Topological Band Research Articles

Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings

Topological flat bands, valley polarization, and interband superconductivity in magic-angle twisted bilayer graphene with proximitized spin-orbit couplings

Design of fragile topological flat bands in an optical microcavity array

Design of fragile topological flat bands in an optical microcavity array

Homotopy, symmetry, and non-Hermitian band topology

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal line-gap and point-gap classifications of non-Hermitian systems using K-theory have deepened the understanding of many physical phenomena. However, ample systems remain beyond this description; reference points and lines do not in general distinguish whether multiple non-Hermitian bands exhibit intriguing exceptional points, spectral braids and crossings. To address this we consider two different notions: non-Hermitian band gaps and separation gaps that crucially encompass a broad class of multi-band scenarios, enabling the description of generic band structures with symmetries. With these concepts, we provide a unified and comprehensive classification of both gapped and nodal systems in the presence of physically relevant parity-time ( PT ) and pseudo-Hermitian symmetries using homotopy theory. This uncovers new stable topology stemming from both eigenvalues and wave functions, and remarkably also implies distinct fragile topological phases. In particular, we reveal different Abelian and non-Abelian phases in PT -symmetric systems, described by frame and braid topology. The corresponding invariants are robust to symmetry-preserving perturbations that do not induce (exceptional) degeneracy, and they also predict the deformation rules of nodal phases. We further demonstrate that spontaneous PT symmetry breaking is captured by Chern–Euler and Chern–Stiefel–Whitney descriptions, a fingerprint of unprecedented non-Hermitian topology previously overlooked. These results open the door for theoretical and experimental exploration of a rich variety of novel topological phenomena in a wide range of physical platforms.

Intriguing Low-Temperature Phase in the Antiferromagnetic Kagome Metal FeGe.

The properties of kagome metals are governed by the interdependence of band topology and electronic correlations resulting in remarkably rich phase diagrams. Here, we study the temperature evolution of the bulk electronic structure of the antiferromagnetic kagome metal FeGe using infrared spectroscopy. We uncover drastic changes in the low-energy interband absorption at the 100K structural phase transition that has been linked to a charge-density-wave (CDW) instability. We explain this effect by the minuscule Fe displacement in the kagome plane, which results in parallel bands in the vicinity of the Fermi level. In contrast to conventional CDW materials, however, the spectral weight shifts to low energies, ruling out the opening of a CDW gap in FeGe.

Resonant edge-state switching across topological bulk bands

We propose a physical mechanism allowing topological excitations with the same Bloch momentum belonging to distinct gaps to be resonant switched. This offers an opportunity to observe both intra-gap and inter-gap resonant edge-state switching. Increasing modulation depth significantly accelerates the resonant switching, while frequency de-tuning inhibits the switching. However, for the same set of parameters, the inter-gap conversion is always faster and more efficient than the intra-gap conversion. Furthermore, weak nonlinearity nearly completely hinders intra-gap switching, but it has almost no effect on inter-gap switching. This fact indicates that inter-gap resonant edge-state switching is more applicable for the nonlinear polaritons system. Additionally, we found that the dependence of switching time on the Bloch momentum qualitatively differed for these two different types of resonant edge-state switching. The results can be applied to a Bose Einstein condensate system to realize cold-atom resonant edge-state switching.

A multi-frequency interpolation method for bi-material topology optimization of vibro-acoustic problems

In practical vibro-acoustic problems, external excitation normally contains a certain frequency band structure, and system optimization needs to be performed through frequency band analysis. To reduce the high computation burden in frequency band optimization, we propose a multi-frequency interpolation method for bi-material topology optimization of the vibro-acoustic interaction system. A highly accurate solution of the vibro-acoustic interaction problem is achieved by combining the advantages of the structural finite element method and the acoustic boundary element method. A structural material interpolation model is established using the solid isotropic material with penalization method, and the topological sensitivity formulation is derived based on the adjoint variable method. On the basis of the smoothness property of the radiation impedance matrix, the matrix interpolation method is adopted to obtain the objective function at the frequency points in the frequency band of interest, thus improving the computational efficiency of frequency band topology optimization. The zero points of the Chebyshev polynomial are selected as the interpolation nodes to improve calculation accuracy. The effectiveness of the proposed multi-frequency interpolation method is verified by several numerical tests, and the radiated sound power is reduced considerably after the developed bi-material topology optimization.

