Spatial and energy distribution of topological edge states in single Bi(111) bilayer

Colossal Shift Currents in Band-Inverted Bi Nanotubes Driven by the Interplay of Curvature and Spin-Orbit Coupling

The concept of non-trivial electronic structure combined with reduced dimensionality presents a promising strategy for advancing optical applications and energy harvesting technologies. Symmetry breaking in low dimensional system enables the emergence of non-linear optical responses, which are greatly amplified by the singular points of band inversion. Here, using first-principles calculations, the significant enhancement of the shift current in Bi nanotubes is investigated, driven by the combined effects of 1D geometry and non-trivial band order. By rolling a 2D Bi monolayer, which exhibits a quantum spin Hall phase, into a 1D nanotube, an extraordinarily large shift current of 4.94 A·Å2 V-2 is generated, two orders of magnitude larger than the experimental values in WS2 nanotubes. The enhancement of the shift current in Bi nanotubes is demonstrated and attributed to the state mixing induced by the interplay of strong spin-orbit coupling, the curvature of the tube, and the non-trivial band order of Bi nanotubes. The robustness of this enhanced shift current against various perturbations is also discussed, such as oxidation and doping. The novel approach integrating non-trivial band order with reduced dimensionality sheds new light on advanced photovoltaic applications by harnessing both geometric advantages and exotic electronic structures for energy conversion.

Two-Dimensional Transition Metal Dichalcogenides: A Theory and Simulation Perspective

Two-dimensional transition metal dichalcogenides (2D TMDs) are a promising class of functional materials for fundamental physics explorations and applications in next-generation electronics, catalysis, quantum technologies, and energy-related fields. Theory and simulations have played a pivotal role in recent advancements, from understanding physical properties and discovering new materials to elucidating synthesis processes and designing novel devices. The key has been developments in ab initio theory, deep learning, molecular dynamics, high-throughput computations, and multiscale methods. This review focuses on how theory and simulations have contributed to recent progress in 2D TMDs research, particularly in understanding properties of twisted moiré-based TMDs, predicting exotic quantum phases in TMD monolayers and heterostructures, understanding nucleation and growth processes in TMD synthesis, and comprehending electron transport and characteristics of different contacts in potential devices based on TMD heterostructures. The notable achievements provided by theory and simulations are highlighted, along with the challenges that need to be addressed. Although 2D TMDs have demonstrated potential and prototype devices have been created, we conclude by highlighting research areas that demand the most attention and how theory and simulation might address them and aid in attaining the true potential of 2D TMDs toward commercial device realizations.

Electron-phonon interactions at the topological edge states in single bilayer Bi(111)

An intriguing feature of two-dimensional topological insulators is the topologically protected electronic edge state, which allows one-way carrier transport without backscattering. Although this feature has strong potential applications in lossless electronics, the ideal behavior of the edge states may be fragile due to electron-phonon (e-ph) interactions at room temperatures. Using density functional perturbation theory calculations for single bilayer Bi(111) as a prototypical 2D topological insulator, we show that e-ph scattering can be a significant source of backscattering at the topological edge states. We also show that e-ph interactions strongly correlate to the dispersions of the electronic edge states. In particular, the e-ph interactions increase significantly with temperature and are much stronger at the nonlinearly dispersed edge states of native edges compared to the linearly dispersed edge states of passivated edges, causing a significant energy dissipation in the temperature range of 200-400 K. Overall, we argue that the e-ph interactions can be a crucial factor at finite temperatures in controlling the electronic transport at the topologically protected edge states.

Modulation of Kondo Behavior in a Two-Dimensional Epitaxial Bilayer Bi(111)/Fe3GeTe2 Moiré Heterostructure

Artificial two-dimensional (2D) moiré superlattices provide a platform for generating exotic quantum matter or phenomena. Here, an epitaxial heterostructure composed of bilayer Bi(111) and an Fe3GeTe2 substrate with a zero-twist angle is acquired by molecular beam epitaxy. Scanning tunneling microscopy and spectroscopy studies reveal the spatially tailored Kondo resonance and interfacial magnetism within this moiré superlattice. Combined with first-principles calculations, it is found that the modulation effect of the moiré superlattice originates from the interfacial orbital hybridization between Bi and Fe atoms. Our work provides a tunable platform for strong electron correlation studies to explore 2D artificial heavy Fermion systems and interface magnetism.

Robust Edge States of Quasi-1D Material Ta2NiSe7 and Applications in Saturable Absorbers

The helical edge states (ESs) protected by underlying Z2 topology in two-dimensional topological insulators (TIs) arouse upsurges in saturable absorptions thanks to the strong photon-electron coupling in ESs. However, limited TIs demonstrate clear signatures of topological ESs at liquid nitrogen temperatures, hindering the applications of such exotic quantum states. Here, we demonstrate the existence of one-dimensional (1D) ESs at the step edge of the quasi-1D material Ta2NiSe7 at 78 K by scanning tunneling microscopy. Such ESs are rather robust against the irregularity of the edges, suggesting a possible topological origin. The exfoliated Ta2NiSe7 flakes were used as saturable absorbers (SAs) in an Er-doped fiber laser, hosting a mode-locked pulse with a modulation depth of up to 52.6% and a short pulse duration of 225 fs, far outstripping existing TI-based SAs. This work demonstrates the existence of robust 1D ESs and the superior SA performance of Ta2NiSe7.

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.

