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

Evidence of Topological Edge States in Buckled Antimonene Monolayers

Two-dimensional topological materials have attracted intense research efforts owing to their promise in applications for low-energy, high-efficiency quantum computations. Group-VA elemental thin films with strong spin-orbit coupling have been predicted to host topologically nontrivial states as excellent two-dimensional topological materials. Herein, we experimentally demonstrated for the first time that the epitaxially grown high-quality antimonene monolayer islands with buckled configurations exhibit significantly robust one-dimensional topological edge states above the Fermi level. We further demonstrated that these topologically nontrivial edge states arise from a single p-orbital manifold as a general consequence of atomic spin-orbit coupling. Thus, our findings establish monolayer antimonene as a new class of topological monolayer materials hosting the topological edge states for future low-power electronic nanodevices and quantum computations.

Observation of Topological Edge States at the Step Edges on the Surface of Type-II Weyl Semimetal TaIrTe4

Topological materials harbor topologically protected boundary states. Recently, TaIrTe₄, a ternary transition-metal dichalcogenide, was identified as a type-II Weyl semimetal with the minimal nonzero number of Weyl points allowed for a time-reversal invariant Weyl semimetal. Monolayer TaIrTe₄ was proposed to host topological edge states, which, however, lacks of experimental evidence. Here, we report on the topological edge states localized at the monolayer step edges of the type-II Weyl semimetal TaIrTe₄ using scanning tunneling microscopy. One-dimensional electronic states that show substantial robustness against the edge irregularity are observed at the step edges. Theoretical calculations substantiate the topologically nontrivial nature of the edge states and their robustness against the edge termination and layer stacking. The observation of topological edge states at the step edges of TaIrTe₄ surfaces suggests that monolayer TaIrTe₄ is a two-dimensional topological insulator, providing TaIrTe₄ as a promising material for topological physics and devices.

Topological phase transition induced by px,y and pz band inversion in a honeycomb lattice

The search for more types of band inversion-induced topological states is of great scientific and experimental interest. Here, we proposed that the band inversion between p_x,y and p_z orbitals can produce a topological phase transition in honeycomb lattices based on tight-binding model analyses. The corresponding topological phase diagram was mapped out in the parameter space of orbital energy and spin-orbit coupling. Specifically, the quantum anomalous Hall (QAH) effect could be achieved when ferromagnetism was introduced. Moreover, our first-principles calculations demonstrated that the two systems of half-iodinated silicene (Si₂I) and one-third monolayer of bismuth epitaxially grown on the Si(111)-√3 ×√3 surface are ideal candidates for realizing the QAH effect with Curie temperatures of ∼101 K and 118 K, respectively. The underlying physical mechanism of this scheme is generally applicable, offering broader opportunities for the exploration of novel topological states and high-temperature QAH effect systems.

Topological electronic structure and Rashba effect in Bi thin layers: theoretical predictions and experiments

The goal of the present review is to cross-compare theoretical predictions with selected experimental results on bismuth thin films exhibiting topological properties and a strong Rashba effect. The theoretical prediction that a single free-standing Bi(1 1 1) bilayer is a topological insulator has triggered a large series of studies of ultrathin Bi(1 1 1) films grown on various substrates. Using selected examples we review theoretical predictions of atomic and electronic structure of Bi thin films exhibiting topological properties due to interaction with a substrate. We also survey experimental signatures of topological surface states and Rashba effect, as obtained mostly by angle- and spin-resolved photoelectron spectroscopy.

Gas sensing properties of buckled bismuthene predicted by first-principles calculations

First-principles calculations are used to study the structural, electronic, transport and optical properties of buckled bismuthene with the adsorption of various gas molecules such as CO, O₂, H₂O, NH₃, SO₂, NO and NO₂. By considering the van der Waals interactions between the gas molecules and buckled bismuthene, we find that the buckled bismuthene shows superior gas sensing performance to other 2D materials such as graphene and MoS₂. The adsorption of CO, O₂, H₂O and NH₃ molecules is physisorption, whereas SO₂, NO and NO₂ are chemisorbed on the buckled bismuthene with large charge transfer and strong adsorption energy. After adsorption, charges are transferred from buckled bismuthene to the molecules and the quantum conductance is changed by the adsorbed molecules. Furthermore, the work function of buckled bismuthene is changed with the adsorption of different molecules. Our results show that the electronic, transport and optical properties of buckled bismuthene are sensitive to the adsorption of gas molecules, which suggests that buckled bismuthene holds great potential for application in gas sensors.

A 2D nonsymmorphic Dirac semimetal in a chemically modified group-VA monolayer with a black phosphorene structure

A symmetry-protected 2D Dirac semimetal has attracted intense interest for its intriguing material properties. Here, we report a 2D nonsymmorphic Dirac semimetal state in a chemically modified group-VA 2D puckered structure. Based on first-principles calculations, we demonstrate the existence of 2D Dirac fermions in a one-side modified phosphorene structure in two different types: one with a Dirac nodal line (DNL) structure for light elements with negligible spin-orbit coupling (SOC) and the other having an hourglass band protected by a nonsymmorphic symmetry for heavy elements with strong SOC. In the absence of SOC, the DNL exhibits an anisotropic behavior and unique electronic properties, such as constant density of states. The Dirac node is protected from gap opening by the nonsymmorphic space group symmetry. In the presence of SOC, the DNL states split and form an hourglass-shaped dispersion due to the broken inversion symmetry and the Rashba SOC interaction. Moreover, around certain high symmetry points in the Brillouin zone, the spin orientation is enforced to be along a specific direction. We construct an effective tight-binding model to characterize the 2D nonsymmorphic Dirac states. Our result provides a promising material platform for exploring the intriguing properties of essential nodal-line and nodal-point fermions in 2D systems.

