Tuning topological edge states of Bi(111) bilayer film by edge adsorption

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.

Topological Nodal-Point Superconductivity in Two-Dimensional Ferroelectric Hybrid Perovskites

Two-dimensional (2D) hybrid organic-inorganic perovskites (HOIPs) with enhanced stability, high tunability, and strong spin-orbit coupling have shown great potential in vast applications. Here, we extend the already rich functionality of 2D HOIPs to a new territory, realizing topological superconductivity and Majorana modes for fault-tolerant quantum computation. Especially, we predict that room-temperature ferroelectric BA2PbCl4 (BA for benzylammonium) exhibits topological nodal-point superconductivity (NSC) and gapless Majorana modes on selected edges and ferroelectric domain walls when proximity-coupled to an s-wave superconductor and an in-plane Zeeman field, attractive for experimental verification and application. Since NSC is protected by spatial symmetry of 2D HOIPs, we envision more exotic topological superconducting states to be found in this class of materials due to their diverse noncentrosymmetric space groups, which may open a new avenue in the fields of HOIPs and topological superconductivity.

Emergence of quasi-1D spin-polarized states in ultrathin Bi films on InAs(111)A for spintronics applications

The discovery, characterization, and control of heavy-fermion low-dimensional materials are central to nanoscience since quantum phenomena acquire an exotic and highly tunable character. In this work, through a variety of comprehensive experimental and theoretical techniques, it was observed and predicted that the synthesis of ultrathin Bi films on the InAs(111)A surface produces quasi-one-dimensional spin-polarized states, providing a platform for the realization of a unique spin-transport regime in the system. Scanning tunneling microscopy and low-energy electron diffraction measurements revealed that the InAs(111)A substrate facilitates the formation of the Bi-dimer phase of 2√3 × 3 periodicity with an admixture of the Bi-bilayer phase under submonolayer Bi deposition. X-ray photoelectron spectroscopy (XPS) measurements have shown the chemical stability of the Bi-induced phases, while spin and angle resolved photoemission spectroscopy (SARPES) observations combined with state-of-the-art DFT calculations have revealed that the electronic spectrum of the Bi-dimer phase holds a quasi-1D hole-like spin-split state at the Fermi level with advanced spin texture, whereas the Bi-bilayer phase demonstrates metallic states with large Rashba spin-splitting. The band structure of the Bi/InAs(111)A interface is discovered to hold great potential as a high-performance spintronics material fabricated in the ultimate two-dimensional limit.

Morphology of Bi(110) quantum islands on epitaxial graphene

Proximitized 2D materials present exciting prospects for exploring new quantum properties, enabled by precise control of structures and interfaces through epitaxial methods. In this study, we investigated the structure of ultrathin coverages formed by depositing high-Z element bismuth (Bi) on monolayer graphene (MLG)/SiC(0001). By utilizing electron diffraction and scanning tunneling microscopy, ultrathin Bi nanostructures epitaxially grown on MLG were studied. Deposition at 300 K resulted in formation of needle-like Bi(110)-terminated islands elongated in the zig-zag direction and aligned at an angle of approximately 1.75∘with respect to the MLG armchair direction. By both strain and quantum size effects, the shape, the orientation and the thickness of the Bi(110) islands can be rationalized. Additionally, a minority phase of Bi(110) islands orthogonally aligned to the former ones were seen. The four sub-domains of this minority structure are attributed to the formation of mirror twin boundaries, resulting in two potential alignments of Bi(110) majority and minority domains with respect to each other, in addition to two possible alignments of the majority domain with respect to graphene. Notably, an annealing step at 410 K or lowering the deposition temperature, significantly increases the concentration of the Bi(110) minority domain. Our findings shed light on the structural control of proximitized 2D materials, showcasing the potential for manipulating 2D interfaces.

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.

Electronic properties and interface contact of graphene/CrSiTe3 van der Waals heterostructures

Electronic properties and interface contact of Graphene-based heterostructure Graphene/CrSiTe3 (Gr/CrSiTe3) is modulated by tuning the interfacial distance, along with appling an external electric field. Our first-principles calculations show that the...

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.

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.

