Evidence of a room-temperature quantum spin Hall edge state in a higher-order topological insulator

Lattice-guided assembly of optoelectronically active π-conjugated peptides on 1D van der Waals single crystals

The deployment of organic molecules in high-performance devices strongly relies on the formation of well-ordered domains, which is often complicated by the dynamic and sensitive nature of supramolecular interactions. Here, we engineered the assembly of water-processable, optoelectronic π-conjugated peptides into well-defined organic-inorganic heterointerfaced assemblies by leveraging the long-range anisotropic ordering of 1D van der Waals (vdW) crystals composed of subnanometer-thick transition metal sulfide chains (MS3; M = Nb, Ta) as assembly templates. We found that the monomers can readily form 1D supramolecular assemblies onto the underlying crystal surface, owing to the structural correspondence between the π-π interactions of the quaterthiophene (4T)-based peptide units (DDD-4T) and sulfur atom ordering along the NbS3 (100) surface. The heterointerfaced assemblies exhibited substantially red-shifted photoluminescence and enhanced visible-range photocurrent generation compared to solution-assembled films. Our results underscore the role of lattice matching in forming ordered supramolecular assemblies, offering an emergent approach to assembling organic building blocks endowed with improved physical properties.

Topologically Protected Photovoltaics in Bi Nanoribbons

Photovoltaic efficiency in solar cells is hindered by many unwanted effects. Radiative channels (emission of photons) sometimes mediated by nonradiative ones (emission of phonons) are principally responsible for the decrease in exciton population before charge separation can take place. One such mechanism is electron-hole recombination at surfaces or defects where the in-gap edge states serve as the nonradiative channels. In topological insulators (TIs), which are rarely explored from an optoelectronics standpoint, we show that their characteristic surface states constitute a nonradiative decay channel that can be exploited to generate a protected photovoltaic current. Focusing on two-dimensional TIs, and specifically for illustration purposes on a Bi(111) monolayer, we obtain the transition rates from the bulk excitons to the edge states. By breaking the appropriate symmetries of the system, one can induce an edge charge accumulation and edge currents under illumination, demonstrating the potential of TI nanoribbons for photovoltaics.

Realization of monolayer ZrTe5 topological insulators with wide band gaps

Two-dimensional topological insulators hosting the quantum spin Hall effect have application potential in dissipationless electronics. To observe the quantum spin Hall effect at elevated temperatures, a wide band gap is indispensable to efficiently suppress bulk conduction. Yet, most candidate materials exhibit narrow or even negative band gaps. Here, via elegant control of van der Waals epitaxy, we have successfully grown monolayer ZrTe5 on a bilayer graphene/SiC substrate. The epitaxial ZrTe5 monolayer crystalizes in two allotrope isomers with different intralayer alignments of ZrTe3 prisms. Our scanning tunneling microscopy/spectroscopy characterization unveils an intrinsic full band gap as large as 254 meV and one-dimensional edge states localized along the periphery of the ZrTe5 monolayer. First-principles calculations further confirm that the large band gap originates from strong spin-orbit coupling, and the edge states are topologically nontrivial. These findings thus provide a highly desirable material platform for the exploration of the high-temperature quantum spin Hall effect.

Br-Vacancies Induced Variable Ranging Hopping Conduction in High-Order Topological Insulator Bi4Br4

The defects have a remarkable influence on the electronic structures and the electric transport behaviors of the matter, providing the additional means to engineering their physical properties. In this work, a comprehensive study on the effect of Br-vacancies on the electronic structures and transport behaviors in the high-order topological insulator Bi4Br4 is performed by the combined techniques of the scanning tunneling microscopy (STM), angle-resolved photoemission spectroscopy (ARPES), and physical properties measurement system along with the first-principle calculations. The STM results show the defects on the cleaved surface of a single crystal and reveal that the defects are correlated to the Br-vacancies with the support of the simulated STM images. The role of the Br-vacancies in the modulation of the band structures has been identified by ARPES spectra and the calculated energy-momentum dispersion. The relationship between the Br-vacancies and the semiconducting-like transport behaviors at low temperature has been established, implying a Mott variable ranging hopping conduction in Bi4Br4. The work not only resolves the unclear transport behaviors in this matter, but also paves a way to modulate the electric conduction path by the defects engineering.