Topological quantum states of matter in iron-based superconductors: from concept to material realization

We review recent progress in the exploration of topological quantum states of matter in iron-based superconductors. In particular, we focus on the non-trivial topology existing in the band structures and superconducting states of iron's 3d orbitals. The basic concepts, models, materials and experimental results are reviewed. The natural integration between topology and high-temperature superconductivity in iron-based superconductors provides great opportunities to study topological superconductivity and Majorana modes at high temperature.

Epitaxial Growth of PbSe Few-Layers on SrTiO3: The Effect of Compressive Strain and Potential Two-Dimensional Topological Crystalline Insulator

The freestanding PbSe monolayer has been predicted as a candidate of the two-dimensional topological crystalline insulator, which possesses the Dirac-cone-like edge states resided at the edge. Up to now, however, direct experimental evidence of topological PbSe monolayer has not yet been reported. Here, we report the epitaxial growth and scanning tunneling microscopy study of few-layers PbSe islands grown on SrTiO₃ substrate. From the investigation of different thickness, we discover the release of compressive strain and the reduction of bandgap as the thickness becomes thick. Following detailed spectroscopic measurements, a signature of Dirac-like edge states is observed at the edge of seventh-layer PbSe. In conjunction with first-principle calculations, we find that compressive-strain-induced buckling adjusts the topological band inversion and eventually leads to a phase transition from nontrivial two-dimensional topological crystalline insulator to trivial insulator, which match well with our experimental observations. Therefore, both theoretical calculations and experimental observations reveal that the strain can effectively affect the property of epitaxial PbSe, meanwhile demonstrate seventh-layer PbSe as a potential candidate of 2D TCI.

Topologically nontrivial phase and tunable Rashba effect in half-oxidized bismuthene

Bismuth based (Bi-based) materials exhibit promising potential for the study of two-dimensional (2D) topological insulators or quantum spin Hall (QSH) insulators due to their intrinsic strong spin-orbit coupling (SOC). Herein, we theoretically propose a new inversion-asymmetry topological phase with tunable Rashba effect in a 2D bismuthene monolayer, which is driven by the sublattices half-oxidation (SHO). The nontrivial topology is identified by the SHO induced p-p band inversion at the Γ point, the Z2 topological number, and the metallic edge states. Interestingly, the SOC opens a band gap as large as 0.26 eV at Γ, which is twice as large as that of the freestanding bismuthene monolayer, revealing a predominant contribution of the orbital filtering effect. Inversion-symmetry breaking leads to a substantial Rashba constant of 11.5 eV Å near the valence band top, which is about twice as large as that of the freestanding bismuthene monolayer due to the SHO effect. In particular, the topological insulator-to-topological semimetal phase-transition and the tunable Rashba effect were achieved by exerting a moderate strain. We demonstrate that 3% stretching is the most desirable strain to obtain superior properties. Hexagonal boron nitrogen (h-BN) is proposed to serve as a suitable substrate for SHO-Bi in practical applications. Our findings not only provide a new route to engineering a 2D inversion-asymmetry topological insulator but also represent a significant advance in the exploration of 2D Bi-based topological materials.

Optical properties of monolayer bismuthene in electric fields

Optical excitations of monolayer bismuthene present very rich and unique absorption spectra. The optical energy gap corresponding to the threshold frequency is not equal to an indirect energy gap, and it becomes zero under the critical electric field. The frequency, number, intensity, and form of the absorption structures are dramatically changed when an external electric field is applied. The prominent peaks and the observable shoulders, respectively, arise from the constant-energy loop and the band-edge states of parabolic dispersions. These directly reflect the unusual electronic properties, being very different from those in monolayer graphene. The novel optical properties of bismuthine that are easily manipulated by electric fields may find a lot of various applications in optoelectronics, either combined with or complementary to those graphene-based systems.

Kinetic pathways towards mass production of single crystalline stanene on topological insulator substrates

As a highly appealing new member of the two-dimensional (2D) materials family, stanene was first epitaxially grown on a three-dimensional topological insulator of Bi2Te3; yet, to date, a standing challenge is to drastically improve the overall quality of such stanene overlayers for a wide range of potential applications in next-generation quantum devices. Here we use state-of-the-art first-principles approaches to explore the atomistic growth mechanisms of stanene on different Bi2Te3(111)-based substrates, with intriguing discoveries. We first show that, when grown on experimentally studied Te-terminated Bi2Te3, stanene would follow an unusual partial-layer-by-partial-layer growth mode, characterized by short-range repulsive pairwise interactions of the Sn adatoms; the resultant stanene overlayer is destined to contain undesirable grain boundaries. More importantly, we find that stanene growth on Bi2Te3(111) pre-covered with a Bi bilayer follows a highly desirable nucleation-and-growth mechanism, strongly favoring single crystalline stanene. We further show that both systems exhibit pronounced Rashba spin-orbit couplings, while the latter system also provides new opportunities for the potential realization of topological superconductivity in 2D heterostructures. The novel kinetic pathways revealed here will be instrumental in achieving the mass production of high-quality stanene with emergent physical properties of technological significance.