Semimetallic Bismuthene with Edge-Rich Dangling Bonds: Broad-Spectrum-Driven and Edge-Confined Electron Enhancement Boosting CO2 Hydrogenation Reduction

Broad-spectrum-driven high-performance artificial photosynthesis is quite challenging. Herein, atomically ultrathin bismuthene with semimetallic properties is designed and demonstrated for broad-spectrum (ultraviolet-visible-near infrared light) (UV-vis-NIR)-driven photocatalytic CO2 hydrogenation. The trap states in the bandgap produced by edge dangling bonds prolong the lifetime of the photogenerated electrons from 90 ps in bulk Bi to 1650 ps in bismuthine, and excited-state electrons are enriched at the edge of bismuthine. The edge dangling bonds of bismuthene as the active sites for adsorption/activation of CO2 increase the hybridization ability of the Bi 6p orbital and O 2p orbital to significantly reduce the catalytic reaction energy barrier and promote the formation of C─H bonds until the generation of CH4. Under λ ≥ 400 nm and λ ≥ 550 nm irradiation, the utilization ratios of photogenerated electron reduction CO2 hydrogenation to CO and CH4 for bismuthene are 58.24 and 300.50 times higher than those of bulk Bi, respectively. Moreover, bismuthene can extend the CO2 hydrogenation reaction to the near-infrared region (λ ≥ 700 nm). This pioneering work employs the single semimetal element as an artificial photosynthetic catalyst to produce a broad spectral response.

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.

Sandwiched Epitaxy Growth of 2D Single-Crystalline Hexagonal Bismuthene Nanoflakes for Electrocatalytic CO2 Reduction

Two-dimensional (2D) bismuthene is predicted to possess intriguing physical properties, but its preparation remains challenging due to the high surface energy constraint. Herein, we report a sandwiched epitaxy growth strategy for the controllable preparation of 2D bismuthene between a Cu foil substrate and a h-BN covering layer. The top h-BN layer plays a crucial role in suppressing the structural transformation of bismuthene and compensating for the charge transfer from the bismuthene to the Cu(111) surface. The bismuthene nanoflakes present a superior thermal stability up to 500 °C in air, attributed to the passivation effect of the h-BN layer. Moreover, the bismuthene nanoflakes demonstrate an ultrahigh faradaic efficiency of 96.3% for formate production in the electrochemical CO2 reduction reaction, which is among the highest reported for Bi-based electrocatalysts. This study offers a promising approach to simultaneously synthesize and protect 2D bismuthene nanoflakes, which can be extended to other 2D materials with a high surface energy.

Engineering topological states in a two-dimensional honeycomb lattice

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr3, CrCl3, and VBr3 monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr3), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.

Topological quantum devices: a review

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Realizing a Superconducting Square-Lattice Bismuth Monolayer

Interplay of crystal symmetry, strong spin-orbit coupling (SOC), and many-body interactions in low-dimensional materials provides a fertile ground for the discovery of unconventional electronic and magnetic properties and versatile functionalities. Two-dimensional (2D) allotropes of group 15 elements are appealing due to their structures and controllability over symmetries and topology under strong SOC. Here, we report the heteroepitaxial growth of a proximity-induced superconducting 2D square-lattice bismuth monolayer on superconducting Pb films. The square lattice of monolayer bismuth films in a C₄ symmetry together with a stripey moiré structure is clearly resolved by our scanning tunneling microscopy, and its atomic structure is revealed by density functional theory (DFT) calculations. A Rashba-type spin-split Dirac band is predicted by DFT calculations to exist at the Fermi level and becomes superconducting through the proximity effect from the Pb substrate. We suggest the possibility of a topological superconducting state in this system with magnetic dopants/field. This work introduces an intriguing material platform with 2D Dirac bands, strong SOC, topological superconductivity, and the moiré superstructure.

Bulk-surface coupling in dual topological insulator Bi1Te1and Sb-doped Bi1Te1single crystals via electron-phonon interaction

Recently,Bi1Te1has been proved to be a dual topological insulator (TI), a new subclass of symmetry-protected topological phases, and predicted to be higher order topological insulator (HOTI). Being a dual TI (DTI), Bi₁Te₁is said to host quasi-1D surface states (SSs) due to weak TI phase and topological crystalline insulating SSs at the same time. On the other hand, HOTI supports topologically protected hinge states. So,Bi1Te1is a unique platform to study the electrical signature of topological SS (TSS) of fundamentally different origins. Though there is a report of magneto-transport measurements on large-scale Bi₁Te₁thin films, the Bi₁Te₁single crystal is not studied experimentally to date. Even the doping effect in a DTI Bi₁Te₁is missing in the literature. In this regard, we performed the perpendicular and parallel field magneto-transport measurement on the exfoliated microflake of Bi₁Te₁and Sb-doped Bi₁Te₁single crystals, grown by the modified Bridgmann method. Ourmetallicsample shows the weak anti-localization behavior analyzed by the multi-channel Hikami-Larkin-Nagaoka equation. We observed the presence of a pair of decoupled TSS. Further, we extracted the dephasing index (β) from temperature (T)-dependence of phase coherence length (Lϕ), following the power law equation (Lϕ∝T-β). The thickness-dependent value ofβindicates the transition in the dephasing mechanism from electron-electron to electron-phonon interaction with the increase in thickness, indicating the enhancement in the strength of bulk-surface coupling. Sb-doped system shows weakened bulk-surface coupling, hinted by the reduced dephasing indices.

