, we reveal an unconventional HOTI phase with vanishing dipole and quadrupole polarizations. This phase arises in the array of evanescently coupled waveguides hosting degenerate $s$- and $d$-type orbital modes arranged in a square lattice with four waveguides in the unit cell. As we prove, the degeneracy of the modes with the different symmetry gives rise to the nontrivial topological properties rendering the system topologically equivalent to the two copies of the anisotropic two-dimensional Su-Schrieffer-Heeger model rotated by ${90}^{\ensuremath{\circ}}$ with respect to each other and based on $s\ifmmode\pm\else\textpm\fi{}d$ hybridized orbitals. We probe the unusual topology of the model by constructing a quantized Fu-Kane-type pseudospin pump. Our results introduce a route to tailor higher-order band topology leveraging both crystalline symmetries and accidental degeneracies of the different orbital modes.

Nondiagonal disorder enhanced topological properties of graphene with laser irradiation

Laser irradiation, as a versatile tool to tune topological properties of electronic systems, is under intensive studies. Experimentally, laser irradiation induced anomalous Hall effect in graphene has been observed (McIver et al., Nat. Phys. 16, 38 (2020)). Disorder is ubiquitous in real materials, and it has been shown that diagonal disorders, i.e., onsite disorder, can enhance topological properties of time-periodically driven quantum materials (Titum et al., Phys. Rev. Lett. 114, 056801 (2015)). Here, we investigate circularly polarized laser irradiated graphene with non-diagonal disorders, i.e., disordered tunneling, and find that disorder can induce nontrivial topological properties, characterized by Bott index and the real-space Chern number. Moreover, we show that one can turn on the laser irradiation non-adiabatically to drive the disordered graphene into non-trivial topological phase. It is a scheme which is especially interesting for experimental implementations.

Complete classification of band nodal structures and massless excitations

Nodal structures (NSrs) where energy bands meet to be degenerate in the Brillouin zone (BZ) in the form of point, line or surface, received immense research interest in the past decade. However, the nearly NSrs with negligible gaps, can also own many exotic quantum responses and nontrivial topological properties and deserve a systematic investigation. Here, we provide a complete list of all symmetry-diagonalizable strictly and nearly NSrs in the 1651 magnetic space groups (MSGs) and 528 magnetic layer groups (MLGs) in both spinful and spinless settings. We first apply compatibility relations (CRs) which encode how bands split from a band node (BN) (located at a symmetric point of BZ), to obtain all NSrs (emanating from the BN). The NSrs by CRs are definitely strict and are exhaustively enumerated based on all irreducible representations of the little groups for all BNs. We then construct $k\cdot p$ models around BNs and prove that there is a cutoff $k\cdot p$ order (6 at most) for any BN which is sufficient to predict the corresponding strictly NSrs and including higher-order $k\cdot p$ terms cannot gap the NSrs. We provide all $k\cdot p$ models up to the cutoff orders around all the BNs, and comprehensively explore all the nearly NSrs by lowering the $k\cdot p$ order. Our results reveal that the same as BNs, the NSrs, especially the nearly NSrs, are also ubiquitous. For example, while strictly nodal surface can only exist in some nonsymmorphic MSGs, nearly nodal surface can occur even in many low symmetric MSGs. Moreover, we also find that for some BNs, the method of $k\cdot p$ modeling could give more strictly NSrs than CRs. With our complete list, one can conveniently obtain all possible NSrs for any two/three-dimensional and nonmagnetic/magnetic material, and given a target NSr, one can also design/search for materials realizations based on the MSGs/MLGs.

Unusual Electrical and Magnetic Properties in Layered EuZn2As2

AbstractEu‐based compounds often exhibit unusual magnetism, which is critical for nontrivial topological properties seen in materials such as EuCd2As2. The authors investigate the structure and physical properties of EuZn2As2 through measurements of the electrical resistivity, Hall effect, magnetization, and neutron diffraction. Their data show that EuZn2As2 orders antiferromagnetically with an A‐type spin configuration belowTN = 19 K. Surprisingly, there is strong evidence for dominant ferromagnetic fluctuations aboveTN, as reflected by positive Curie–Weiss temperature and extremely large negative magnetoresistance (MR) betweenTNandTfl≈200 K. Furthermore, the angle dependence of the MRabindicates field‐induced spin reorientation from theab‐plane to a direction ≈45° from theabplane. Compared to EuCd2As2, the doubledTNandTflmake EuZn2As2 a better platform for exploring nontrivial magnetic and electronic properties in both magnetic fluctuation (TN < T < Tfl) and ordered (T < TN) regimes.

Bad topological semimetals in layered honeycomb compounds

The Mott transition in honeycomb compounds with significant spin-orbit coupling is explored. At finite temperatures we identify a novel semimetallic phase located between a topological insulator and a topological Mott insulator. This semimetal is characterized by having no charge gap, no quasiparticles, and gapped spin excitations with nontrivial topological properties. While charge conduction is incoherent involving mean-free paths violating the Mott-Ioffe-Regel limit, spin excitations can be transported ballistically along the edges giving rise to a quantized spin conductance. Such bad topological semimetal could be searched for close to the Mott transition in certain twisted bilayers of transition metal dicalchogenides.

Emergence of Floquet edge states in the coupled Su–Schrieffer–Heeger model

The emergence of non equilibrium topological phases in low dimensional systems offers an interesting route for material properties engineering. We analyze the dynamical modulation of two coupled one-dimensional chains, described by the Su–Schrieffer–Heeger model. We find that the interplay of driving interactions and interchain coupling leads to the emergence of non-equilibrium edge states with nontrivial topological properties. Using an effective Hamiltonian approach, we quantify the emergent topological phases via the winding number and show that oscillations in the mean pseudospin polarization arise as a consequence of the periodic modulation. The patterns of these pseudospin oscillations are different for the static trivial and topological phases offering a dynamical means to distinguish both physical configurations. The system also exhibits non integer values of the winding number, which have been recently reported experimentally in connection to spin textures.