Nanostructured Bi Grown on Epitaxial Graphene/SiC

Controllable growth of metal nanostructures on epitaxial graphene (EG) is particularly interesting and important for the applications in electric devices. Bi nanostructures on EG/SiC are fabricated through thermal decomposition of SiC and subsequent low-flux evaporation of Bi. The orientation, atomic structure, and thickness-dependent electronic states of Bi are investigated by scanning tunneling microscopy/spectroscopy. It is found that metallic Bi nanoflakes and nanorods prefer to grow on the SiC buffer layer region with higher diffusion barrier, but Bi nanoribbons are formed on regularly ordered EG. Although the thicker Bi nanoribbons of 11 monolayers on EG are still metallic, the thinner ones become semiconducting owing to the interfacial effect. This indicates that the electronic states and physical properties of Bi are substrate-dependent. The results are helpful for the design of Bi- and graphene-based electronic and spintronic devices.

Observation of topologically protected states at crystalline phase boundaries in single-layer WSe2

Transition metal dichalcogenide materials are unique in the wide variety of structural and electronic phases they exhibit in the two-dimensional limit. Here we show how such polymorphic flexibility can be used to achieve topological states at highly ordered phase boundaries in a new quantum spin Hall insulator (QSHI), 1T'-WSe2. We observe edge states at the crystallographically aligned interface between a quantum spin Hall insulating domain of 1T'-WSe2 and a semiconducting domain of 1H-WSe2 in contiguous single layers. The QSHI nature of single-layer 1T'-WSe2 is verified using angle-resolved photoemission spectroscopy to determine band inversion around a 120 meV energy gap, as well as scanning tunneling spectroscopy to directly image edge-state formation. Using this edge-state geometry we confirm the predicted penetration depth of one-dimensional interface states into the two-dimensional bulk of a QSHI for a well-specified crystallographic direction. These interfaces create opportunities for testing predictions of the microscopic behavior of topologically protected boundary states.

Bi2Se3 topological insulator at the 2D-limit: role of halide-doping on Dirac point

2D topological insulators exhibit insulating bulk and conducting edge states with a Dirac point, which at times is within the energy gap and could be on either side of the Fermi energy. In this study, we demonstrate a method to tune the energy of the Dirac edge state by introducing halides as dopants in Bi₂Se₃. We chose halides to substitute the anion, so that due to higher atomic number (of iodine, for example) with respect to selenium, the spin-orbit coupling parameter could be enhanced, leading to the significant separation of the Dirac point from the Fermi energy. With different halogens having different atomic numbers on either side of selenium, the Dirac point could hence be tuned towards both directions. The dopants, due to their heterovalent nature with respect to selenide, introduce carriers in the lattice and consequently, also shift the Fermi energy. We show that the Dirac point with respect to Fermi energy could be correlated to the dopant's atomic number and thus the atomic-number-induced spin-orbit coupling parameter. Strains developed in the lattice due to a mismatch in the effective ionic radii of the dopants and the host anion affected distribution of band energies, leaving the (distribution of) Dirac point unaffected due to its topologically protected nature.

Two-Dimensional In-Sb Compound on Silicon as a Quantum Spin Hall Insulator

Two-dimensional (2D) topological insulator is a promising quantum phase for achieving dissipationless transport due to the robustness of the gapless edge states resided in the insulating gap providing realization of the quantum spin Hall effect. Searching for two-dimensional realistic materials that are able to provide the quantum spin Hall effect and possessing the feasibility of their experimental preparation is a growing field. Here we report on the two-dimensional (In, Sb)2[Formula: see text]2[Formula: see text] compound synthesized on Si(111) substrate and its comprehensive experimental and theoretical investigations based on an atomic-scale characterization by using scanning tunneling microscopy and angle-resolved photoelectron spectroscopy as well as ab initio density functional theory calculations identifying the synthesized 2D compound as a suitable system for realization of the quantum spin Hall effect without additional functionalization like chemical adsorption, applying strain, or gating.

Formation of a large gap quantum spin Hall phase in a 2D trigonal lattice with three p-orbitals

The quantum spin Hall (QSH) phase in a trigonal lattice requires typically a minimal basis of three orbitals with one even parity s and two odd parity p orbitals. Here, based on first-principles calculations combined with tight-binding model analyses and calculations, we demonstrate that depositing 1/3 monolayer Bi or Te atom layers on an existing experimental Ag/Si(111) surface can produce a QSH phase readily but with three p-orbitals (p_x, p_y and p_z). The essential mechanism can be understood by the fact while in 3D, the p_z orbital has an odd parity, its parity becomes even when it is projected onto a 2D surface so as to act in place of the s orbital in the original minimum basis. Furthermore, non-trivial large gaps, i.e., 275.0 meV for Bi and 162.5 meV for Te systems, arise from a spin-orbit coupling induced quadratic p_x-p_y band opening at the Γ point. Our findings will significantly expand the search for a substrate supported QSH phase with a large gap, especially in the Si surface, to new orbital combinations and hence new elements.

Entanglement entropy and entanglement spectrum of Bi1-x Sb x (1 1 1) bilayers

We study topological properties of Bi_1-x Sb _x bilayers in the (1 1 1) plane using entanglement measures. Electronic structures are investigated within multi-orbital tight-binding model and structural stability is confirmed through first-principles calculations. The topologically non-trivial nature of the bismuth bilayer is proved by the presence of spectral flow in the entanglement spectrum. We consider topological phase transitions driven by a composition change x, an applied external electric field in Bi bilayers and strain in Sb bilayers. Composition- and strain-induced phase transitions reveal a finite discontinuity in the entanglement entropy. This quantity remains a continuous function of the electric field strength, but shows a finite discontinuity in the first derivative. We relate the difference in behavior of the entanglement entropy to the breaking of inversion symmetry in the last case.