Evolution of an Overlapped Bandgap and Topological Flat Bands in a Higher‐Order Valley Photonic Insulator Based on Dendritic Structure

AbstractRobust edge states and corner states in photonic topological insulators provide effective ways to manipulate the propagation of electromagnetic waves. Bandgaps of the previously reported photonic topological insulators are independent of each other. In this paper, a higher‐order valley photonic insulator composed of arrays of dendritic structure is designed. The band structure shows an overlapped bandgap is observed, and the overlapped bandgap divides the band structure into three bandgaps. The evolution of the overlapped bandgap is investigated by changing the geometric parameters and increasing the fractal to break the C3v symmetry drastically. Besides, it is notable that the band structure of the proposed valley photonic insulator is flat bands. It is demonstrated that undistorted transmission can be observed as a plane electromagnetic wave transmits through the proposed valley photonic insulator. The interface consisting of two valley photonic structures with distinct topological nontrivial phases is constructed. Edge states and corner states with strong energy localization are obtained in multi‐band frequencies. Remarkably, two triangular structures with different Wannier center configurations both have corner states in the same bandgap, which does not obey the valley selectivity. The phenomenon is caused by the weak valley locking property due to the overlapped bandgap. The proposed valley photonic insulators are expected to benefit applications in optical devices such as topological lasers.

Orbital Ingredients and Persistent Dirac Surface State for the Topological Band Structure in FeTe0.55Se0.45

FeTe0.55Se0.45 (FTS) occupies a special spot in modern condensed matter physics at the intersections of electron correlation, topology, and unconventional superconductivity. The bulk electronic structure of FTS is predicted to be topologically nontrivial due to the band inversion between the dxz and pz bands along Γ−Z. However, there remain debates in both the authenticity of the Dirac surface states (DSSs) and the experimental deviations of band structure from the theoretical band inversion picture. Here we resolve these debates through a comprehensive angle-resolved photoemission spectroscopy investigation. We first observe a persistent DSS independent of kz. Then, by comparing FTS with FeSe, which has no band inversion along Γ−Z, we identify the spectral weight fingerprint of both the presence of the pz band and the inversion between the dxz and pz bands. Furthermore, we propose a renormalization scheme for the band structure under the framework of a tight-binding model preserving crystal symmetry. Our results highlight the significant influence of correlation on modifying the band structure and make a strong case for the existence of topological band structure in this unconventional superconductor. Published by the American Physical Society 2024

Crystal structure, properties and pressure-induced insulator-metal transition in layered kagome chalcogenides

Layered materials with kagome lattice have attracted a lot of attention due to the presence of nontrivial topological bands and correlated electronic states with tunability. In this work, we investigate a unique van der Waals (vdW) material system, A 2 M 3 X 4 (A = K, Rb, Cs; M = Ni, Pd; X = S, Se), where transition metal kagome lattices, chalcogen honeycomb lattices and alkali metal triangular lattices coexist simultaneously. A notable feature of this material is that each Ni/Pd atom is positioned in the center of four chalcogen atoms, forming a local square-planar environment. This crystal field environment results in a low spin state S= 0 of Ni2+/Pd2+. A systematic study of the crystal growth, crystal structure, magnetic and transport properties of two representative compounds, Rb2Ni3S4 and Cs2Ni3Se4, has been carried out on powder and single crystal samples. Both compounds exhibit nonmagnetic p-type semiconducting behavior, closely related to the particular chemical environment of Ni2+ ions and the alkali metal intercalated vdW structure. Additionally, Cs2Ni3Se4 undergoes an insulator-metal transition (IMT) in transport measurements under pressure up to 87.1 GPa without any structural phase transition, while Rb2Ni3S4 shows the tendency to be metalized.

Superfluid stiffness and Josephson quantum capacitance: Adiabatic approach and topological effects

We bring forward a unified framework for the study of the superfluid stiffness and the quantum capacitance of superconducting platforms exhibiting conventional spin-singlet pairing. We focus on systems which in their normal phase contain topological band touching points or crossings, while in their superconducting regime feature a fully gapped energy spectrum. Our unified description relies on viewing these two types of physical quantities as the charge current and density response coefficients obtained for slow spatiotemporal variations of the superconducting phase. Within our adiabatic formalism, the two coefficients are given in terms of Berry curvatures defined in synthetic spaces. Our paper lays the foundation for the systematic description of topological diagonal superfluid responses induced by singularities dictating the synthetic Berry curvatures. We exemplify our approach for concrete one- and two-dimensional models of superconducting topological (semi)metals. We discuss topological phenomena which arise in the superfluid stiffness of bulk systems and the quantum capacitance of Josephson junctions. We show that both coefficients become proportional to a topological invariant which counts the number of topological touchings or crossings of the normal phase band structure. These topological effects can be equivalently viewed as manifestations of chiral anomaly. Our predictions appear experimentally testable in topological semimetals with proximity-induced pairing, such as in graphene-superconductor hybrids at charge neutrality. Published by the American Physical Society 2024

Non-Abelian Braiding of Topological Edge Bands.

