Topological Bulk Research Articles

Non-Hermitian Boundary in a Surface Selective Reconstructed Magnetic Weyl Semimetal.

Non-Hermitian physics, studying systems described by non-Hermitian Hamiltonians, reveals unique phenomena not present in Hermitian systems. Unlike Hermitian systems, non-Hermitian systems have complex eigenvalues, making their effects less directly observable. Recently, significant efforts have been devoted to incorporating the non-Hermitian effects into condensed matter physics. However, progress is hindered by the absence of a viable experimental approach. Here, the discovery of the surface-selectively spontaneous reconstructed Weyl semimetal NdAlSi provides a feasible experimental platform for studying non-Hermitian physics. Utilizing angle-resolved photoemission spectroscopy (ARPES) measurements, surface-projected density functional theory (DFT) calculations, and scanning tunneling microscopy (STM) measurements, it is demonstrated that surface reconstruction in NdAlSi alters surface Fermi arc (SFA) connectivity and generates new isolated non-topological SFAs (NTSFAs) by introducing non-Hermitian terms. The surface-selective spontaneous reconstructed Weyl semimetal NdAlSi can be viewed as a Hermitian bulk - non-Hermitian boundary system. The isolated non-topological SFAs on the reconstructed surface act as a loss mechanism and open boundary condition (OBC) for the topological electrons and bulk states, serving as non-Hermitian boundary states. This discovery provides a good experimental platform for exploring new physical phenomena and potential applications based on boundary non-Hermitian effects, extending beyond purely mathematical concepts. Furthermore, it provides important enlightenment for constructing topological photonic crystals with surface reconstruction and studying their topologicalproperties.

Observation of planar Hall effect in the topological insulator NaCd4As3

The observation of the planar Hall effect (PHE) illuminates the spin textures and topological properties of materials, indicating potential applications in quantum computing and electronic devices. Here, we present a study on the planar Hall transport of topological insulator NaCd4As3 single crystals. When the magnetic field is rotated within the sample plane relative to the current direction, we observe remarkable planar Hall resistivity and giant planar anisotropic magnetoresistance (AMR), both consistent with the theoretical expression of the PHE. Further analysis reveals that the orbital magnetoresistance effect, unrelated to surface electrons from topological surface states or bulk electrons from nontrivial Berry phases, lays a dominant role in the PHE in NaCd4As3. Additionally, the AMR ratio reaches −43% at 3 K under 14 T and remains −9% at room temperature, markedly exceeding that of traditional ferromagnetic metals. These findings provide a platform for understanding the PHE mechanism in topological insulators and highlight the potential of NaCd4As3 for angle and magnetic field detection applications.

Kekulé-modulated topological bulk cavity for intrinsic lateral beam shifting of high-purity linear-polarized light emission

Beam shaping and polarization manipulation are of great importance for the design of microcavity lasers. Recently, topological photonic cavities have emerged as excellent platforms for surface-emitting lasers. In this class of lasers, beam engineering has not thus far been extensively studied. Here, we demonstrate how to achieve an intrinsic lateral shift of the beam emitted by a topological laser. This is achieved by designing a Kekulé-modulated topological bulk cavity, in which the continuous Kekulé modulation partially lifts a set of fourfold-degenerate Dirac cones into two twofold degeneracies. The resulting photonic cavity supports a range of interesting beam emission profiles, including vector beams with polarization winding, and laterally-shifted linearly-polarized Gaussian beams. It is possible to achieve lateral beam shifts in opposite directions and orthogonal polarizations for the degenerate photonic p-/d-orbitals, a feature that may be useful for photonic sensing applications.

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.