Higher-order topological phases in crystalline and non-crystalline systems: a review

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases due to the higher-order bulk-boundary correspondence. In this review, we summarize current research progress on higher-order topological phases in both crystalline and non-crystalline systems. We firstly introduce prototypical models of higher-order topological phases in crystals and their topological characterizations. We then discuss effects of quenched disorder on higher-order topology and demonstrate disorder-induced higher-order topological insulators. We also review the theoretical studies on higher-order topological insulators in amorphous systems without any crystalline symmetry and higher-order topological phases in non-periodic lattices including quasicrystals, hyperbolic lattices, and fractals, which have no crystalline counterparts. We conclude the review by a summary of experimental realizations of higher-order topological phases and discussions on potential directions for future study.

A hybrid topological quantum state in an elemental solid

Topology1-3 and interactions are foundational concepts in the modern understanding of quantum matter. Their nexus yields three important research directions: (1) the competition between distinct interactions, as in several intertwined phases, (2) the interplay between interactions and topology that drives the phenomena in twisted layered materials and topological magnets, and (3) the coalescence of several topological orders to generate distinct novel phases. The first two examples have grown into major areas of research, although the last example remains mostly unexplored, mainly because of the lack of a material platform for experimental studies. Here, using tunnelling microscopy, photoemission spectroscopy and a theoretical analysis, we unveil a 'hybrid' topological phase of matter in the simple elemental-solid arsenic. Through a unique bulk-surface-edge correspondence, we uncover that arsenic features a conjoined strong and higher-order topology that stabilizes a hybrid topological phase. Although momentum-space spectroscopy measurements show signs of topological surface states, real-space microscopy measurements unravel a unique geometry of topologically induced step-edge conduction channels revealed on various natural nanostructures on the surface. Using theoretical models, we show that the existence of gapless step-edge states in arsenic relies on the simultaneous presence of both a non-trivial strong Z2 invariant and a non-trivial higher-order topological invariant, which provide experimental evidence for hybrid topology. Our study highlights pathways for exploring the interplay of different band topologies and harnessing the associated topological conduction channels in engineered quantum or nano-devices.

Dual quantum spin Hall insulator by density-tuned correlations in TaIrTe4

The convergence of topology and correlations represents a highly coveted realm in the pursuit of new quantum states of matter1. Introducing electron correlations to a quantum spin Hall (QSH) insulator can lead to the emergence of a fractional topological insulator and other exotic time-reversal-symmetric topological order2-8, not possible in quantum Hall and Chern insulator systems. Here we report a new dual QSH insulator within the intrinsic monolayer crystal of TaIrTe4, arising from the interplay of its single-particle topology and density-tuned electron correlations. At charge neutrality, monolayer TaIrTe4 demonstrates the QSH insulator, manifesting enhanced nonlocal transport and quantized helical edge conductance. After introducing electrons from charge neutrality, TaIrTe4 shows metallic behaviour in only a small range of charge densities but quickly goes into a new insulating state, entirely unexpected on the basis of the single-particle band structure of TaIrTe4. This insulating state could arise from a strong electronic instability near the van Hove singularities, probably leading to a charge density wave (CDW). Remarkably, within this correlated insulating gap, we observe a resurgence of the QSH state. The observation of helical edge conduction in a CDW gap could bridge spin physics and charge orders. The discovery of a dual QSH insulator introduces a new method for creating topological flat minibands through CDW superlattices, which offer a promising platform for exploring time-reversal-symmetric fractional phases and electromagnetism2-4,9,10.