Magnetism and electronic structures of bismuth (stannum) films at the CrI3 (CrBr3) interface

From first-principles calculations, the magnetism and electronic structures of bilayer bismuth (stannum) films at the monolayer CrI3 (CrBr3) interface are studied. The Curie temperature (TC) of CrX3 (X = Br, I) can be enhanced by coupling bilayer bismuth (Bi) with van der Waals (vdW) heterostructures. The n-doping of CrX3, induced by interlayer charge-transfer from the Bi film, leads to the enhancement of TC. The quantum spin Hall phases of bilayer bismuth and stannum films are destroyed by the magnetic substrate. Although the interface system of the bilayer stannum (Sn) film on a CrBr3 monolayer shows a band gap (57 meV), the inexistence of edge states with valence and conduction bands connected across the insulating gap is a manifestation of the trivial state without the feature of quantized anomalous Hall effect in the interface. The percentage reduction of the corresponding work function is 22.6%, 12.7%, 25.4% and 16.5% for Bi/CrI3, Sn/CrI3, Bi/CrBr3 and Sn/CrBr3 interface systems, respectively. Our findings demonstrate that the Bi(Sn)-CrI3(CrBr3) interface system with vdW engineering is an efficient way to tune magnetism and electronic structures, which is of importance for future applications in spintronics and nanoelectronics devices.

Controlling the Quantum Spin Hall Edge States in Two-Dimensional Transition Metal Dichalcogenides

Two-dimensional transition metal dichalcogenides (TMDs) of Mo and W in their 1T' crystalline phase host the quantum spin Hall (QSH) insulator phase. We address the electronic properties of the QSH edge states by means of first-principles calculations performed on realistic models of edge terminations of different stoichiometries. The QSH edge states show a tendency to have complex band dispersions and coexist with topologically trivial edge states. We nevertheless identify two stable edge terminations that allow isolation of a pair of helical edge states within the band gap of TMDs, with monolayer 1T'-WSe₂ being the most promising material. We also characterize the finite-size effects in the electronic structure of 1T'-WSe₂ nanoribbons. Our results provide guidance to the experimental studies and possible practical applications of QSH edge states in monolayer 1T'-TMDs.

1D topological phases in transition-metal monochalcogenide nanowires

The Su-Schrieffer-Heeger (SSH) model is a prototypical one-dimensional (1D) diatomic lattice model for non-trivial topological phases and topological excitations. Theoretically, many variations and extensions of the SSH model have been proposed and explored to better understand the novel aspects of topological physics in low dimensions on the nanoscale. However, the outstanding challenge remains to find real nanomaterials with robust structural stability for realizing the 1D topological states. Here, we develop an extended version of the SSH model with multi-atomic bases of four, six and eight atoms and an imposed screw rotation symmetry. Furthermore, based on first-principles calculations, we demonstrate the realization of this model in transition metal monochalcogenide M6X6 (M = Mo and W; X = S, Se and Te) nanowires. The topological features of the doped M6X6 nanowires are confirmed with non-trivial edge modes and e/2 fractional charges, representative of the 1D non-trivial Zak phase. Our finding not only sheds new light on our fundamental understanding of 1D topological physics, but also significantly extends the scope of 1D topological materials that will attract immediate experimental interest, since isolated M6X6 nanowires have already been synthesized in experiments.

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.

Band Topology of Bismuth Quantum Films

Bismuth has been the key element in the discovery and development of topological insulator materials. Previous theoretical studies indicated that Bi is topologically trivial and it can transform into the topological phase by alloying with Sb. However, recent high-resolution angle-resolved photoemission spectroscopy (ARPES) measurements strongly suggested a topological band structure in pure Bi, conflicting with the theoretical results. To address this issue, we studied the band structure of Bi and Sb films by ARPES and first-principles calculations. The quantum confinement effectively enlarges the energy gap in the band structure of Bi films and enables a direct visualization of the Z 2 topological invariant of Bi. We find that Bi quantum films in topologically trivial and nontrivial phases respond differently to surface perturbations. This way, we establish experimental criteria for detecting the band topology of Bi by spectroscopic methods.

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.

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 edge states in high-temperature superconductiving FeSe/SrTiO3 films with Te substitution

Using first principles theory, we investigated the behavior of the one-dimensional (1D) topological edge states of high temperature superconductiviing FeSe/SrTiO3 films with Te atoms substitution to Se atoms in the bottom (top) layer in single-layer FeSe, as a function of strain. It was discovered that the 1D topological edge states are present in single-unit-cell FeSe film on SrTiO3, but are absent when more than 50% Se atoms are replaced by Te atoms. Stress induced displacive phase transformation exists in FeSe/SrTiO3 film when Te atoms substitute Se atoms in the bottom (top) layer in single-layer FeSe under 3% strain respectively. The 1D topological edge states are present under 3% (1.8%) strain in FeSe/SrTiO3 films with Te substitution Se in the bottom (top) layer in single-layer FeSe, even up to 5%, respectively. This indicates that the bonding angle of Se-Fe-Se (Te) and the distance of Te (or Se) atoms to the Fe plane are correlated with the topological edge states. Our findings provide an effective interface system that provides both superconducting and topological states, opening a new route for realizing 2D topological superconductors with proximity effect.

