Robust two-dimensional topological insulators in methyl-functionalized bismuth, antimony, and lead bilayer films

Large-Gap Quantum Spin Hall Insulators in Two-Dimensional Hafnium Halides: Unraveling the Impact of Strain and Substrate

Two-dimensional (2D) topological insulators (TIs) or quantum spin Hall (QSH) insulators, characterized by insulating 2D electronic band structures and metallic helical edge states protected by time-reversal symmetry, offer a platform for realizing the quantum spin Hall effect, making them promising candidates for future spintronic devices and quantum computing. However, observing a high-temperature quantum spin Hall effect requires large-gap 2D TIs, and only a few 2D systems have been experimentally confirmed to possess this property. In this study, we employ first-principles calculations, combined with a structural search based on an evolutionary algorithm, to predict a class of 2D QSH insulators in hafnium halides, namely, HfF, HfCl, and HfBr with sizable band gaps of 0.12, 0.19, and 0.38 eV. Their topological nontrivial nature is confirmed by a Z2 invariant which equals to 1 and the presence of gapless edge states. Furthermore, the QSH effect in these materials remains robust under biaxial tensile strain of up to 10%, and the use of h-BN as a substrate effectively preserves the QSH states in these materials. Our findings pave the way for future theoretical and experimental investigations of 2D hafnium halides and their potential for realizing the QSH effect.

2D Helium Atom Diffraction from a Microscopic Spot

A method for measuring helium atom diffraction with micron-scale spatial resolution is demonstrated in a scanning helium microscope (SHeM) and applied to study a micron-scale spot on the (100) plane of a lithium fluoride (LiF) crystal. The positions of the observed diffraction peaks provide an accurate measurement of the local lattice spacing, while a combination of close-coupled scattering calculations and Monte Carlo ray-tracing simulations reproduce the main variations in diffracted intensity. Subsequently, the diffraction results are used to enhance image contrast by measuring at different points in reciprocal space. The results open up the possibility for using helium microdiffraction to characterize the morphology of delicate or electron-sensitive materials on small scales. These include many fundamentally and technologically important samples which cannot be studied in conventional atom scattering instruments, such as small grain size exfoliated 2D materials, polycrystalline samples, and other surfaces that do not exhibit long-range order.

Exploring strong and weak topological states on isostructural substitutions in TlBiSe[Formula: see text]

Topological Insulators (TIs) are unique materials where insulating bulk hosts linearly dispersing surface states protected by the Time-Reversal Symmetry. These states lead to dissipationless current flow, which makes this class of materials highly promising for spintronic applications. Here, we predict TIs by employing state-of-the-art first-principles based methodologies, viz., density functional theory and many-body perturbation theory (G[Formula: see text]W[Formula: see text]) combined with spin-orbit coupling effects. For this, we take a well-known 3D TI, TlBiSe[Formula: see text] and perform complete substitution with suitable materials at different sites to check if the obtained isostructural materials exhibit topological properties. Subsequently, we scan these materials based on SOC-induced parity inversion at Time-Reversal Invariant Momenta. Later, to confirm the topological nature of selected materials, we plot their surface states along with calculation of Z[Formula: see text] invariants. Our results show that GaBiSe[Formula: see text] is a strong Topological Insulator, besides, we report six weak Topological Insulators, viz., PbBiSe[Formula: see text], SnBiSe[Formula: see text], SbBiSe[Formula: see text], Bi[Formula: see text]Se[Formula: see text], TlSnSe[Formula: see text] and PbSbSe[Formula: see text]. We have further verified that all the reported TIs are dynamically stable, showing all real phonon modes of vibration.

Strain-induced two-dimensional topological insulators in monolayer 1T'-RuO2

Because of their unique structure and novel physical properties, two-dimensional (2D) transition metal dichalcogenides (TMDs) have received a lot of attention in recent years. In this paper, we propose a new 2D TMD 1T'-RuO₂with tunable topological properties. Based on first-principles calculations, we demonstrate that it has good dynamics, thermodynamic, energetic stability, and anisotropic mechanical properties. Although 1T'-RuO₂is a typical semiconductor with a direct bandgap, it can be transformed into topological insulator by applying uniaxial tensile strains. The topological phase transition is attributed to thed-dband inversion at Γ point. The nontrivial topological property is further validated by the topological edge states. We predict that monolayer 1T'-RuO₂is an excellent material for future electronic devices with tunable topological properties.

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

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

DFTB Parameters for the Periodic Table: Part III, Spin-Orbit Coupling

Spin-orbit coupling (SOC) is crucially important for the correct description of the electronic structure and transport properties of inorganic semiconductors, and for assessing topological properties as in topological insulators. We present a consistent set of SOC parameters for the density-functional based tight-binding (DFTB) method covering the elements throughout the periodic table. The parameters are based on atomic SOC data calculated at the level of density-functional theory (DFT). We tested these parameters for representative systems with significant SOC, including transition metal dichalcogenide two-dimensional crystals, III-V bulk semiconductors, and topological insulators. Our parameterization opens the door for DFTB-based electronic structure and transport calculations of very large systems, such as twisted van der Waals heterostructures.

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

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

Nanomaterials for Quantum Information Science and Engineering

Quantum information science and engineering (QISE)-which entails the use of quantum mechanical states for information processing, communications, and sensing-and the area of nanoscience and nanotechnology have dominated condensed matter physics and materials science research in the 21st century. Solid-state devices for QISE have, to this point, predominantly been designed with bulk materials as their constituents. This review considers how nanomaterials (i.e., materials with intrinsic quantum confinement) may offer inherent advantages over conventional materials for QISE. The materials challenges for specific types of qubits, along with how emerging nanomaterials may overcome these challenges, are identified. Challenges for and progress toward nanomaterials-based quantum devices are condidered. The overall aim of the review is to help close the gap between the nanotechnology and quantum information communities and inspire research that will lead to next-generation quantum devices for scalable and practical quantum applications.