Optical absorption measurement of spin Berry curvature and spin Chern marker

In two-dimensional time-reversal symmetric topological insulators described by Dirac models, theZ2topological invariant can be described by the spin Chern number. We present a linear response theory for the spin Berry curvature that integrates to the spin Chern number, and introduce its spectral function that can be measured at finite temperature by momentum- and spin-resolved circular dichroism, which may be achieved by pump-probe type of experiments using spin- and time-resolved ARPES. As a result, the sign of the Pfaffian of theZ2invariant can be directly measured. A spin Chern number spectral function is further introduced from the optical spin current response, and is shown to be measurable from the spin-resolved opacity of two-dimensional materials under circularly polarized light, pointing to an optical measurement of theZ2invariant and a frequency sum rule. The spin Chern number expressed in real space is known to yield a spin Chern marker, and we propose that it may be measurable from spin-resolved local heating rate caused by circularly polarized light. A nonlocal spin Chern marker is further proposed to characterize the quantum criticality near topological phase transitions, and is shown to be equivalent to an overlap between spin-selected Wannier states.

Molecular beam epitaxy growth and scanning tunneling microscopy study of 2D layered materials on epitaxial graphene/silicon carbide

Since the advent of atomically flat graphene, two-dimensional (2D) layered materials have gained extensive interest due to their unique properties. The 2D layered materials prepared on epitaxial graphene/silicon carbide (EG/SiC) surface by molecular beam epitaxy (MBE) have high quality, which can be directly applied without further transfer to other substrates. Scanning tunneling microscopy and spectroscopy (STM/STS) with high spatial resolution and high-energy resolution are often used to study the morphologies and electronic structures of 2D layered materials. In this review, recent progress in the preparation of various 2D layered materials that are either monoelemental or transition metal dichalcogenides on EG/SiC surface by MBE and their STM/STS investigations are introduced.

Discovery of Charge Order and Corresponding Edge State in Kagome Magnet FeGe

Kagome materials often host exotic quantum phases, including spin liquids, Chern gap, charge density wave, and superconductivity. Existing scanning microscopy studies of the kagome charge order have been limited to nonkagome surface layers. Here, we tunnel into the kagome lattice of FeGe to uncover features of the charge order. Our spectroscopic imaging identifies a 2×2 charge order in the magnetic kagome lattice, resembling that discovered in kagome superconductors. Spin mapping across steps of unit cell height demonstrates the existence of spin-polarized electrons with an antiferromagnetic stacking order. We further uncover the correlation between antiferromagnetism and charge order anisotropy, highlighting the unusual magnetic coupling of the charge order. Finally, we detect a pronounced edge state within the charge order energy gap, which is robust against the irregular shape fluctuations of the kagome lattice edges. We discuss our results with the theoretically considered topological features of the kagome charge order including unconventional magnetism and bulk-boundary correspondence.

Topological current divider in a Chern insulator junction

A Chern insulator is a two-dimensional material that hosts chiral edge states produced by the combination of topology with time reversal symmetry breaking. Such edge states are perfect one-dimensional conductors, which may exist not only on sample edges, but on any boundary between two materials with distinct topological invariants (or Chern numbers). Engineering of such interfaces is highly desirable due to emerging opportunities of using topological edge states for energy-efficient information transmission. Here, we report a chiral edge-current divider based on Chern insulator junctions formed within the layered topological magnet MnBi2Te4. We find that in a device containing a boundary between regions of different thickness, topological domains with different Chern numbers can coexist. At the domain boundary, a Chern insulator junction forms, where we identify a chiral edge mode along the junction interface. We use this to construct topological circuits in which the chiral edge current can be split, rerouted, or switched off by controlling the Chern numbers of the individual domains. Our results demonstrate MnBi2Te4 as an emerging platform for topological circuits design.

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

Room-temperature realization of macroscopic quantum phases is one of the major pursuits in fundamental physics^1,2. The quantum spin Hall phase^3-6 is a topological quantum phase that features a two-dimensional insulating bulk and a helical edge state. Here we use vector magnetic field and variable temperature based scanning tunnelling microscopy to provide micro-spectroscopic evidence for a room-temperature quantum spin Hall edge state on the surface of the higher-order topological insulator Bi₄Br₄. We find that the atomically resolved lattice exhibits a large insulating gap of over 200 meV, and an atomically sharp monolayer step edge hosts an in-gap gapless state, suggesting topological bulk-boundary correspondence. An external magnetic field can gap the edge state, consistent with the time-reversal symmetry protection inherent in the underlying band topology. We further identify the geometrical hybridization of such edge states, which not only supports the Z₂ topology of the quantum spin Hall state but also visualizes the building blocks of the higher-order topological insulator phase. Our results further encourage the exploration of high-temperature transport quantization of the putative topological phase reported here.

Converting a Monolayered NbSe2 into an Ising Superconductor with Nontrivial Band Topology via Physical or Chemical Pressuring

Two-dimensional transition metal dichalcogenides possessing superconductivity and strong spin-orbit coupling exhibit high in-plane upper critical fields due to Ising pairing. Yet to date, whether such systems can become topological Ising superconductors remains to be materialized. Here we show that monolayered NbSe₂ can be converted into Ising superconductors with nontrivial band topology via physical or chemical pressuring. Using first-principles calculations, we first demonstrate that a hydrostatic pressure higher than 2.5 GPa can induce a p-d band inversion, rendering nontrivial band topology to NbSe₂. We then illustrate that Te-doping can function as chemical pressuring in inducing nontrivial topology in NbSe_2-xTe_x with x ≥ 0.8, due to a larger atomic radius and stronger spin-orbit coupling of Te. We also evaluate the upper critical fields within both approaches, confirming the enhanced Ising superconductivity nature, as experimentally observed. Our findings may prove to be instrumental in material realization of topological Ising superconductivity in two-dimensional systems.