Braiding is a geometric concept that manifests itself in a variety of scientific contexts from biology to physics, and has been employed to classify bulk band topology in topological materials. Topological edge states can also form braiding structures, as demonstrated recently in a type of topological insulators known as Möbius insulators, whose topological edge states form two braided bands exhibiting a Möbius twist. While the formation of Möbius twist is inspiring, it belongs to the simple Abelian braid group B_{2}. The most fascinating features about topological braids rely on the non-Abelianness in the higher-order braid group B_{N} (N≥3), which necessitates multiple edge bands, but so far it has not been discussed. Here, based on the gauge enriched symmetry, we develop a scheme to realize non-Abelian braiding of multiple topological edge bands. We propose tight-binding models of topological insulators that are able to generate topological edge states forming non-Abelian braiding structures. Experimental demonstrations are conducted in two acoustic crystals, which carry three and four braided acoustic edge bands, respectively. The observed braiding structure can correspond to the topological winding in the complex eigenvalue space of projective translation operator, akin to the previously established point-gap winding topology in the bulk of the Hatano-Nelson model. Our Letter also constitutes the realization of non-Abelian braiding topology on an actual crystal platform, but not based on the "virtual" synthetic dimensions.

Delocalization and higher-order topology in a nonlinear elastic lattice

Topological elastic waves provide novel and robust ways for manipulating mechanical energy transfer and information transmission, with potential applications in vibration control, analog computation, and more. Recently discovered higher-order topological insulators (HOTIs) with multidimensional and hierarchical edge states can further expand the capabilities of topological elastic waves. However, the effects of nonlinearity on elastic HOTIs remain elusive. In this paper, we propose a nonlinear elastic higher-order topological Kagome lattice. After briefly reviewing its linear properties, we explore the effects of nonlinearity on the higher-order band topology and topological states. To do this, we have developed a method to calculate approximate nonlinear modes in order to identify the bulk polarization and probe the higher-order topological phase in the nonlinear lattice. We find that nonlinearity induces unusual delocalization of topological corner states, band crossing, and higher-order topological phase transition. The delocalization reveals that intracell hardening nonlinearity leads to direct delocalization of topological corner states while intracell softening nonlinearity first enhances and then reduces localization. The nonlinear higher-order topological phase is amplitude dependent, and we demonstrate a transition from a trivial to a non-trivial phase, enabling amplitude induced topological corner and edge states. Additionally, this phase transition corresponds to the closing and reopening of the bandgap, accompanied by an unusual band crossing. By examining the band topology before and after the band crossing, we find that the bulk polarization becomes quantized with respect to amplitude and can predict higher-order topological phases in nonlinear lattices. The obtained results are expected to be beneficial for the development of tunable and robust elastic wave devices.

Static topological mechanics with local resonance

The locally resonant band gaps that lie in the vicinity of resonant frequency have been extensively employed in metamaterials for ultralow-frequency wave control, such as vibration isolation, negative refraction, superlensing, and cloaking. The combination of local resonance and band topology allows for the broadband tunable topological boundary modes, ranging from audible to ultrasonic frequencies. Recently, nontrivial topological boundary modes have been reported in static mechanical systems beyond frequency-based wave dynamics, in which the band gap is typically Bragg-like. In this paper, the concept of local resonance is extended from dynamic to static systems where the inertial effects are absent, and is leveraged to customize the topological modes. We impart a pseudo-mass to the static systems and retrieve the locally resonant band gap. The eigenvalues and associated bulk deformation fields of the topological mode can be tailored by shifting the pseudo-resonant frequency. Moreover, an effective non-reciprocity is achieved by passively breaking the lattice symmetry, and its cooperation with local resonances enables the static metamaterial to shield eccentric deformations and selectively filter boundary loads. All of these models are experimentally validated in an assembled truss-like lattice. This study is expected to provide a platform for exploring locally resonant topological phases without relying on wave motion.

Topological spectral bands with frieze groups

Topological spectral bands with frieze groups

Asymmetric frequency multiplexing topological devices based on a floating edge band

Topological photonics provides a platform for robust energy transport regardless of sharp corners and defects. Recently, the frequency multiplexing topological devices have attracted much attention due to the ability to separate optical signals by wavelength and hence the potential application in optical communication systems. Existing frequency multiplexing topological devices are generally based on the slow light effect. However, the resulting static local spatial mode or finely tuned flat band has zero-group velocity, making it difficult for both experimental excitation and channel out-coupling. Here, we propose and experimentally demonstrate an alternative prototype of asymmetric frequency multiplexing devices including a topological rainbow and frequency router based on floating topological edge mode (instead of localized ones); hence the multiple wavelength channels can be collectively excited with a point source and efficiently routed to separate output ports. The channel separation in our design is achieved by gradually tuning the band gap truncation on a topological edge band over a wide range of frequencies. A crucial feature lies in that the topological edge band is detached from bulk states and floating within the upper and lower photonic band gaps. More interestingly, due to the sandwiched morphology of the edge band, the top and bottom band gaps will each truncate into transport channels that support topological propagation towards opposite directions, and the asymmetrical transportation is realized for the frequency multiplexing topological devices.