Strain-Tuned Topological Insulator and Rashba-Induced Anisotropic Momentum-Locked Dirac Cones in Two-Dimensional SeTe Monolayers

Rashba spin-orbit coupling (SOC) in topological insulators (TIs) is a very interesting phenomenon and has received extensive attention in two-dimensional (2D) materials. However, the coexistence of Rashba SOC and band topology, especially for materials with a square lattice, is still lacking. Here, by using first-principles calculations, we propose for the first time a SeTe monolayer as a 2D candidate with these novel properties. We find that the square lattice exhibits anisotropic band dispersions near the Fermi level and a Rashba effect related to large SOC and inversion asymmetry, which leads to a Dirac semimetal state. Another prominent feature is that SeTe can achieve a topological state under a tensile strain of only 1%, characterized by the Z₂ invariant and helical edge states. Our findings demonstrate that SeTe is a promising material for novel electronic and spintronics applications.

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.

Topological Insulator in Two-Dimensional SiGe Induced by Biaxial Tensile Strain

Strain-engineered two-dimensional (2D) SiGe is predicted to be a topological insulator (TI) based on first-principle calculations. The dynamical and thermal stabilities were ascertained through phonon spectra and ab initio molecular dynamics simulations. 2D SiGe remains dynamically stable under tensile strains of 4 and 6%. A band inversion was observed at the Γ-point with a band gap of 25 meV for 6% strain due to spin-orbit coupling interactions. Nontrivial of the TI phase was determined by its topological invariant (υ = 1). For SiGe nanoribbon with edge states, the valence band and conduction band cross at the Γ-point to create a topologically protected Dirac cone inside the bulk gap. We found that hexagonal boron nitride (h-BN) with high dielectric constant and band gap can be a very stable support to experimentally fabricate 2D SiGe as the h-BN layer does not alter its nontrivial topological character. Unlike other heavy-metal-based 2D systems, because SiGe has a sufficiently large gap, it can be utilized for spintronics and quantum spin Hall-based applications under ambient condition.

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.

Chemically driven surface effects in polar intermetallic topological insulators A3Bi

Surface electronic spectra, surface and bulk properties as well as the underlying chemical bonding characteristics in topological insulators with complex bonding patterns are considered for the example of cubic, polar intermetallics KNa₂Bi, K₃Bi and Rb₃Bi (with the general formula A₃Bi, A – alkali metal).

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.

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.

Strain Effect on Electronic Structure and Work Function in α-Fe₂O₃ Films

We investigate the electronic structure and work function modulation of α-Fe₂O₃ films by strain based on the density functional method. We find that the band gap of clean α-Fe₂O₃ films is a function of the strain and is influenced significantly by the element termination on the surface. The p_x and p_y orbitals keep close to Fermi level and account for a pronounced narrowing band gap under compressive strain, while unoccupied d_z₂ orbitals from conduction band minimum draw nearer to Fermi level and are responsible for the pronounced narrowing band gap under tensile strain. The spin polarized surface state, arising from localized dangling-bond states, is insensitive to strain, while the bulk band, especially for p_z orbital, arising from extended Bloch states, is very sensitive to strain, which plays an important role for work function decreasing (increasing) under compressive (tensile) strain in Fe termination films. In particular, the work function in O terminated films is insensitive to strain because p_z orbitals are less sensitive to strain than that of Fe termination films. Our findings confirm that the strain is an effective means to manipulate electronic structures and corrosion potential.

Unveiling orbital coupling at the CoPc/Bi(111) surface by ab initio calculations and photoemission spectroscopy

Orbital coupling is revealed at the CoPc/Bi(111) interface with the local magnetic moment retained in CoPc.

Giant spin-orbit coupling topological insulator h-Ga2Bi2 with exotic O-bridge states

The two-dimensional (2D) topological insulator (TI) is a promising material for designing dissipationless spintronic devices. Although many candidates have been found, few of them have a massive spin-orbit coupling (SOC) strength with high stability. In the present work, we demonstrate that h-Ga₂Bi₂ is a highly stable 2D TI with a massive E_g(Γ) at the Γ point of 1.477 eV, while the global band gap is 0.20 eV, which is sufficiently large for room temperature (∼26 meV). The edge states are greatly affected by the geometrical configuration of ribbon edges. The linear dispersive edge states still hold when the nanoribbon is limited to 1.7 nm, which actually realizes the ideal nanowire as theoretically derived in the field of TI. Most excitingly, an exotic 'O-atom bridge' is proposed here, and resides in the inner part of the nanoribbon, and so is thus highly protected from damage. The corresponding 'O-bridge states' display the interaction of electrons in a clear pattern, which leads to a better understanding of the 2D TI.