Electronic Transport and Interaction of Lattice Dynamics in Topological Nodalline Semimetal HfAs2 Single Crystals

AbstractTopological semimetals represent a novel class of quantum materials displaying non‐trivial topological states that host Dirac/Weyl fermions. The intersection of Dirac/Weyl points gives rise to essential properties in a wide range of innovative transport phenomena, including extreme magnetoresistance, high mobilities, weak antilocalization, electron hydrodynamics, and various electro‐optical phenomena. In this study, the electronic, transport, phonon scattering, and interrelationships are explored in single crystals of the topological semimetal HfAs2. It reveals a weak antilocalization effect at low temperatures with high carrier density, which is attributed to perfectly compensated topological bulk and surface states. The angle‐resolved photoemission spectroscopy (ARPES) results show anisotropic Fermi surfaces and surface states indicative of the topological semimetal, further confirmed by first‐principle density functional theory (DFT) calculations. Moreover, the lattice dynamics in HfAs2 are investigated both with the Raman scattering and density functional theory. The phonon dispersion, density of states, lattice thermal conductivity, and the phonon lifetimes are computed to support the experimental findings. The softening of phonons, the broadening of Raman modes, and the reduction of phonon lifetimes with temperature suggest the enhancement of phonon anharmonicity in this new topological material, which is crucial for boosting the thermoelectric performance of topological semimetals.

Topological modes and spectral flows in inhomogeneous PT-symmetric continuous media

In classical Hermitian continuous media, the spectral-flow index of topological modes is linked to the bulk topology via index theorem. However, the interface between two bulks is usually non-Hermitian due to the inhomogeneities of system parameters. We show that the connection between topological modes and bulk topology still exists despite the non-Hermiticity at the interface if the system is endowed with PT symmetry. The theoretical framework developed is applied to the Hall magnetohydrodynamic model to identify a topological mode called topological Alfvén sound wave in magnetized plasmas. Published by the American Physical Society 2024

Low-temperature magnetoresistance hysteresis in vanadium-doped Bi2−xTe2.4Se0.6 bulk topological insulators

Bi2−xTe2.4Se0.6 single crystals show gapless topological surface states, and doping (x) with vanadium allows to shift the chemical potential in the bulk bandgap. Accordingly, the resistivity, carrier density, and mobility are constant below 10 K, and the magnetoresistance shows weak antilocalization as expected for low-temperature transport properties dominated by gapless surface states of so-called three-dimensional topological insulators. However, the magnetoresistance also shows a hysteresis depending on the sweep rate and the magnetic field direction. Here, we provide evidence that such magnetoresistance hysteresis is enhanced if both three-dimensional bulk states and quasi-two-dimensional topological states contribute to the transport (x = 0 and 0.03), and it is mostly suppressed if the topological states govern transport (x = 0.015). It is proposed that the hysteresis in the magnetoresistance results from different spin-dependent scattering rates of the topological surface and bulk states. Generally, this observation is of relevance to the studies of topologically insulating materials in which both topological surface and bulk states exist.

Entanglement spectroscopy of anomalous surface states

We study the entanglement spectra of surface states of symmetry-protected topological phases. The topological bulk imprints the surface with an anomaly that does not permit it to form a trivial “vacuum” state that is gapped, unfractionalized, and symmetry preserving. Any surface wave function encodes the topology of the underlying bulk in addition to a specific surface phase. We show that the real-space entanglement spectrum of such surface wave functions are dominated by the bulk topology and do not readily permit identifying the surface phase. We thus use a modified form of entanglement spectra that incorporates the anomaly and argue that they correspond to physical edge states between different surface states. We support these arguments by explicit analytical and numerical calculations for free and interacting surfaces of three-dimensional topological insulators of electrons. Published by the American Physical Society 2024

Democratic Lagrangians from topological bulk

Chiral form fields in d dimensions can be effectively described as edge modes of topological Chern-Simons theories in d+1 dimensions. At the same time, manifestly Lorentz-invariant Lagrangian description of such fields directly in terms of a d-dimensional field theory is challenging and requires introducing nontrivial auxiliary gauge fields eliminated on shell with extra gauge symmetries. A recent work by Arvanitakis demonstrates (emphasizing the case of 2d chiral bosons) that the two approaches are related, and a peculiar reduction on the (d+1)-dimensional topological Lagrangian automatically leads to d-dimensional Lagrangians with appropriate sets of auxiliary fields. We develop this setup in three distinct directions. First, we demonstrate how arbitrary Abelian self-interactions for chiral forms can be included using nonlinear boundary terms in the Chern-Simons theory. Second, by generalizing the Chern-Simons theory to the BF-theory, we obtain an analogous democratic description of nonchiral form fields, where electric and magnetic potentials appear as explicit dynamical variables. Third, we discuss the effects of introducing topological interactions in the higher-dimensional bulk, which produce extra interaction terms in the boundary theory. When applied to a topological 4-form field in 12 dimensions, this construction results in a democratic description of the 3-form gauge field of the eleven-dimensional supergravity. Published by the American Physical Society 2024