Observation of 1D Fermi arc states in Weyl semimetal TaAs

Fermi arcs on Weyl semimetals exhibit many exotic quantum phenomena. Usually found on atomically flat surfaces with approximate translation symmetry, Fermi arcs are rooted in the peculiar topology of bulk Bloch bands of 3D crystals. The fundamental question of whether a 1D Fermi arc can be probed remains unanswered. Such an answer could significantly broaden potential applications of Weyl semimetals. Here, we report a direct observation of robust edge states on atomic-scale ledges in TaAs using low-temperature scanning tunneling microscopy/spectroscopy. Spectroscopic signatures and theoretical calculations reveal that the 1D Fermi arcs arise from the chiral Weyl points of bulk crystals. The crossover from 2D Fermi arcs to eventual complete localization on 1D edges was arrested experimentally on a sequence of surfaces. Our results demonstrate extreme robustness of the bulk-boundary correspondence, which offers topological protection for Fermi arcs, even in cases in which the boundaries are at the atomic-scale. The persistent 1D Fermi arcs can be profitably exploited in miniaturized quantum devices.

Rashba Splitting and Electronic Valley Characteristics of Janus Sb and Bi Topological Monolayers

Janus Sb and Bi monolayers as a new class of 2D topological insulator materials, which could be fulfilled by asymmetrical functionalizations with methyl or hydroxyl, are demonstrated by first-principles spin–orbit coupling (SOC) electronic structure calculations to conflate nontrivial topology, Rashba splitting and valley-contrast circular dichroism. Cohesive energies and phonon frequency dispersion spectra indicate that all Janus Sb and Bi monolayers possess a structural stability in energetic statics but represent virtual acoustic phonon vibrations of the hydrogen atoms passivating on monolayer surfaces. Band structures of Janus Sb and Bi monolayers and their nanoribbons demonstrate they are nontrivial topological insulators. Rashba spin splitting at G point in Brillouin zone of Janus Bi monolayers arises from the strong SOC p_x and p_y orbitals of Bi bonding atoms together with the internal out-of-plane electric field caused by asymmetrical functionalization. Janus Sb and Bi monolayers render direct and indirect giant bandgaps, respectively, which are derived from the strong SOC p_x and p_y orbitals at band-valley Brillouin points K and K′ where valley-selective circular dichroism of spin valley Hall insulators is also exhibited.

Observation of Magnetism-Induced Topological Edge State in Antiferromagnetic Topological Insulator MnBi4Te7

Breaking time reversal symmetry in a topological insulator may lead to quantum anomalous Hall effect and axion insulator phase. MnBi₄Te₇ is a recently discovered antiferromagnetic topological insulator with T_N ∼ 12.5 K, which is composed of an alternatively stacked magnetic layer (MnBi₂Te₄) and nonmagnetic layer (Bi₂Te₃). By means of scanning tunneling spectroscopy, we clearly observe the electronic state present at a step edge of a magnetic MnBi₂Te₄ layer but absent at nonmagnetic Bi₂Te₃ layers at 4.5 K. Furthermore, we find that as the temperature rises above T_N the edge state vanishes, while the point defect induced state persists upon an increase in temperature. These results confirm the observation of magnetism-induced edge states. Our analysis based on an axion insulator theory reveals that the nontrivial topological nature of the observed edge state.

Spin-Orbit Coupling Electronic Structures of Organic-Group Functionalized Sb and Bi Topological Monolayers

Electronic band-gap is a key factor in applying two-dimensional (2D) topological insulators into room-temperature quantum spin Hall effect (QSH) spintronic devices. Employing pseudopotential plane-wave first-principles calculations, we investigate spin-orbit coupling (SOC) electronic structures of the novel 2D topological insulator series of antimony (Sb) and bismuth (Bi) monolayers (isolated double atomic layers) functionalized by organic-groups (methyl, amino and hydroxyl). Cohesive energies and phonon frequency dispersion spectra indicate that these organic-group decorated Sb and Bi monolayers possess structural stability in both energetic statics and lattice dynamics. The giant electronic band-gaps adequate for room-temperature applications are attributed to the effective SOC enhancement of group functionalization. The nontrivial topology of these novel 2D monolayer materials is verified by the Z₂ invariant derived from wave-function parity and edge-states of their nanoribbons, which is prospective for QSH spintronic devices. The chemical functional group changes the p-orbital component of Fermi level electrons, leading to strong intra-layer spin-orbit coupling, opening a large band-gap of approaching 1.4 eV at Dirac-cone point and resulting in a global indirect band-gap of 0.75 eV, which, even underestimated, is adequate for room-temperature operations. Sb and Bi monolayers functionalized by organic groups are also predicted to maintain stable nontrivial topology under in-layer biaxial strain, which is suitable for epitaxy technology to realize QSH spintronic devices.

Hot-Pressed Two-Dimensional Amorphous Metals and Their Electronic Properties

As an emerging research field, two-dimensional (2D) metals have been the subject of increasing research efforts in recent years due to their potential applications. However, unlike typical 2D layered materials, such as graphene, which can be exfoliated from their bulk parent compounds, it is hardly possible to produce 2D metals through exfoliation techniques due to the absence of Van der Waals gaps. Indeed, the lack of effective material preparation methods severely limits the development of this research field. Here, we report a PDMS-assisted hot-pressing method in glovebox to obtain ultraflat nanometer-thick 2D metals/metal oxide amorphous films of various low-melting-point metals and alloys, e.g., gallium (Ga), indium (In), tin (Sn), and Ga0.87Ag0.13 alloy. The valence states extracted from X-ray photoelectron spectroscopy (XPS) indicate that the ratios of oxidation to metal in our 2D films vary among metals. The temperature-dependent electronic measurements show that the transport behavior of 2D metal/metal oxide films conform with the 2D Mott’s variable range hopping (VRH) model. Our experiments provide a feasible and effective approach to obtain various 2D metals.