Quantum phase transitions in Sn bilayer based interfacial systems by an external strain

Using first-principle calculations, we report for the first time, the changes in electronic structures of a single bilayer Sn stacked on a single bilayer Sb(Bi) and on a single quintuple layer Sb2Te3 induced by both interface polarization and strain. With BL Bi and QL Sb2Te3 substrates, the stanene tends to have a low-buckled configuration, whereas with BL Sb substrate, the stanene prefers to form high-buckled configurations. For strained Sn/Sb(Bi) system, we find that the Dirac cone state is not present in the band gap, whereas in strained Sn/Sb2Te3 system, spin-polarized Dirac cone can be introduced into the band gap. We discuss why tensile strain can result in the Dirac cone emerging at the K point based on a tight-binding lattice model. This theoretical study implies the feasibility of realizing quantum phase transitions for Sn thin films on suitable substrates. Our findings provide an effective manner in manipulating electronic structures and topological states in interfacial systems by using interface polarization and strain, which opens a new route for realizing atomically thin spintronic devices.

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.

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.

Spin rectification by orbital polarization in Bi-bilayer nanoribbons

We investigate the edge states of quantum spin-Hall phase Bi(111) bilayer nano-ribbons (BNRs) and their spin-rectifying effect using first-principles calculations and a non-equilibrium transport method. As low-dimensional materials, BNRs have tunable electronic properties, which are not only dependent on the edge shape, chemical passivation, or external electric fields but also governed by geometrical deformation. Depending on the passivation types, the interaction of the helical edge states in BNRs exhibits various patterns, enabling the valley engineering of the Dirac cones. In addition, the spin texture of the Dirac state is significantly tuned by edge passivation, external electric fields and geometric deformations. We demonstrate that curved BNRs can be used as the spin valves to rectify the electric currents via the edge states. Our results provide a practical way of utilizing two-dimensional topological insulator Bi bilayers for spintronic devices.

The effect of substrate and external strain on electronic structures of stanene film

From first-principles calculations, the effects of h-BN and AlN substrates on the topological nontrivial properties of stanene are studied with different strains. We find that the quantum spin Hall phase can be induced in stanene film on a h-BN substrate under a tensile strain of between 6.0% and 9.3% with a stable state confirmed by the phonon spectrum, while for stanene on 5 × 5 h-BN, the quantum spin Hall phase can be preserved without strain. However, for stanene on a AlN substrate, the quantum spin Hall phase cannot be found under compressive or tensile strains less than 10%, while for 2 × 2 stanene on 3 × 3 AlN, the compressive strain needed to induce the quantum spin Hall phase is just 2%. These theoretical results will be helpful in understanding the effect of substrate and strain on stanene and in further realizing the quantum spin Hall effect in stanene on semiconductor substrates.

In situ video-STM studies of the mechanisms and dynamics of electrochemical bismuth nanostructure formation on Au

The microscopic mechanisms of Bi electrodeposition on Au(111) and Au(100) electrodes in the overpotential regime were studied by in situ scanning tunneling microscopy with high spatial and temporal resolution. Atomic resolution images of the needle-like Bi(110) deposits formed on Au(111) reveal the central influence of covalent Bi–Bi bonds on the deposit morphology. In the straight steps along the needle edges the Bi atoms are interlinked by these bonds, whereas at the needle tip and at kinks along the needle edges dangling bonds exist, explaining the rapid structural fluctuations at these sites. For ultrathin Bi deposits on Au(100) a more open atomic arrangement was found within the surface plane, which was tentatively assigned to an epitaxially stabilised Bi(111) film. Furthermore, well-defined nanowires, consisting of zigzag chains of Bi surface atoms, were observed on this surface.

Quantum spin Hall state in cyanided dumbbell stanene

Searching for two-dimensional (2D) quantum spin Hall (QSH) insulators with a large band gap, in which the Quantum spin Hall effect (QSHE) can be observed at high temperature, is an important goal for condensed matter physics researchers.