Unveiling surface and bulk contributions in temperature dependent THz emission from Bi2Te3

We report evolution of the pulsed terahertz (THz) emission from Bi2Te3 topological insulator in a wide temperature range, where an interplay between the topological surface and bulk contributions can be addressed in a distinguishable manner. A circular photogalvanic effect-induced topological surface current contribution to THz generation can be clearly identified in the signal, otherwise, overwhelmed by the hot carrier decoherence in the bulk states. With the decreasing temperature, an initial sharp increase in the topological surface THz signal is observed before it attains a constant value below ∼200 K. The scattering channels between topological surface and bulk regions via carrier-phonon scattering are dominantly active only above the bulk-Debye temperature of ∼180 K, and the temperature-independent behavior of it at lower temperatures is indicative of robust nature of topological surface states. THz emission due to ultrafast photon-drag current in the bulk states is almost independent of temperature in the entire range, while the combined photo-Dember and band-bending effects induced photocurrent is doubled at 10 K.

Topological Heusler Magnets‐Driven High‐Performance Transverse Nernst Thermoelectric Generators

AbstractTopological magnets (TMs) with the coupled topology of electronic band structures and spin configuration have exhibited exotic transport properties that are overwhelmingly appealing for transverse thermoelectric applications. Despite the continuous discovery of TMs in recent years, the development of Nernst generators has much lagged. Here, high‐performance Nernst generators are developed utilizing polycrystalline topological Heusler bulk magnets. Benefiting from the robustness of topological effect to grain boundary scattering, polycrystalline Co2MnGa is found to exhibit a large Nernst thermopower of ≈6.5 µV K−1 at 300 K, which is comparable to the previously reported record value in its single crystal. The developed Nernst generators thereby exhibit excellent performance with an output voltage of 5.4 mV and power of 14.3 µW, significantly higher than that of Nernst thermopiles assembled using conventional ferromagnets. These results pave the way to advancing TMs with intrinsically large Berry curvature for transverse thermoelectric applications.

Spin resolved topological bulk state in acoustics

Extremely rare topologically protected acoustic energy sink is presented in this article. Acoustic topological phenomena are generally described using quantum anomalous hall effects (QAHE), quantum valley hall effects (QVHE), and quantum spin hall effects (QSHE) where spin orbit coupling is predominant. Topological edge states are demonstrated by bulk-boundary distinction when the bulk is insulated. In this article topological acoustic conductor and its phenomena are theoretically demonstrated where the boundaries are insulated. This is exactly opposite to the behavior of a topological acoustic insulator. Phenomena presented in this article could not be explained by any of the trio Quantum Hall effects. To explain the phenomenon phononic crystals or PnCs were designed to obtain accidental triple degeneracies, resulting a Dirac-like cone at the Γ point (k→=0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\overrightarrow{k}=0$$\\end{document}). The phenomenon is microarchitecture and microrotation field independent. Here time reversal symmetry or the space inversion symmetry is not broken, and the degenerated ‘Deaf band’ dominates the local dispersion with a syncline top band. This scenario results in continuously changing ‘up spin’ and ‘down spin’ of the wave energy in the media and remain trapped without specific preferential direction of wave transport. The spin was found to generate the spin angular momentum, causing the switching in geometric phase from 0-2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$0-2\\pi$$\\end{document} in cyclic pattern, keeping the energy trapped inside the bulk media.