Observation of Anomalous Planar Hall Effect Induced by One-Dimensional Weak Antilocalization

The confinement of electrons in one-dimensional (1D) space highlights the prominence of the role of electron interactions or correlations, leading to a variety of fascinating physical phenomena. The quasi-1D electron states can exhibit a unique spin texture under spin-orbit interaction (SOI) and thus could generate a robust spin current by forbidden electron backscattering. Direct detection of such 1D spin or SOI information, however, is challenging due to complicated techniques. Here, we identify an anomalous planar Hall effect (APHE) in the magnetotransport of quasi-1D van der Waals (vdW) topological materials as exemplified by Bi4Br4, which arises from the quantum interference correction of 1D weak antilocalization (WAL) to the ordinary planar Hall effect and demonstrates a deviation from the usual sine and cosine curves. The occurrence of 1D WAL is correlated to the line-shape Fermi surface and persistent spin texture of (100) topological surface states of Bi4Br4, as revealed by both our angle-resolved photoemission spectroscopy and first-principles calculations. By generalizing the observation of APHE to other non-vdW bulk materials, this work provides a possible characteristic of magnetotransport for identifying the spin/SOI information and quantum interference behavior of 1D states in 3D topological material.

Single Quasi-1D Chains of Sb2Se3 Encapsulated within Carbon Nanotubes

The realization of stable monolayers from 2D van der Waals (vdW) solids has fueled the search for exfoliable crystals with even lower dimensionalities. To this end, 1D and quasi-1D (q-1D) vdW crystals comprising weakly bound subnanometer-thick chains have been discovered and demonstrated to exhibit nascent physics in the bulk. Although established micromechanical and liquid-phase exfoliation methods have been applied to access single isolated chains from bulk crystals, interchain vdW interactions with nonequivalent strengths have greatly hindered the ability to achieve uniform single isolated chains. Here, we report that encapsulation of the model q-1D vdW crystal, Sb2Se3, within single-walled carbon nanotubes (CNTs) circumvents the relatively stronger c-axis vdW interactions between the chains and allows for the isolation of single chains with structural integrity. High-resolution transmission electron microscopy and selected area electron diffraction studies of the Sb2Se3@CNT heterostructure revealed that the structure of the [Sb4Se6]n chain is preserved, enabling us to systematically probe the size-dependent properties of Sb2Se3 from the bulk down to a single chain. We show that ensembles of the [Sb4Se6]n chains within CNTs display Raman confinement effects and an emergent band-like absorption onset around 600 nm, suggesting a strong blue shift of the near-infrared band gap of Sb2Se3 into the visible range upon encapsulation. First-principles density functional theory calculations further provided qualitative insight into the structures and interactions that could manifest in the Sb2Se3@CNT heterostructure. Spatial visualization of the calculated electron density difference map of the heterostructure indicated a minimal degree of electron donation from the host CNT to the guest [Sb4Se6]n chain. Altogether, this model system demonstrates that 1D and q-1D vdW crystals with strongly anisotropic vdW interactions can be precisely studied by encapsulation within CNTs with suitable diameters, thereby opening opportunities in understanding dimension-dependent properties of a plethora of emergent vdW solids at or approaching the subnanometer regime.

Spin-resolved topology and partial axion angles in three-dimensional insulators

Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ([Formula: see text]-) invariant (helical) 3D TCIs-termed higher-order TCIs (HOTIs)-the boundary signatures can manifest as a sample-dependent network of 1D hinge states. We here introduce nested spin-resolved Wilson loops and layer constructions as tools to characterize the intrinsic bulk topological properties of spinful 3D insulators. We discover that helical HOTIs realize one of three spin-resolved phases with distinct responses that are quantitatively robust to large deformations of the bulk spin-orbital texture: 3D quantum spin Hall insulators (QSHIs), "spin-Weyl" semimetals, and [Formula: see text]-doubled axion insulator (T-DAXI) states with nontrivial partial axion angles indicative of a 3D spin-magnetoelectric bulk response and half-quantized 2D TI surface states originating from a partial parity anomaly. Using ab-initio calculations, we demonstrate that β-MoTe2 realizes a spin-Weyl state and that α-BiBr hosts both 3D QSHI and T-DAXI regimes.