Thickness dependent band structure of-bismuthene grown on epitaxial graphene

Along with the great interest in two-dimensional elemental materials that has emerged in recent years, atomically thin layers of bismuth have attracted attention due to physical properties on account of a strong spin-orbit coupling. Thickness dependent electronic band structure must be explored over the whole Brillouin zone in order to further explore their topological electronic properties. The anisotropic band structures along zig-zag and armchair directions of α-bismuthene (α-Bi) were resolved using the two-dimensional mapping of angle-resolved photoemission spectra. An increase in the number of layers from 1- to 2-bilayers (BLs) shifts the top of a hole band onΓ¯-X¯1line to high wavenumber regions. Subsequently, an electron pocket onΓ¯-X¯1line and a hole pocket centred atΓ¯point appears in the 3 BL α-Bi. Gapless Dirac-cone features with a large anisotropy were clearly resolved onX¯2point in the 1-BL and 2-BL α-Bi, which can be attributed to the strong spin-orbit coupling and protection by the nonsymmorphic symmetry of the α-Bi lattice.

Epitaxial Growth of Ultraflat Bismuthene with Large Topological Band Inversion Enabled by Substrate-Orbital-Filtering Effect

Quantum spin Hall (QSH) systems hold promises of low-power-consuming spintronic devices, yet their practical applications are extremely impeded by the small energy gaps. Fabricating QSH materials with large gaps, especially under the guidance of design principles, is essential for both scientific research and practical applications. Here, we demonstrate that large on-site atomic spin-orbit coupling can be directly exploited via the intriguing substrate-orbital-filtering effect to generate large-gap QSH systems and experimentally realized on the epitaxially synthesized ultraflat bismuthene on Ag(111). Theoretical calculations reveal that the underlying substrate selectively filters Bi p_z orbitals away from the Fermi level, leading p_xy orbitals with nonzero magnetic quantum numbers, resulting in large topological gap of ∼1 eV at the K point. The corresponding topological edge states are identified through scanning tunneling spectroscopy combined with density functional theory calculations. Our findings provide general strategies to design large-gap QSH systems and further explore their topology-related physics.

Observation of Topological Edge States on α-Bi4Br4 Nanowires Grown on TiSe2 Substrates

A time-reversal invariant two-dimensional (2D) topological insulator (TI) is characterized by the gapless helical edge states propagating along the perimeter of the system. However, the small band gap in the 2D TIs discovered so far hinders their applications. Recently, we predicted that single-layer Bi₄Br₄ is a 2D TI with a remarkable band gap and that α-Bi₄Br₄ crystals can host topological edge states at the step edges. Here we report the growth of α-Bi₄Br₄ nanowires with (102)-oriented top surfaces on the TiSe₂ substrates and the direct observation of the predicted topological edge states at the step edges of the nanowires using scanning tunneling microscopy. The coupling between the edge states leads to the formation of surface states at the (102) top surfaces of the nanowires. Our work demonstrates the existence of topological edge states in α-Bi₄Br₄ and paves the way for developing α-Bi₄Br₄-based devices for a high-temperature quantum spin Hall effect.

Ultrathin epitaxial Bi film growth on 2D HfTe2template

Among ultrathin monoelemental two-dimensional (2D) materials, bismuthene, the single layer of heavier group-VΑ element bismuth (Bi), has been predicted to have large non trivial gap. Here, we demonstrate the growth of Bi films by molecular beam epitaxy on 2D-HfTe₂template. At the initial stage of Bi deposition (1-2 bilayers, BL), both the pseudocubic Bi(110) and the hexagonal Bi(111) phases are formed. When reaching 3 BL Bi, a transformation to pure hexagonal Bi(111) occurs. The electronic band structure of 3 BL Bi(111) films was measured by angle-resolved photoemission spectroscopy showing very good matching with the density functional theory band structure calculations of 3 BL free standing Bi(111). The grown Bi(111) thin film was capped with a protective Al₂O₃layer and its stability under ambient conditions, necessary for practical applications and device fabrication, was confirmed by x-ray photoelectron spectroscopy and Raman spectroscopy.

Epitaxial Growth of Quasi-One-Dimensional Bismuth-Halide Chains with Atomically Sharp Topological Non-Trivial Edge States

Quantum spin Hall insulators (QSHIs) have one-dimensional (1D) spin-momentum locked topological edge states (ES) inside the bulk band gap, which can serve as dissipationless channels for the practical applications in low consumption electronics and high performance spintronics. However, obtaining the clean and atomically sharp ES which serves as ideal 1D spin-polarized nondissipative conducting channels is demanding and still a challenge. Here, we report the formation of the quasi-1D Bi₄I₄ nanoribbons on the surface of Bi(111) with the support of the graphene-terminated 6H-SiC(0001) and the direct observation of the topological ES at the step edges by the scanning tunneling microscopy (STM) and spectroscopic-imaging results. The ES reside surround the edge of Bi₄I₄ nanoribbons and exhibits noteworthy robustness against nontime reversal symmetry (non-TRS) perturbations. The theoretical simulations verify the topological nontriviality of 1D ES, which is retained after considering the presence of the underlying Bi(111). Our study supports the existence of topological ES in Bi₄I₄ nanoribbons, benefiting to engineer the topological features by using the 1D nanoribbons as building blocks.