Electronic structure of Fe1.08Te bulk crystals and epitaxial FeTe thin films on Bi2Te3

The electronic structure of thin films of FeTe grown on Bi₂Te₃ is investigated using angle-resolved photoemission spectroscopy, scanning tunneling microscopy and first principles calculations. As a comparison, data from cleaved bulk Fe_1.08Te taken under the same experimental conditions is also presented. Due to the substrate and thin film symmetry, FeTe thin films grow on Bi₂Te₃ in three domains, rotated by 0°, 120°, and 240°. This results in a superposition of photoemission intensity from the domains, complicating the analysis. However, by combining bulk and thin film data, it is possible to partly disentangle the contributions from three domains. We find a close similarity between thin film and bulk electronic structure and an overall good agreement with first principles calculations, assuming a p-doping shift of 65 meV for the bulk and a renormalization factor of around two. By tracking the change of substrate electronic structure upon film growth, we find indications of an electron transfer from the FeTe film to the substrate. No significant change of the film's electronic structure or doping is observed when alkali atoms are dosed onto the surface. This is ascribed to the film's high density of states at the Fermi energy. This behavior is also supported by the ab initio calculations.

Prediction of topological property in TlPBr2 monolayer with appreciable Rashba effect

A quantum spin Hall (QSH) insulator with high stability, large bulk band gap and tunable topological properties is crucial for both fundamental research and practical application due to the presence of dissipationless edge conducting channels. Recently, chemical functionalization has been proposed as an effective route to realize the QSH effect. Based on first-principles calculations, we predict that a two-dimensional TlP monolayer would convert into a topological insulator with the effect of bromination, accompanied by a large bulk band gap of 76.5 meV, which meets the requirement for room-temperature application. The topological nature is verified by the calculation of Z₂ topological invariant and helical edge states. Meanwhile, an appreciable Rashba spin splitting of 77.2 meV can be observed. The bulk band gap can be effectively tuned with external strain and electric field, while the Rashba spin splitting shows a parabolic variation trend under an external electric field. We find that the topological property is available for the TlP film when the coverage rate is more than 0.75. BN and SiC are demonstrated as promising substrates to support the topological nature of TlPBr₂ film. Our findings suggest that a TlPBr₂ monolayer is an appropriate candidate for hosting the nontrivial topological state and controllable Rashba spin splitting, and shows great potential applications in spintronics.

Nanoscale magnetism and novel electronic properties of a bilayer bismuth(111) film with vacancies and chemical doping

Magnetically doped topological insulators (TIs) exhibit several exotic phenomena including the magnetoelectric effect and quantum anomalous Hall effect. However, from an experimental perspective, incorporation of spin moment into 3D TIs is still challenging. Thus, instead of 3D TIs, the 2D form of TIs may open up new opportunities to induce magnetism. Based on first principles calculations, we demonstrate a novel strategy to realize robust magnetism and exotic electronic properties in a 2D TI [bilayer Bi(111) film: abbreviated as Bi(111)]. We examine the magnetic and electronic properties of Bi(111) with defects such as bismuth monovacancies (MVs) and divacancies (DVs), and these defects decorated with 3d transition metals (TMs). It has been observed that the MV in Bi(111) can induce novel half metallicity with a net magnetic moment of 1 μB. The origin of half metallicity and magnetism in MV/Bi(111) is further explained by the passivation of the σ-dangling bonds near the defect site. Furthermore, in spite of the nonmagnetic nature of DVs, the TMs (V, Cr, Mn, and Fe) trapped at the 5/8/5 defect structure of DVs can not only yield a much higher spin moment than those trapped at the MVs but also display intriguing electronic properties such as metallic, semiconducting and spin gapless semiconducting properties. The predicted magnetic and electronic properties of TM/DV/Bi(111) systems are explained through density of states, spin density distribution and Bader charge analysis.

Effect of Amidogen Functionalization on Quantum Spin Hall Effect in Bi/Sb(111) Films

Knowledge about chemical functionalization is of fundamental importance to design novel two-dimensional topological insulators. Despite theoretical predictions of quantum spin Hall effect (QSH) insulator via chemical functionalization, it is quite challenging to obtain a high-quality sample, in which the toxicity is also an important factor that cannot be ignored. Herein, using first-principles calculations, we predict an intrinsic QSH effect in amidogen-functionalized Bi/Sb(111) films (SbNH₂ and BiNH₂), characterized by nontrivial Z₂ invariant and helical edge states. The bulk gaps derived from p_x,y orbitals reaches up to 0.39 and 0.83 eV for SbNH₂ and BiNH₂ films, respectively. The topological properties are robust against strain engineering, electric field, and rotation angle of amidogen, accompanied with sizable bulk gaps. Besides, the topological phases are preserved with different arrangements of amidogen. The H-terminated SiC(111) is verified as a good candidate substrate for supporting the films without destroying their QSH effect. These results have substantial implications for theoretical and experimental studies of functionalized Bi/Sb films, which also provide a promising platform for realizing practical application in dissipationless transport devices at room temperature.

Nanostructured topological state in bismuth nanotube arrays: inverting bonding-antibonding levels of molecular orbitals

We demonstrate a new class of nanostructured topological materials that exhibit a topological quantum phase arising from nanoscale structural motifs. Based on first-principles calculations, we show that an array of bismuth nanotubes (Bi-NTs), a superlattice of Bi-NTs with periodicity in the order of tube diameter, behaves as a nanostructured two-dimensional (2D) quantum spin Hall (QSH) insulator, as confirmed from the calculated band topology and 1D helical edge states. The underpinning mechanism of the QSH phase in the Bi-NT array is revealed to be inversion of bonding-antibonding levels of molecular orbitals of constituent nanostructural elements in place of atomic-orbital band inversion in conventional QSH insulators. The quantized edge conductance of the QSH phase in a Bi-NT array can be more easily isolated from bulk contributions and their properties can be highly tuned by tube size, representing distinctive advantages of nanostructured topological phases. Our finding opens a new avenue for topological materials by extending topological phases into nanomaterials with molecular-orbital-band inversion.