Topological electronic structure and spin texture of quasi-one-dimensional higher-order topological insulator Bi4Br4

The notion of topological insulators (TIs), characterized by an insulating bulk and conducting topological surface states, can be extended to higher-order topological insulators (HOTIs) hosting gapless modes localized at the boundaries of two or more dimensions lower than the insulating bulk. In this work, by performing high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements with submicron spatial and spin resolution, we systematically investigate the electronic structure and spin texture of quasi-one-dimensional (1D) HOTI candidate Bi4Br4. In contrast to the bulk-state-dominant spectra on the (001) surface, we observe gapped surface states on the (100) surface, whose dispersion and spin-polarization agree well with our ab-initio calculations. Moreover, we reveal in-gap states connecting the surface valence and conduction bands, which is a signature of the hinge states inside the (100) surface gap. Our findings provide compelling evidence for the HOTI phase of Bi4Br4. The identification of the higher-order topological phase promises applications based on 1D spin-momentum locked current in electronic and spintronic devices.

Generation of higher-order topological insulators using periodic driving

Topological insulators (TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs (HOTIs) are a new class of TIs in dimensionsd > 1. These HOTIs possess(d-1)-dimensional boundaries that, unlike those of conventional TIs, do not conduct via gapless states but are themselves TIs. Precisely, annth orderd-dimensional higher-order TI is characterized by the presence of boundary modes that reside on itsdc=(d-n)-dimensional boundary. For instance, a three-dimensional second (third) order TI hosts gapless (localized) modes on the hinges (corners), characterized bydc=1(0). Similarly, a second-order TI (SOTI) in two dimensions only has localized corner states (dc=0). These higher-order phases are protected by various crystalline as well as discrete symmetries. The non-equilibrium tunability of the topological phase has been a major academic challenge where periodic Floquet drive provides us golden opportunity to overcome that barrier. Here, we discuss different periodic driving protocols to generate Floquet HOTIs while starting from a non-topological or first-order topological phase. Furthermore, we emphasize that one can generate the dynamical anomalousπ-modes along with the concomitant 0-modes. The former can be realized only in a dynamical setup. We exemplify the Floquet higher-order topological modes in two and three dimensions in a systematic way. Especially, in two dimensions, we demonstrate a Floquet SOTI (FSOTI) hosting 0- andπcorner modes. Whereas a three-dimensional FSOTI and Floquet third-order TI manifest one- and zero-dimensional hinge and corner modes, respectively.

Anisotropy-Driven Crystallization of Dimensionally Resolved Quasi-1D Van der Waals Nanostructures

Unusual behavior in solids emerges from the complex interplay between crystalline order, composition, and dimensionality. In crystals comprising weakly bound one-dimensional (1D) or quasi-1D (q-1D) chains, properties such as charge density waves, topologically protected states, and indirect-to-direct band gap crossovers have been predicted to arise. However, the experimental demonstration of many of these nascent physics in 1D or q-1D van der Waals (vdW) crystals is obscured by the highly anisotropic bonding between the chains, stochasticity of top-down exfoliation, and the lack of synthetic strategies to control bottom-up growth. Herein, we report the directed crystallization of a model q-1D vdW phase, Sb2S3, into dimensionally resolved nanostructures. We demonstrate the uncatalyzed growth of highly crystalline Sb2S3 nanowires, nanoribbons, and quasi-2D nanosheets with thicknesses in the range of 10 to 100 nm from the bottom-up crystallization of [Sb4S6]n chains. We found that dimensionally resolved nanostructures emerge from two distinct chemical vapor growth pathways defined by diverse covalent intrachain and anisotropic vdW interchain interactions and controlled precursor ratios in the vapor phase. At sub-100 nm nanostructure thicknesses, we observe the hardening of phonon modes, blue-shifting of optical band gaps, and the emergence of a new high-energy photoluminescence peak. The directional growth of weakly bound 1D ribbons or chains into well-resolved nanocrystalline morphologies provides opportunities to develop ordered nanostructures and hierarchical assemblies that are suitable for a wide range of optoelectronic and quantum devices.