Selective Substrate-Orbital-Filtering Effect to Realize the Large-Gap Quantum Spin Hall Effect

Although Pb harbors a strong spin-orbit coupling effect, pristine plumbene (the last group-IV cousin of graphene) hosts topologically trivial states. Based on first-principles calculations, we demonstrate that epitaxial growth of plumbene on the BaTe(111) surface converts the trivial Pb lattice into a quantum spin Hall (QSH) phase with a large gap of ∼0.3 eV via a selective substrate-orbital-filtering effect. Tight-binding model analyses show the p_z orbital in half of the Pb overlayer is selectively removed by the BaTe substrate, leaving behind a p_z-p_x,y band inversion. Based on the same working principle, the gap can be further increased to ∼0.5-0.6 eV by surface adsorption of H or halogen atoms that filters out the other half of the Pb p_z orbitals. The mechanism of selective substrate-orbital-filtering is general, opening an avenue to explore large-gap QSH insulators in heavy-metal-based materials. It is worth noting that plumbene has already been widely grown on various substrates experimentally.

Dual Dirac points and odd-even oscillated energy gap in zigzag chlorinated stanene nanoribbon

Stanene has been predicted to be a two-dimensional topological insulator, providing an ideal platform for the realization of quantum spin Hall effect even at room temperature. Based on first-principles calculations, we studied the topological edge states in zigzag chlorinated stanene nanoribbon. From our calculations, dual Dirac points can be found near Fermi level. One Dirac point is localized at the edges and emerges in a narrow nanoribbon, while another is widespread and can only be found in a wide nanoribbon due to the coupling of two opposite edges. At the localized Dirac point, there is an interesting odd-even oscillated energy gap with the change of the width of nanoribbon. The energy gaps at both Dirac points and the coupling of two opposite edges can be modified by edge adsorption. Asymmetric adsorption of two edges was also discussed. Our calculations may be helpful for the potential applications of tin-based topological nanoribbons in nanodevices.

Systematic Investigation of the Coupling between One-Dimensional Edge States of a Topological Crystalline Insulator

The interaction of spin-polarized one-dimensional (1D) topological edge modes localized along single-atomic steps of the topological crystalline insulator Pb_{0.7}Sn_{0.3}Se(001) has been studied systematically by scanning tunneling spectroscopy. Our results reveal that the coupling of adjacent edge modes sets in at a step-to-step distance d_{ss}≤25  nm, resulting in a characteristic splitting of a single peak at the Dirac point in tunneling spectra. Whereas the energy splitting exponentially increases with decreasing d_{ss} for single-atomic steps running almost parallel, we find no splitting for single-atomic step edges under an angle of 90°. The results are discussed in terms of overlapping wave functions with p_{x}, p_{y} orbital character.

Atomically Thin Quantum Spin Hall Insulators

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.

Sierpiński Structure and Electronic Topology in Bi Thin Films on InSb(111)B Surfaces

Deposition of Bi on InSb(111)B reveals a striking Sierpiński-triangle (ST)-like structure in Bi thin films. Such a fractal geometric topology is further shown to turn off the intrinsic electronic topology in a thin film. Relaxation of a huge misfit strain of about 30% to 40% between Bi adlayer and substrate is revealed to drive the ST-like island formation. A Frenkel-Kontrova model is developed to illustrate the enhanced strain relief in the ST islands offsetting the additional step energy cost. Besides a sufficiently large tensile strain, forming ST-like structures also requires larger adlayer-substrate and intra-adlayer elastic stiffnesses, and weaker intra-adlayer interatomic interactions.

Schottky barrier heights in two-dimensional field-effect transistors: from theory to experiment

Over the past decade, two-dimensional semiconductors (2DSCs) have aroused wide interest due to their extraordinary electronic, magnetic, optical, mechanical, and thermal properties, which hold potential in electronic, optoelectronic, thermoelectric applications, and so forth. The field-effect transistor (FET), a semiconductor gated with at least three terminals, is pervasively exploited as the device geometry for these applications. For lack of effective and stable substitutional doping techniques, direct metal contact is often used in 2DSC FETs to inject carriers. A Schottky barrier (SB) generally exists in the metal-2DSC junction, which significantly affects and even dominates the performance of most 2DSC FETs. Therefore, low SB or Ohmic contact is highly preferred for approaching the intrinsic characteristics of the 2DSC channel. In this review, we systematically introduce the recent progress made in theoretical prediction of the SB height (SBH) in the 2DSC FETs and the efforts made both in theory and experiments to achieve low SB contacts. From the comparison between the theoretical and experimentally observed SBHs, the emerging first-principles quantum transport simulation turns out to be the most powerful theoretical tool to calculate the SBH of a 2DSC FET. Finally, we conclude this review from the viewpoints of state-of-the-art electrode designs for 2DSC FETs.

Surface Modification and Subsequent Fermi Density Enhancement of Bi(111)

Defects introduced to the surface of Bi(111) break the translational symmetry and modify the surface states locally. We present a theoretical and experimental study of the 2D defects on the surface of Bi(111) and the states that they induce. Bi crystals cleaved in ultrahigh vacuum (UHV) at low temperature (110 K) and the resulting ion-etched surface are investigated by low-energy electron diffraction (LEED), X-ray photoelectron spectroscopy, ultraviolet photoelectron spectroscopy (UPS), and scanning tunneling microscopy (STM) as well as spectroscopy (STS) techniques in combination with density functional theory (DFT) calculations. STS measurements of cleaved Bi(111) reveal that a commonly observed bilayer step edge has a lower density of states (DOS) around the Fermi level as compared to the atomic-flat terrace. Following ion bombardment, the Bi(111) surface reveals anomalous behavior at both 110 and 300 K: Surface periodicity is observed by LEED, and a significant increase in the number of bilayer step edges and energetically unfavorable monolayer steps is observed by STM. It is suggested that the newly exposed monolayer steps and the type A bilayer step edges result in an increase to the surface Fermi density as evidenced by UPS measurements and the Kohn-Sham DOS. These states appear to be thermodynamically stable under UHV conditions.