Stanene cyanide: a novel candidate of Quantum Spin Hall insulator at high temperature

The search for quantum spin Hall (QSH) insulators with high stability, large and tunable gap and topological robustness, is critical for their realistic application at high temperature. Using first-principle calculations, we predict the cyanogen saturated stanene SnCN as novel topological insulators material, with a bulk gap as large as 203 meV, which can be engineered by applying biaxial strain and electric field. The band topology is identified by Z₂ topological invariant together with helical edge states, and the mechanism is s-p_xy band inversion at G point induced by spin-orbit coupling (SOC). Remarkably, these systems have robust topology against chemical impurities, based on the calculations on halogen and cyano group co-decorated stanene SnXxX′1−x (X,X′  =  F, Cl, Br, I and CN), which makes it an appropriate and flexible candidate material for spintronic devices.

Quantum phase transitions in interfacing two gapped systems of ordinary fermions driven by external strain and atomic adsorption

We study how the electronic structure of a single bilayer Bi on a single quintuple layer Bi2Se3 (Bi2Te3) changes with interface polarization, strain and H adsorption using first-principles calculations. We find that for strained systems the Dirac cone state does not show in the band gap. Coupled with strain and H adsorption, the six spin-polarized Dirac cones in the band gap are created by the interfacing two gapped films. The internal electrical field can result in variations in the work function relative to Bi and Bi2Se3 surfaces. Our findings confirm that the interface polarization, strain and atomic adsorption are the effective means to manipulate electronic structures and topological states on non-metallic surfaces, which could be helpful for realizing atomically thin spintronic devices.

Two-Dimensional Pnictogen Honeycomb Lattice: Structure, On-Site Spin-Orbit Coupling and Spin Polarization

Because of its novel physical properties, two-dimensional materials have attracted great attention. From first-principle calculations and vibration frequencies analysis, we predict a new family of two-dimensional materials based on the idea of octet stability: honeycomb lattices of pnictogens (N, P, As, Sb, Bi). The buckled structures of materials come from the sp(3) hybridization. These materials have indirect band gap ranging from 0.43 eV to 3.7 eV. From the analysis of projected density of states, we argue that the s and p orbitals together are sufficient to describe the electronic structure under tight-binding model, and the tight-binding parameters are obtained by fitting the band structures to first-principle results. Surprisingly large on-site spin-orbit coupling is found for all the pnictogen lattices except nitrogen. Investigation on the electronic structures of both zigzag and armchair nanoribbons reveals the possible existence of spin-polarized ferromagnetic edge states in some cases, which are rare in one-dimensional systems. These edge states and magnetism may exist under the condition of high vacuum and low temperature. This new family of materials would have promising applications in electronics, optics, sensors, and solar cells.

Quantum anomalous Hall and quantum spin-Hall phases in flattened Bi and Sb bilayers

Discovery of two-dimensional topological insulator such as Bi bilayer initiates challenges in exploring exotic quantum states in low dimensions. We demonstrate a promising way to realize the Kane-Mele-type quantum spin Hall (QSH) phase and the quantum anomalous Hall (QAH) phase in chemically-modified Bi and Sb bilayers using first-principles calculations. We show that single Bi and Sb bilayers exhibit topological phase transitions from the band-inverted QSH phase or the normal insulator phase to Kane-Mele-type QSH phase upon chemical functionalization. We also predict that the QAH effect can be induced in Bi or Sb bilayers upon nitrogen deposition as checked from calculated Berry curvature and the Chern number. We explicitly demonstrate the spin-chiral edge states to appear in nitrogenated Bi-bilayer nanoribbons.

Giant topological nontrivial band gaps in chloridized gallium bismuthide

Quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices but presently is achieved only at extremely low temperature. Searching for the large-gap QSH insulators with strong spin-orbit coupling (SOC) is the key to increase the operating temperature. We demonstrate theoretically that this can be solved in the chloridized gallium bismuthide (GaBiCl2) monolayer, which has nontrivial gaps of 0.95 eV at the Γ point, and 0.65 eV for bulk, as well as gapless edge states in the nanoribbon structures. The nontrivial gaps due to the band inversion and SOC are robust against external strain. The realization of the GaBiCl2 monolayer will be beneficial for achieving QSH effect and related applications at high temperatures.

Dumbbell stanane: a large-gap quantum spin hall insulator

Hydrogenating DB stanene improves its stability and spin–orbit coupling effect, leading to a stable large-gap quantum spin Hall insulator.

Topological states modulation of Bi and Sb thin films by atomic adsorption

Based on first-principles calculations, we systematically investigated the topological surface states of Bi and Sb thin films of 1–5 bilayers in (111) orientation without and with H(F) adsorption, respectively.