Atomically Abrupt Topological p-n Junction

Topological insulators (TI's) are a new class of quantum matter with extraordinary surface electronic states, which bear great potential for spintronics and error-tolerant quantum computing. In order to put a TI into any practical use, these materials need to be fabricated into devices whose basic units are often p-n junctions. Interesting electronic properties of a 'topological' p-n junction were proposed theoretically such as the junction electronic state and the spin rectification. However, the fabrication of a lateral topological p-n junction has been challenging because of materials, process, and fundamental reasons. Here, we demonstrate an innovative approach to realize a p-n junction of topological surface states (TSS's) of a three-dimensional (3D) topological insulator (TI) with an atomically abrupt interface. When a ultrathin Sb film is grown on a 3D TI of Bi₂Se₃ with a typical n-type TSS, the surface develops a strongly p-type TSS through the substantial hybridization between the 2D Sb film and the Bi₂Se₃ surface. Thus, the Bi₂Se₃ surface covered partially with Sb films bifurcates into areas of n- and p-type TSS's as separated by atomic step edges with a lateral electronic junction of as short as 2 nm. This approach opens a different avenue toward various electronic and spintronic devices based on well-defined topological p-n junctions with the scalability down to atomic dimensions.

Topological phases in double layers of bismuthene and antimonene

Two-dimensional topological insulators show great promise for spintronic applications. Much attention has been placed on single atomic or molecular layers, such as bismuthene. The selections of such materials are, however, limited. To broaden the base of candidate materials with desirable properties for applications, we report herein an exploration of the physics of double layers of bismuthene and antimonene. The electronic structure of a film depends on the number of layers, and it can be modified by epitaxial strain, by changing the effective spin-orbit coupling strength, and by the manner in which the layers are geometrically stacked. First-principles calculations for the double layers reveal a number of phases, including topological insulators, topological semimetals, Dirac semimetals, trivial semimetals, and trivial insulators. Their phase boundaries and the stability of the phases are investigated. The results illustrate a rich pattern of phases that can be realized by tuning lattice strain and effective spin-orbit coupling.

Observation of topological states residing at step edges of WTe2

Topological states emerge at the boundary of solids as a consequence of the nontrivial topology of the bulk. Recently, theory predicts a topological edge state on single layer transition metal dichalcogenides with 1T' structure. However, its existence still lacks experimental proof. Here, we report the direct observations of the topological states at the step edge of WTe2 by spectroscopic-imaging scanning tunneling microscopy. A one-dimensional electronic state residing at the step edge of WTe2 is observed, which exhibits remarkable robustness against edge imperfections. First principles calculations rigorously verify the edge state has a topological origin, and its topological nature is unaffected by the presence of the substrate. Our study supports the existence of topological edge states in 1T'-WTe2, which may envision in-depth study of its topological physics and device applications.Two-dimensional topological insulators support edge conduction electrons but its realization in real materials is rare. Here, Peng et al. report the direct observation of topological states at the step edge of WTe2.

Unconventional band inversion and intrinsic quantum spin Hall effect in functionalized group-V binary films

Adequately understanding band inversion mechanism, one of the significant representations of topological phase, has substantial implications for design and regulation of topological insulators (TIs). Here, by identifying an unconventional band inversion, we propose an intrinsic quantum spin Hall (QSH) effect in iodinated group-V binary (ABI₂) monolayers with a bulk gap as large as 0.409 eV, guaranteeing its viable application at room temperature. The nontrivial topological characters, which can be established by explicit demonstration of Z₂ invariant and gapless helical edge states, are derived from the band inversion of antibonding states of p _x,y orbitals at the K point. Furthermore, the topological properties are tunable under strain engineering and external electric field, which supplies a route to manipulate the spin/charge conductance of edge states. These findings not only provide a new platform to better understand the underlying origin of QSH effect in functionalized group-V films, but also are highly desirable to design large-gap QSH insulators for practical applications in spintronics.

Monolayer Bismuthene-Metal Contacts: A Theoretical Study

Bismuthene, a bismuth analogue of graphene, has a moderate band gap, has a high carrier mobility, has a topological nontriviality, has a high stability at room temperature, has an easy transferability, and is very attractive for electronics, optronics, and spintronics. The electrical contact plays a critical role in an actual device. The interfacial properties of monolayer (ML) bismuthene in contact with the metal electrodes spanning a wide work function range in a field-effect transistor configuration are systematically studied for the first time by using both first-principles electronic structure calculations and quantum transport simulations. The ML bismuthene always undergoes metallization upon contact with the six metal electrodes owing to a strong interaction. According to the quantum transport simulations, apparent metal-induced gap states (MIGSs) formed in the semiconductor-metal interface give rise to a strong Fermi-level pinning. As a result, the ML bismuthene forms an n-type Schottky contact with Ir/Ag/Ti electrodes with electron Schottky barrier heights (SBHs) of 0.17, 0.22, and 0.25 eV, respectively, and a p-type Schottky contact with Pt/Al/Au electrodes with hole SBHs of 0.09, 0.16, and 0.38 eV, respectively. The effective channel length of the ML bismuthene transistors is also significantly reduced by the MIGSs. However, the MIGSs are eliminated and the effective channel length is increased when ML graphene is used as an electrode, accompanied by a small hole SBH of 0.06 eV (quasi-Ohmic contact). Hence, an insight is provided into the interfacial properties of the ML bismuthene-metal composite systems and a guidance is provided for the choice of metal electrodes in ML bismuthene devices.

Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material

Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high-atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.

Tunability of the Quantum Spin Hall Effect in Bi(110) Films: Effects of Electric Field and Strain Engineering

The quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to their robust gapless edge states inside insulating bulk gap. However, the currently discussed QSH insulators usually suffer from ultrahigh vacuum or low temperature due to the small bulk gap, which limits their practical applications. Searching for large-gap QSH insulators is highly desirable. Here, the tunable QSH state of a Bi(110) films with a black phosphorus (BP) structure, which is robust against structural deformation and electric field, is explored by first-principles calculations. It is found that the two-monolayer BP-Bi(110) film obtains a tunable large bulk gap by strain engineering and its QSH effect shows a favorable robustness within a wide range of combinations of in-plane and out-of-plane strains, although a single in-plane compression or out-of-plane extension may restrict the topological phase due to the self-doping effect. More interestingly, in view of biaxial strain, two competing physics on band topology induced by bonding-antibonding and p_x,y-p_z band inversions are obtained. Meanwhile, the QSH effect can be persevered under an electric field of up to 0.9 V/Å. Moreover, with appropriate in-plane strain engineering, a nontrivial topological phase in a four-monolayer BP-Bi(110) film is identified. Our findings suggest that these two-dimensional BP-Bi(110) films are ideal platforms of the QSH effect for low-power dissipation devices.

Resolving the one-dimensional singularity edge states of Bi(1 1 1) thin films

We report our investigation on the electronic properties of the step edges on a Bi(1 1 1) surface in epitiaxially grown thin films, using scanning tunneling microscopy and spectroscopy. Our results show three differential conductance peaks including the previously reported peak in the spectra recorded at the step edges. Our analysis indicates that all of the three peaks can be ascribed to the van Hove singularities and thus to the band extrema of the one-dimensional edge bands, according to the quasiparticle interference and the Fourier transform patterns. These edge states show an overall penetration length of about 5 nm, but they also show different spatial distributions perpendicular to the edge. The well-determined band extrema may provide information for establishing a better model to describe the electronic topology of the step edge in the Bi(1 1 1) films.

Coexistence of Topological Edge State and Superconductivity in Bismuth Ultrathin Film

Ultrathin freestanding bismuth film is theoretically predicted to be one kind of two-dimensional topological insulators. Experimentally, the topological nature of bismuth strongly depends on the situations of the Bi films. Film thickness and interaction with the substrate often change the topological properties of Bi films. Using angle-resolved photoemission spectroscopy, scanning tunneling microscopy or spectroscopy and first-principle calculation, the properties of Bi(111) ultrathin film grown on the NbSe₂ superconducting substrate have been studied. We find the band structures of the ultrathin film is quasi-freestanding, and one-dimensional edge state exists on Bi(111) film as thin as three bilayers. Superconductivity is also detected on different layers of the film and the pairing potential exhibits an exponential decay with the layer thicknesses. Thus, the topological edge state can coexist with superconductivity, which makes the system a promising platform for exploring Majorana Fermions.

Bi1Te1 is a dual topological insulator

New three-dimensional (3D) topological phases can emerge in superlattices containing constituents of known two-dimensional topologies. Here we demonstrate that stoichiometric Bi₁Te₁, which is a natural superlattice of alternating two Bi₂Te₃ quintuple layers and one Bi bilayer, is a dual 3D topological insulator where a weak topological insulator phase and topological crystalline insulator phase appear simultaneously. By density functional theory, we find indices (0;001) and a non-zero mirror Chern number. We have synthesized Bi₁Te₁ by molecular beam epitaxy and found evidence for its topological crystalline and weak topological character by spin- and angle-resolved photoemission spectroscopy. The dual topology opens the possibility to gap the differently protected metallic surface states on different surfaces independently by breaking the respective symmetries, for example, by magnetic field on one surface and by strain on another surface.

Coexistence of a topological insulator phase and a topological crystalline insulator phase helps to maintain topological properties under a controlled symmetry breaking perturbation. Here, Eschback et al. report a superlattice of Bi and Bi₂Te₃ to be such a dual topological insulator.

Stability of topological properties of bismuth (1 1 1) bilayer

We investigate the electronic and transport properties of the bismuth (1 1 1) bilayer in the context of the stability of its topological properties against different perturbations. The effects of spin-orbit coupling variations, geometry relaxation and interaction with a substrate are considered. The transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within the multi-orbital tight-binding model and density functional theory methods. A band inversion process in the bismuth (1 1 1) infinite bilayer and an evolution of the edge state dispersion in ribbons as a function of spin-orbit coupling strength are analyzed. A significant change in the orbital composition of the conduction and valence bands is observed during a topological phase transition. The topological edge states are shown to be weakly affected by the effect of ribbon geometry relaxation. The interaction with a substrate is considered for narrow ribbons on top of another bismuth (1 1 1) bilayer. This corresponds to a weakly interacting case and the effect is similar to an external perpendicular electric field. Robust quantized conductance is observed when the Fermi energy lies within the energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, scattering is possible between the channels lying close in the k-space. When the energy of the edge states overlaps the valence states, no topological protection is observed.

Controlling the growth of Bi(110) and Bi(111) films on an insulating substrate

We demonstrate the controlled growth of Bi(110) and Bi(111) films on an α-Al₂O₃(0001) substrate by surface x-ray diffraction and x-ray reflectivity using synchrotron radiation. At temperatures as low as 40 K, unanticipated pseudo-cubic Bi(110) films are grown with thicknesses ranging from a few to tens of nanometers. The roughness at the film-vacuum as well as the film-substrate interface, can be reduced by mild heating, where a crystallographic orientation transition of Bi(110) towards Bi(111) is observed at 400 K. From 450 K onwards high quality ultrasmooth Bi(111) films form. Growth around the transition temperature results in the growth of competing Bi(110) and Bi(111) domains.