Enhanced Terahertz Radiation by Efficient Spin-to-Charge Conversion in Rashba-Mediated Dirac Surface States

The enhancement of terahertz (THz) radiation is of extreme significance for the realization of the THz probe and imaging. However, present THz technologies are far from being enough to realize high-performance and room-temperature THz sources. Fortunately, topological insulators (TIs), with spin-momentum-locked Dirac surface states, are expected to exhibit a high terahertz emission efficiency. In this work, the novel concept of a Rashba-state-enhanced spintronic THz emitter is demonstrated on the basis of ferromagnet/heavy metal/topological insulator (FM/HM/TI) heterostructure. We find that the THz emission intensity changes as a function of HM interlayer thickness, and a 1.98 times higher intensity compared to that of FM/TI can be achieved when a meticulously designed thickness of the HM layer is inserted. The improvement of terahertz radiation is ascribed to the additive effect of Rashba splitting and topological surface states at the HM/TI interface. These results offer new possibilities for realizing spintronic THz emitters in TI-based magnetic heterostructures.

Metal-organic frameworks: possible new two-dimensional magnetic and topological materials

Finding new two-dimensional (2D) materials with novel quantum properties is highly desirable for technological innovations. In this work, we studied a series of metal-organic frameworks (MOFs) with different metal cores and discovered various attractive properties, such as room-temperature magnetic ordering, strong perpendicular magnetic anisotropy, huge topological band gap (>200 meV), and excellent spin-filtering performance. As many MOFs have been successfully synthesized in experiments, our results suggest realistic new 2D functional materials for the design of spintronic nanodevices.

Thermoelectric power generation efficiency of zigzag monolayer nanoribbon of bismuth

The thermoelectric power generation efficiency of a bismuth monolayer nanoribbon has been studied theoretically. We calculate the conductance of such a structure using the multi-orbital tight-binding model and also recursive Green's function method, in the presence of a substrate and on-site potential. For the case of the [Formula: see text] substrate-supported bismuth nanoribbon and by proper selection of on-site potential, a boxcar shape conductance in terms of energy has been obtained. Using the Landauer-Büttiker formalism in the non-linear response regime, we calculate heat and charge currents at low temperatures. By calculation of the electrical output power and power conversion thermoelectric efficiency, we have illustrated that such a structure can operate at high thermoelectric efficiency and also a considerable power generation rate.

Folding Graphene into a Chern Insulator with Light Irradiation

Recently, the precise folding of flexible graphene is reported experimentally [ Science, 2019, 365, 1036-1040], demonstrating an efficient approach to manipulate its electronic and optoelectronic properties. Here, we propose a light-induced high-Chern-number Chern insulator (CI) in the folded graphene. Along both armchair and zigzag folding directions, we demonstrate that there are two-handedness-dependent chiral interface states localized at the curved region. Physically, they can be attributed to the light-induced mass-term inversion across the folded graphene. Most remarkably, by rationally designing the folding processes, 2D and 3D CIs are also realizable in a single-wall carbon nanotube and periodic folded graphene, respectively, illustrating a high tunability of the folding degree of freedom. We envision that this intriguing form of "foldtronics" will provide a new platform for investigating the topological state in 2D materials to draw immediate experimental attention.

Early-Stage Growth Mechanism and Synthesis Conditions-Dependent Morphology of Nanocrystalline Bi Films Electrodeposited from Perchlorate Electrolyte

Bi nanocrystalline films were formed from perchlorate electrolyte (PE) on Cu substrate via electrochemical deposition with different duration and current densities. The microstructural, morphological properties, and elemental composition were studied using scanning electron microscopy (SEM), atomic force microscopy (AFM), and energy-dispersive X-ray microanalysis (EDX). The optimal range of current densities for Bi electrodeposition in PE using polarization measurements was demonstrated. For the first time, it was shown and explained why, with a deposition duration of 1 s, co-deposition of Pb and Bi occurs. The correlation between synthesis conditions and chemical composition and microstructure for Bi films was discussed. The analysis of the microstructure evolution revealed the changing mechanism of the films’ growth from pillar-like (for Pb-rich phase) to layered granular form (for Bi) with deposition duration rising. This abnormal behavior is explained by the appearance of a strong Bi growth texture and coalescence effects. The investigations of porosity showed that Bi films have a closely-packed microstructure. The main stages and the growth mechanism of Bi films in the galvanostatic regime in PE with a deposition duration of 1–30 s are proposed.

Visualizing coexisting surface states in the weak and crystalline topological insulator Bi2TeI

Dual topological materials are unique topological phases that host coexisting surface states of different topological nature on the same or on different material facets. Here, we show that Bi₂TeI is a dual topological insulator. It exhibits band inversions at two time reversal symmetry points of the bulk band, which classify it as a weak topological insulator with metallic states on its 'side' surfaces. The mirror symmetry of the crystal structure concurrently classifies it as a topological crystalline insulator. We investigated Bi₂TeI spectroscopically to show the existence of both two-dimensional Dirac surface states, which are susceptible to mirror symmetry breaking, and one-dimensional channels that reside along the step edges. Their mutual coexistence on the step edge, where both facets join, is facilitated by momentum and energy segregation. Our observation of a dual topological insulator should stimulate investigations of other dual topology classes with distinct surface manifestations coexisting at their boundaries.