Topological boundary states in micropolar gyroelastic continua

The study of topology in elastic media has been primarily focused on achieving non-trivial topological states in discrete elastic lattices through active or chiral microscopic interactions. Realization of such topological states in continuous elastic media remains largely unexplored. In this study, a new continuum theory of micropolar gyroelasticity is developed and applied to attain non-trivial topological boundary states in elastic continua. According to the new theory, an elastic continuum is composed of elastically interacting micro-volume elements that can translate and rotate and are connected at their mass centers to gyroscopes, which contribute to the linear and orbital angular momenta but not to the spin angular momentum of the continuum. By applying this micropolar gyroelasticity theory to elastic media with both periodic and finite domains, the emergence of topological boundary states in 2D micropolar gyroelastic continua is demonstrated. Through using the Floquet–Bloch method for periodic domains, the bulk-boundary correspondence is analytically established, and the emergence of non-trivial topological bulk states characterized by Mexican-hat band structures is observed. In addition, by employing an asymptotic analytical model based on the extended Bloch theorem and performing numerical analyses of micropolar gyroelastic continua with finite domains of different geometries, it is shown that the non-trivial Mexican-hat band structure is associated with and provides protection for topological boundary states confined at the boundaries. Finally, the application of the newly developed micropolar gyroelasticity theory to Zinc-blende structured materials (including ZnTe, GaP, InP and ZnS) reveals that the emergence of the topological boundary states in an elastic continuum is not triggered solely by the gyroscopic effect but also depends on the material properties of the micropolar continuum. This study provides new insights into extending notions and methods of topology to analyze elastic continua, paving the way for the practical implementation of topological mechanical systems in various engineering applications.

Topological Microlaser with a Non-Hermitian Topological Bulk.

Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While bulk-edge correspondence has been extensively studied in Hermitian systems, a non-Hermitian bulk could drastically modify the Hermitian topological band theory due to the interplay between non-Hermiticity and topology, and its effect on bulk-edge correspondence is still an ongoing pursuit. Importantly, including non-Hermicity can significantly expand the horizon of topological states of matter and lead to a plethora of unique properties and device applications, an example of which is a topological laser. However, the bulk topology, and thereby the bulk-edge correspondence, in existing topological edge-mode lasers is not well defined. Here, we propose and experimentally probe topological edge-mode lasing with a well-defined non-Hermitian bulk topology in a one-dimensional (1D) array of coupled ring resonators. By modeling the Hamiltonian with an additional degree of freedom (referred to as synthetic dimension), our 1D structure is equivalent to a 2D non-Hermitian Chern insulator with precise mapping. Our Letter may open a new pathway for probing non-Hermitian topological effects and exploring non-Hermitian topological device applications.

Topological network transport in on-chip phononic crystals

Rapid developments for topological materials have promoted the search for topological transport in the fields of condensed-matter physics and materials science. However, topological network transport, proposed in twisted bilayer graphene and soon after being explored in other two-dimensional materials, is still elusive despite extensive experimental efforts. Here, we implemented on-chip phononic crystal networks based on a network unit cell with six channels consisting of triangular prisms on a silicon substrate arranged in a honeycomb array. The topological network bulk transport in the gap of the bulk states of the original phononic crystal and the network edge transport in the gap of the network bulk states were visualized directly. These results offer a controllable platform for exploring topological transport in networks and may enable the realization of on-chip microultrasonic devices, such as splitters, filters, and signal processing in a monolithic elastic network.

Electrically-pumped compact topological bulk lasers driven by band-inverted bound states in the continuum

One of the most exciting breakthroughs in physics is the concept of topology that was recently introduced to photonics, achieving robust functionalities, as manifested in the recently demonstrated topological lasers. However, so far almost all attention was focused on lasing from topological edge states. Bulk bands that reflect the topological bulk-edge correspondence have been largely missed. Here, we demonstrate an electrically pumped topological bulk quantum cascade laser (QCL) operating in the terahertz (THz) frequency range. In addition to the band-inversion induced in-plane reflection due to topological nontrivial cavity surrounded by a trivial domain, we further illustrate the band edges of such topological bulk lasers are recognized as the bound states in the continuum (BICs) due to their nonradiative characteristics and robust topological polarization charges in the momentum space. Therefore, the lasing modes show both in-plane and out-of-plane tight confinements in a compact laser cavity (lateral size ~3λlaser). Experimentally, we realize a miniaturized THz QCL that shows single-mode lasing with a side-mode suppression ratio (SMSR) around 20 dB. We also observe a cylindrical vector beam for the far-field emission, which is evidence for topological bulk BIC lasers. Our demonstration on miniaturization of single-mode beam-engineered THz lasers is promising for many applications including imaging, sensing, and communications.