Angle-resolved photoemission spectroscopy for the study of two-dimensional materials

Quantum systems in confined geometries allow novel physical properties that cannot easily be attained in their bulk form. These properties are governed by the changes in the band structure and the lattice symmetry, and most pronounced in their single layer limit. Angle-resolved photoemission spectroscopy (ARPES) is a direct tool to investigate the underlying changes of band structure to provide essential information for understanding and controlling such properties. In this review, recent progresses in ARPES as a tool to study two-dimensional atomic crystals have been presented. ARPES results from few-layer and bulk crystals of material class often referred as “beyond graphene” are discussed along with the relevant developments in the instrumentation.

Decay length of surface-state wave functions on Bi(1 1 1)

We calculate the decay length in surface normal direction of the surface-state wave functions on a clean Bi(1 1 1) surface as a function of two-dimensional (2D) wave vector [Formula: see text] along the [Formula: see text] line. For this purpose, we perform a first-principles density functional theory (DFT) calculation for semi-infinite Bi(1 1 1) by employing the surface embedded Green's function technique. The decay length of the two surface bands is found to be  ∼24 Bi bilayers at [Formula: see text], while it remains less than 5 Bi bilayers when [Formula: see text] is away from [Formula: see text] and [Formula: see text]. At [Formula: see text], the degenerate surface bands are split from the upper boundary energy of the projected bulk valence bands only by 5 meV. In spite of this, the decay length of these bands at [Formula: see text] is less than 10 Bi bilayers due to the large effective mass (small curvature) of the highest valence band in the surface normal direction.

Simultaneous observation of surface- and edge-states of a 2D topological insulator through scanning tunneling spectroscopy and differential conductance imaging

Gapless edge-states with a Dirac point below the Fermi energy and band-edges at the interior observed in 2D topological insulators.

High repetition pump-and-probe photoemission spectroscopy based on a compact fiber laser system

The paper describes a time-resolved photoemission (TRPES) apparatus equipped with a Yb-doped fiber laser system delivering 1.2-eV pump and 5.9-eV probe pulses at the repetition rate of 95 MHz. Time and energy resolutions are 11.3 meV and ∼310 fs, respectively, the latter is estimated by performing TRPES on a highly oriented pyrolytic graphite (HOPG). The high repetition rate is suited for achieving high signal-to-noise ratio in TRPES spectra, thereby facilitating investigations of ultrafast electronic dynamics in the low pump fluence (p) region. TRPES of polycrystalline bismuth (Bi) at p as low as 30 nJ/mm² is demonstrated. The laser source is compact and is docked to an existing TRPES apparatus based on a 250-kHz Ti:sapphire laser system. The 95-MHz system is less prone to space-charge broadening effects compared to the 250-kHz system, which we explicitly show in a systematic probe-power dependency of the Fermi cutoff of polycrystalline gold. We also describe that the TRPES response of an oriented Bi(111)/HOPG sample is useful for fine-tuning the spatial overlap of the pump and probe beams even when p is as low as 30 nJ/mm².

Large-Gap Quantum Spin Hall State in MXenes: d-Band Topological Order in a Triangular Lattice

MXenes are a large family of two-dimensional (2D) early transition metal carbides that have shown great potential for a host of applications ranging from electrodes in supercapacitors and batteries to sensors to reinforcements in polymers. Here, on the basis of first-principles calculations, we predict that Mo₂MC₂O₂ (M = Ti, Zr, or Hf), belonging to a recently discovered new class of MXenes with double transition metal elements in an ordered structure, are robust quantum spin Hall (QSH) insulators. A tight-binding (TB) model based on the d_z²-, d_xy-, and d_x²-y²-orbital basis in a triangular lattice is also constructed to describe the QSH states in Mo₂MC₂O₂. It shows that the atomic spin-orbit coupling (SOC) strength of M totally contributes to the topological gap at the Γ point, a useful feature advantageous over the usual cases where the topological gap is much smaller than the atomic SOC strength based on the classic Kane-Mele (KM) or Bernevig-Hughes-Zhang (BHZ) model. Consequently, Mo₂MC₂O₂ show sizable gaps from 0.1 to 0.2 eV with different M atoms, sufficiently large for realizing room-temperature QSH effects. Another advantage of Mo₂MC₂O₂ MXenes lies in their oxygen-covered surfaces which make them antioxidative and stable upon exposure to air.

Annealing-Induced Bi Bilayer on Bi2Te3 Investigated via Quasi-Particle-Interference Mapping

Topological insulators (TIs) are renowned for their exotic topological surface states (TSSs) that reside in the top atomic layers, and hence, detailed knowledge of the surface top atomic layers is of utmost importance. Here we present the remarkable morphology changes of Bi2Te3 surfaces, which have been freshly cleaved in air, upon subsequent systematic annealing in ultrahigh vacuum and the resulting effects on the local and area-averaging electronic properties of the surface states, which are investigated by combining scanning tunneling microscopy (STM), scanning tunneling spectroscopy (STS), and Auger electron spectroscopy (AES) experiments with density functional theory (DFT) calculations. Our findings demonstrate that the annealing induces the formation of a Bi bilayer atop the Bi2Te3 surface. The adlayer results in n-type doping, and the atomic defects act as scattering centers of the TSS electrons. We also investigated the annealing-induced Bi bilayer surface on Bi2Te3 via voltage-dependent quasi-particle-interference (QPI) mapping of the surface local density of states and via comparison with the calculated constant-energy contours and QPI patterns. We observed closed hexagonal patterns in the Fourier transform of real-space QPI maps with secondary outer spikes. DFT calculations attribute these complex QPI patterns to the appearance of a "second" cone due to the surface charge transfer between the Bi bilayer and the Bi2Te3. Annealing in ultrahigh vacuum offers a facile route for tuning of the topological properties and may yield similar results for other topological materials.