The effect of moiré superstructures on topological edge states in twisted bismuthene homojunctions

Creating and controlling the topological properties of two-dimensional topological insulators is essential for spintronic device applications. Here, we report the successful growth of bismuth homostructure consisting of monolayer bismuthene and single-layer black phosphorus-like Bi (BP-Bi) on the HOPG surface. Combining scanning tunneling microscopy/spectroscopy with noncontact atomic force microscopy, moiré superstructures with twist angles in the bismuth homostructure and the modulation of topological edge states of bismuthene were observed and studied. First-principles calculations reproduced the moiré superlattice and indicated that the structure fluctuation is ascribed to the stacking modes between bismuthene and BP-Bi, which induce spatially distributed interface interactions in the bismuth homostructure. The modulation of topological edge states is directly related to the variation of interlayer interactions. Our results suggest a promising pathway to tailor the topological states through interfacial interactions.

Robust Hot Electron and Multiple Topological Insulator States in PtBi2

A two-dimensional topological insulator features (only) one bulk gap with nontrivial topology, which protects one-dimensional boundary states at the Fermi level. We find a quantum phase of matter beyond this category: a multiple topological insulator. It possesses a ladder of topological gaps; each gap protects a robust edge state. We prove a monolayer of van der Waals material PtBi₂ as a two-dimensional multiple topological insulator. By means of scanning tunneling spectroscopy, we directly visualize the one-dimensional hot electron (and hole) channels with nanometer size on the samples. Furthermore, we confirm the topological protection of these channels by directly demonstrating their robustness to variations of crystal orientation, edge geometry, and sample temperature. The discovered topological hot electron materials may be applied as efficient photocatalysts in the future.

Advances of 2D bismuth in energy sciences

Since graphene has been successfully exfoliated, two-dimensional (2D) materials constitute a vibrant research field and open vast perspectives in high-performance applications. Among them, bismuthene and 2D bismuth (Bi) are unique with superior properties to fabricate state-of-the-art energy saving, storage and conversion devices. The largest experimentally determined bulk gap, even larger than those of stanene and antimonene, allows 2D Bi to be the most promising candidate to construct room-temperature topological insulators. Moreover, 2D Bi exhibits cyclability for high-performance sodium-ion batteries, and the enlarged surface together with the good electrochemical activity renders it an efficient electrocatalyst for energy conversion. Also, the air-stability of 2D Bi is better than that of silicene, germanene, phosphorene and arsenene, which could enable more practical applications. This review aims to thoroughly explore the fundamentals of 2D Bi and its improved fabrication methods, in order to further bridge gaps between theoretical predictions and experimental achievements in its energy-related applications. We begin with an introduction of the status of 2D Bi in the 2D-material family, which is followed by descriptions of its intrinsic properties along with various fabrication methods. The vast implications of 2D Bi for high-performance devices can be envisioned to add a new pillar in energy sciences. In addition, in the context of recent pioneering studies on moiré superlattices of other 2D materials, we hope that the improved manipulation techniques of bismuthene, along with its unique properties, might even enable 2D Bi to play an important role in future energy-related twistronics.

Real Space Imaging of Topological Edge States in InAs/GaSb and InAs/InxGa1-xSb Quantum Wells

Structure dependent differential tunneling conductance, dI/dV, profiles obtained using scanning tunneling microscopy on both (110)-cleaved surfaces and (001)-growth surfaces in InAs/GaSb and InAs/In_xGa_1-xSb quantum wells (QWs), which are platforms of two-dimensional topological insulator (2D-TI), clearly demonstrated the edge states formed on the 2D-TI surfaces. The results were confirmed by kp-based electronic structure calculations, which demonstrated that the edge states extended to the 10 nm range from cleaved surfaces generated in the appropriately designed InAs/(In)GaSb QW systems.

Resolving the topological classification of bismuth with topological defects

The growing diversity of topological classes leads to ambiguity between classes that share similar boundary phenomenology. This is the status of bulk bismuth. Recent studies have classified it as either a strong or a higher-order topological insulator, both of which host helical modes on their boundaries. We resolve the topological classification of bismuth by spectroscopically mapping the response of its boundary modes to a screw-dislocation. We find that the one-dimensional mode, on step-edges, extends over a wide energy range and does not open a gap near the screw-dislocations. This signifies that this mode binds to the screw-dislocation, as expected for a material with nonzero weak indices. We argue that the small energy gap, at the time reversal invariant momentum L, positions bismuth within the critical region of a topological phase transition between a higher-order topological insulator and a strong topological insulator with nonzero weak indices.

Evidence for Magnetic Skyrmions at the Interface of Ferromagnet/Topological-Insulator Heterostructures

The heterostructures of the ferromagnet (Cr₂Te₃) and topological insulator (Bi₂Te₃) have been grown by molecular beam epitaxy. The topological Hall effect as evidence of the existence of magnetic skyrmions has been observed in the samples in which Cr₂Te₃ was grown on top of Bi₂Te₃. Detailed structural characterizations have unambiguously revealed the presence of intercalated Bi bilayer nanosheets right at the interface of those samples. The atomistic spin-dynamics simulations have further confirmed the existence of magnetic skyrmions in such systems. The heterostructures of ferromagnet and topological insulator that host magnetic skyrmions may provide an important building block for next generation of spintronics devices.