Topological phases and edge modes of an uneven ladder

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

Two-fold symmetry of the in-plane resistance in kagome superconductor Cs(V1–xTax)3Sb5 with enhanced superconductivity

Abstract The kagome superconductor CsV3Sb5 has attracted widespread attention due to its rich correlated electron states including superconductivity, charge density wave (CDW), nematicity, and pair density wave. Notably, the modulation of the intertwined electronic orders by the chemical doping is significant to illuminate the cooperation/competition between multiple phases in kagome superconductors. In this study, we have synthesized a series of tantalum-substituted Cs(V1−x Ta x )3Sb5 by a modified self-flux method. Electrical transport measurements reveal that CDW is suppressed gradually and becomes undetectable as the doping content of x is over 0.07. Concurrently, the superconductivity is enhanced monotonically from T c ∼ 2.8 K at x = 0 to 5.2 K at x = 0.12. Intriguingly, in the absence of CDW, Cs(V1−x Ta x )3Sb5 (x = 0.12) crystals exhibit a pronounced two-fold symmetry of the in-plane angular-dependent magnetoresistance (AMR) in the superconducting state, indicating the anisotropic superconducting properties in the Cs(V1−x Ta x )3Sb5. Our findings demonstrate that Cs(V1−x Ta x )3Sb5 with the non-trivial band topology is an excellent platform to explore the superconductivity mechanism and intertwined electronic orders in quantum materials.

Rashba-splitting-induced topological flat band detected by anomalous resistance oscillations beyond the quantum limit in ZrTe5

Topological flat bands — where the kinetic energy of electrons is quenched — provide a platform for investigating the topological properties of correlated systems. Here, we report the observation of a topological flat band formed by polar-distortion-assisted Rashba splitting in the three-dimensional Dirac material ZrTe5. The polar distortion and resulting Rashba splitting on the band are directly detected by torque magnetometry and the anomalous Hall effect, respectively. The local symmetry breaking further flattens the band, on which we observe resistance oscillations beyond the quantum limit. These oscillations follow the temperature dependence of the Lifshitz–Kosevich formula but are evenly distributed in B instead of 1/B at high magnetic fields. Furthermore, the cyclotron mass gets anomalously enhanced about 102 times at fields ~ 20 T. Our results provide an intrinsic platform without invoking moiré or order-stacking engineering, which opens the door for studying topologically correlated phenomena beyond two dimensions.

Topological pumping induced by spatiotemporal modulation of interaction

Particle-particle interaction provides a new degree of freedom to induce novel topological phenomena. Here, we propose to use spatiotemporal modulation of interaction to realize topological pumping without a single-particle counterpart. Because the modulation breaks time-reversal symmetry, the multiparticle energy bands of bound states have none-zero Chern number, and support topological bound edge states. In a Thouless pump, a bound state that uniformly occupies a topological energy band can be shifted by integer unit cells per cycle, consistent with the corresponding Chern number. We can also realize topological pumping of bound edge state from one end to another. The entanglement entropy between particles rapidly increases at transition points, which is related to the spatial spread of a bounded pair. In addition, we propose to realize hybridized pumping with fractional displacement per cycle by adding an extra tilt potential to separate topological pumping of the bound state and Bloch oscillations of single particle. Our work could trigger further studies of correlated topological phenomena that do not have a single-particle counterpart.

Hydrogenation of Covalent Organic Framework Induces Conjugated π Bonds and Electronic Topological Transition to Enhance Hydrogen Evolution Catalysis.

Recently, many topological materials have been discovered as promising electrocatalysts in chemical conversion processes and energy storage. However, it remains unclear how the topological electronic states specifically modulate the catalytic reaction. Here, the two-dimensional metal phthalocyanine-based covalent organic framework (MPc-COF) is studied by ab initio thermodynamic calculations to clearly reveal the promotional effect on the electrochemical hydrogen evolution reaction (HER) induced by topological gapless bands (TGBs). We find that the prehydrogenated (and fluorinated) H4CdPc-COF(F) shows the best HER performance, with 0.016 V (near zero) overpotential. By tracking changes to the electronic structure and free energy as the prehydrogenation and HER processes occur, we are able to separately attribute the high HER efficiency in part due to the increase of the electron bath by donating electrons to the conjugated π bonds and also to the existence of TGBs. Specifically, the significant catalytic promotion by TGBs is proven to decrease the free energy by 0.218 eV to near zero. When the TGBs are destroyed, e.g., by replacing N with P and opening a band gap, the HER efficiency is reduced. This study opens avenues for deterministically harnessing topological band features to improve electrocatalysis.