Topological phase transition and quantum spin Hall edge states of antimony few layers

While two-dimensional (2D) topological insulators (TI’s) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi₂Te₂Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.

Quantum spin Hall phase in 2D trigonal lattice

The quantum spin Hall (QSH) phase is an exotic phenomena in condensed-matter physics. Here we show that a minimal basis of three orbitals (s, p_x, p_y) is required to produce a QSH phase via nearest-neighbour hopping in a two-dimensional trigonal lattice. Tight-binding model analyses and calculations show that the QSH phase arises from a spin–orbit coupling (SOC)-induced s–p band inversion or p–p bandgap opening at Brillouin zone centre (Γ point), whose topological phase diagram is mapped out in the parameter space of orbital energy and SOC. Remarkably, based on first-principles calculations, this exact model of QSH phase is shown to be realizable in an experimental system of Au/GaAs(111) surface with an SOC gap of ∼73 meV, facilitating the possible room-temperature measurement. Our results will extend the search for substrate supported QSH materials to new lattice and orbital types.

Whilst different models describing the two-dimensional quantum spin Hall effect exist, very few experimental systems have been realized in which to test theory. Here, the authors present a discrete trigonal lattice model for the quantum spin Hall effect and predict its realization in Au/GaAs(111).

Topological edge states in a high-temperature superconductor FeSe/SrTiO3(001) film

Superconducting and topological states are two most intriguing quantum phenomena in solid materials. The entanglement of these two states, the topological superconducting state, will give rise to even more exotic quantum phenomena. While many materials are found to be either a superconductor or a topological insulator, it is very rare that both states exist in one material. Here, we demonstrate by first-principles theory as well as scanning tunnelling spectroscopy and angle-resolved photoemission spectroscopy experiments that the recently discovered 'two-dimensional (2D) superconductor' of single-layer FeSe also exhibits 1D topological edge states within an energy gap of ∼40 meV at the M point below the Fermi level. It is the first 2D material that supports both superconducting and topological states, offering an exciting opportunity to study 2D topological superconductors through the proximity effect.

A new kind of 2D topological insulators BiCN with a giant gap and its substrate effects

Based on DFT calculation, we predict that BiCN, i.e., bilayer Bi films passivated with -CN group, is a novel 2D Bi-based material with highly thermodynamic stability, and demonstrate that it is also a new kind of 2D TI with a giant SOC gap (~1 eV) by direct calculation of the topological invariant Z₂ and obvious exhibition of the helical edge states. Monolayer h-BN and MoS₂ are identified as good candidate substrates for supporting the nontrivial topological insulating phase of the 2D TI films, since the two substrates can stabilize and weakly interact with BiCN via van der Waals interaction and thus hardly affect the electronic properties, especially the band topology. The topological properties are robust against the strain and electric field. This may provide a promising platform for realization of novel topological phases.

Topologically Protected Metallic States Induced by a One-Dimensional Extended Defect in the Bulk of a 2D Topological Insulator

We report ab initio calculations showing that a one-dimensional extended defect generates topologically protected metallic states immersed in the bulk of two-dimensional topological insulators. We find that a narrow extended defect, composed of periodic units consisting of one octagonal and two pentagonal rings (a 558 extended defect), embedded in the hexagonal bulk of a bismuth bilayer, introduces two pairs of one-dimensional counterpropagating helical-Fermion electronic bands with the opposite spin-momentum locking characteristic of the topological metallic states that appear at the edges in two-dimensional topological insulators. Each one of these pairs of helical-Fermion bands is localized, respectively, along each one of the zigzag chains of bismuth atoms at the core of the 558 extended defect, and their hybridization leads to the opening of very small gaps (6 meV or less) in the helical-Fermion dispersions of these defect-related modes. We discuss the connection between the defect-induced metallic modes and the helical-Fermion edge states that occur on bismuth bilayer ribbons.

Electronic structure evolution of single bilayer Bi(1 1 1) film on 3D topological insulator Bi2Se x Te3-x surfaces

The electronic state evolution of single bilayer (1BL) Bi(1 1 1) deposited on three-dimensional (3D) Bi2Se x Te3-x topological insulators at x  =  0, 1.26, 2, 2.46, 3 is systematically investigated by angle-resolved photoemission spectroscopy (ARPES). Our results indicate that the electronic structures of epitaxial Bi films are strongly influenced by the substrate especially the topmost sublayer near the Bi films, manifesting in two main aspects. First, the Se atoms cause a stronger charge transfer effect, which induces a giant Rashba-spin splitting, while the low electronegativity of Te atoms induces a strong hybridization at the interface. Second, the lattice strain notably modifies the band dispersion of the surface bands. Furthermore, our experimental results are elucidated by first-principles band structure calculations.

Topological phases in two-dimensional materials: a review

Topological phases with insulating bulk and gapless surface or edge modes have attracted intensive attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this review, we mainly focus on recent progress in the engineering of topologically nontrivial phases (such as [Formula: see text] topological insulators, quantum anomalous Hall effects, quantum valley Hall effects etc) in two-dimensional systems, including quantum wells, atomic crystal layers of elements from group III to group VII, and the transition metal compounds.