Two types of three-dimensional quantum Hall effects in multilayer WTe2

Interplay between topological surface states and bulk states gives rise to diverse exotic transport phenomena in topological materials. The recently proposed Weyl orbit in topological semimetals in the presence of magnetic field is a remarkable example. This novel closed magnetic orbit consists of Fermi arcs on two spatially separated sample surfaces which are connected by the bulk chiral zero mode, which can contribute to transport. Here we report Shubnikov--de Haas oscillation and its evolution into quantum Hall effect (QHE) in multilayered type-II Weyl semimetal $\mathrm{W}{\mathrm{Te}}_{2}$. We observe both the three-dimensional (3D) QHE from bulk states by parallel stacking of confined two-dimensional layers in the low magnetic field region and the 3D QHE in the quantized surface transport due to Weyl orbits in the high magnetic field region. Our study of the two types of QHEs controlled by magnetic field and our demonstration of the crossover between quantized bulk and surface transport provide an essential platform for the future quantized transport studies in topological semimetals.

Floquet Gauge Anomaly Inflow and Arbitrary Fractional Charge in Periodically Driven Topological-Normal Insulator Heterostructures.

Usually, when coupling in a background gauge field, topological zero modes would yield an anomalous current at the interface, culminating in the zero-mode anomaly inflow, which is ultimately conserved by extra contributions from the topological bulk. However, the anomaly inflow mechanism for guiding Floquet steady states is rarely explored in periodically driven systems. Here we synthesize a driven topological-normal insulator heterostructure and propose a Floquet gauge anomaly inflow, associated with the occurrence of arbitrary fractional charge. Through our photonic modeling, we experimentally observed a Floquet gauge anomaly as the system was driven into anomalous topological phases. Prospectively, we believe our findings could pave a novel avenue on exploring Floquet gauge anomalies in driven systems of condensed matter, photonics, and ultracold atoms.

Higher-order topological insulators by ML-enhanced topology optimization

Energy in lower dimensions, such as edges or corners, can be robustly confined by the higher-order topological insulators (HOTIs) against defects. Being promising for wave manipulation, the unique property of HOTIs is protected by the associated topological invariant and bulk band. Nevertheless, it is still challenging to fast design topologically nontrivial continuum unit cells with highly localized edge/corner modes in photonic and phononic systems. In the present work, with the help of a multitask learning model simultaneously predicting the discrete-valued topological invariant and continuum-valued bandgap range, a fast design framework is developed using an explicit topology optimization method for mechanical HOTIs. In the solution process, the machine learning model and backpropagation algorithm are integrated into a MultiStart solver to accelerate the design efficiency by 3–4 orders than the traditional topology optimization method. Furthermore, a novel programmable mechanical imaging device illustrates the applications of the optimized HOTI with highly localized corner states. This AI-enhanced design paradigm can be easily extended for the fast design of optimized topological materials among various physical systems.

Higher-order topological insulator in a modified Haldane-Hubbard model

We investigate the ground-state phase diagram of a modified spinless Haldane-Hubbard model, with broken threefold rotational symmetry, employing exact diagonalization calculations. The interplay of asymmetry, interactions, and topology gives rise to a rich phase diagram. The noninteracting limit of the Hamiltonian exhibits a higher-order topological insulator characterized by the existence of corner modes, in contrast to known chiral edge metallic states of the standard Haldane model. Our investigation demonstrates that these symmetry-protected states are robust to the presence of finite interactions. Furthermore, in certain regimes of parameters, we show that a topological Mott insulator exists in this model, where a nontrivial topological bulk coexists with an interaction-driven charge-density wave, whose emergence is characterized by a ${Z}_{2}$-symmetry breaking within the $3d\text{-Ising}$ universality class.