Towards layer-selective quantum spin hall channels in weak topological insulator Bi4Br2I2

Weak topological insulators, constructed by stacking quantum spin Hall insulators with weak interlayer coupling, offer promising quantum electronic applications through topologically non-trivial edge channels. However, the currently available weak topological insulators are stacks of the same quantum spin Hall layer with translational symmetry in the out-of-plane direction-leading to the absence of the channel degree of freedom for edge states. Here, we study a candidate weak topological insulator, Bi4Br2I2, which is alternately stacked by three different quantum spin Hall insulators, each with tunable topologically non-trivial edge states. Our angle-resolved photoemission spectroscopy and first-principles calculations show that an energy gap opens at the crossing points of different Dirac cones correlated with different layers due to the interlayer interaction. This is essential to achieve the tunability of topological edge states as controlled by varying the chemical potential. Our work offers a perspective for the construction of tunable quantized conductance devices for future spintronic applications.

Topology Hierarchy of Transition Metal Dichalcogenides Built from Quantum Spin Hall Layers

The evolution of the physical properties of 2D material from monolayer limit to the bulk reveals unique consequences from dimension confinement and provides a distinct tuning knob for applications. Monolayer 1T'-phase transition metal dichalcogenides (1T'-TMDs) with ubiquitous quantum spin Hall (QSH) states are ideal 2D building blocks of various 3D topological phases. However, the stacking geometry has been previously limited to the bulk 1T'-WTe₂ type. Here, the novel 2M-TMDs consisting of translationally stacked 1T'-monolayers are introduced as promising material platforms with tunable inverted bandgaps and interlayer coupling. By performing advanced polarization-dependent angle-resolved photoemission spectroscopy as well as first-principles calculations on the electronic structure of 2M-TMDs, a topology hierarchy is revealed: 2M-WSe₂ , MoS_2, and MoSe₂ are weak topological insulators (WTIs), whereas 2M-WS₂ is a strong topological insulator (STI). Further demonstration of topological phase transitions by tunning interlayer distance indicates that band inversion amplitude and interlayer coupling jointly determine different topological states in 2M-TMDs. It is proposed that 2M-TMDs are parent compounds of various exotic phases including topological superconductors and promise great application potentials in quantum electronics due to their flexibility in patterning with 2D materials.

Gate-tunable transport in van der Waals topological insulator Bi4Br4nanobelts

Bi₄Br₄is a quasi-one-dimensional van der Waals topological insulator with novel electronic properties. Several efforts have been devoted to the understanding of its bulk form, yet it remains a challenge to explore the transport properties in low-dimensional structures due to the difficulty of device fabrication. Here we report for the first time a gate-tunable transport in exfoliated Bi₄Br₄nanobelts. Notable two-frequency Shubnikov-de Haas oscillations oscillations are discovered at low temperatures, with the low- and high-frequency parts coming from the three-dimensional bulk state and the two-dimensional surface state, respectively. In addition, ambipolar field effect is realized with a longitudinal resistance peak and a sign reverse in the Hall coefficient. Our successful measurements of quantum oscillations and realization of gate-tunable transport lay a foundation for further investigation of novel topological properties and room-temperature quantum spin Hall states in Bi₄Br₄.

Optical bulk-boundary dichotomy in a quantum spin Hall insulator

The bulk-boundary correspondence is a critical concept in topological quantum materials. For instance, a quantum spin Hall insulator features a bulk insulating gap with gapless helical boundary states protected by the underlying Z₂ topology. However, the bulk-boundary dichotomy and distinction are rarely explored in optical experiments, which can provide unique information about topological charge carriers beyond transport and electronic spectroscopy techniques. Here, we utilize mid-infrared absorption micro-spectroscopy and pump-probe micro-spectroscopy to elucidate the bulk-boundary optical responses of Bi₄Br₄, a recently discovered room-temperature quantum spin Hall insulator. Benefiting from the low energy of infrared photons and the high spatial resolution, we unambiguously resolve a strong absorption from the boundary states while the bulk absorption is suppressed by its insulating gap. Moreover, the boundary absorption exhibits strong polarization anisotropy, consistent with the one-dimensional nature of the topological boundary states. Our infrared pump-probe microscopy further measures a substantially increased carrier lifetime for the boundary states, which reaches one nanosecond scale. The nanosecond lifetime is about one to two orders longer than that of most topological materials and can be attributed to the linear dispersion nature of the helical boundary states. Our findings demonstrate the optical bulk-boundary dichotomy in a topological material and provide a proof-of-principal methodology for studying topological optoelectronics.