Phononic linear and quadratic nodal points in monolayer XH (XSi, Ge, Sn)

Topological phases in two-dimensional (2D) systems have been attracting tremendous attention since the discovery of graphene. Since the experimental probing could proceed in the whole phonon spectrum, intensive research effort has been devoted to the topological quantum phases in phononic systems. Via first-principles calculations, we predict that a family of 2D hexagonal materials, XH (X = Si, Ge, Sn), hosts ideal linear nodal points (LNPs) and quadratic phononic nodal points (QNPs). Specifically, the LNPs appear at the two inequivalent valleys, akin to the 2D Dirac point in graphene, connecting by an edge arc. The QNP is pinned at the Γ point, two edge states emerge from their projections. Remarkably, both LNPs and QNP enjoy an emergent chiral symmetry, we then show that they feature nontrivial topological charges. As a consequence, our work discusses the nodal points in the phonon spectrum of 2D materials and provides ideal candidates to study the topology for bosonic systems.

Robust Dirac spin gapless semiconductors in a two-dimensional oxalate based organic honeycomb-kagome lattice

Two-dimensional (2D) ferromagnetic materials with intrinsic and robust spin-polarized Dirac cones are of great interest in exploring exciting physics and in realizing spintronic devices. Using comprehensive ab initio calculations, herein we reveal a family of 2D oxalate-based metal-organic frameworks (MOFs) that possess the desired characteristics. We propose that these 2D oxalate-based MOFs may be assembled by oxalate ions (C₂O₄^2-) and two homo-transition metal atoms. We demonstrate that 2D MOFs of Ni₂(C₂O₄)₃ and Re₂(C₂O₄)₃ are intrinsic Dirac spin gapless semiconductors with linear band dispersion, low energy dissipation and high electron carrier velocity. As robust ferromagnets, they also possess large magnetic moments, large perpendicular magnetic anisotropy, and high Curie temperatures, e.g. 208 K for Ni₂(C₂O₄)₃. In particular, spin-orbit coupling triggers a topologically nontrivial band gap of 143 meV in Re₂(C₂O₄)₃, which is promising to realize the quantum anomalous Hall effect at high temperatures.

Large Gap Two-Dimensional Topological Insulators with the Significant Rashba Effect in Ethynyl and Methyl Functionalized PbSn Monolayers

Two-dimensional (2D) topological insulators (TIs) have recently attracted a great deal of attention due to their nondissipation electron transmission, stable performance, and easy device integration. However, a primary obstacle to influencing 2D TIs is the small bandgap, which limits their room-temperature applications. Here, we adopted first-principles to predict inversion-asymmetric group IV monolayers, PbSn(C₂H)₂ and PbSn(CH₃)₂, to be quantum spin Hall (QSH) insulators with large topological gaps of 0.586 and 0.481 eV, respectively. The nontrivial band topologies, which can survive in a wide range of strain, are characterized by topological invariants Z₂, gapless edge states, and the Berry curvature. Another intriguing characteristic is the significant Rashba SOC effect which can also be tuned by feasible compressive and tensile strains. Meanwhile, the hexagonal boron nitride (h-BN) provides a suitable substrate for growth of these films without influencing their topological phases. These novel materials are expected to accelerate the development of advanced quantum devices.

Terahertz emission from ultrathin bismuth layers

Thinner than 10 nm layers of bismuth (Bi) were grown on (111) Si substrates by molecular beam epitaxy. Terahertz (THz) radiation pulses from these layers excited by tunable wavelength femtosecond optical pulses were measured. THz emission sets on when the photon energy exceeds 0.45 eV, which was explained by the semimetal-to-semiconductor transition at this Bi layer thickness. A THz signal has both isotropic and anisotropic components that could be caused by the lack of balance of lateral photocurrent components and the shift currents, respectively.

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

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

Families of asymmetrically functionalized germanene films as promising quantum spin Hall insulators

Topological insulators (TIs), exhibiting the quantum spin Hall (QSH) effect, are promising for developing dissipationless transport devices that can be realized under a wide range of temperatures. The search for new two-dimensional (2D) TIs is essential for TIs to be utilized at room-temperature, with applications in optoelectronics, spintronics, and magnetic sensors. In this work, we used first-principles calculations to investigate the geometric, electronic, and topological properties of GeX and GeMX (M = C, N, P, As; X = H, F, Cl, Br, I, O, S, Se, Te). In 26 of these materials, the QSH effect is demonstrated by a spin-orbit coupling (SOC) induced large band gap and a band inversion at the Γ point, similar to the case of an HgTe quantum well. In addition, engineering the intra-layer strain of certain GeMX species can transform them from a regular insulator into a 2D TI. This work demonstrates that asymmetrical chemical functionalization is a promising method to induce the QSH effect in 2D hexagonal materials, paving the way for practical application of TIs in electronics.

Strain tuning of closed topological nodal lines and opposite pockets in quasi-two-dimensional α-phase FeSi2

Following topological nodal point semimetals, topological nodal line semimetals with one dimensional (1D) topological elements have recently aroused great interest worldwide in the fields of quantum chemistry and condensed matter physics. In this study, by means of first-principles, we predict that quasi-two-dimensional (2D) α-FeSi2 with a P4/mmm space group is a topological nodal line semimetal with two nodal lines close to the Fermi level, in the kz = 0 and kz = π planes. Usually, topological nodal line semimetals can be classified into type I, type II, and hybrid-type categories, each type with different physical properties. Importantly, for the first time, we find that type I, type II, and hybrid-type nodal lines can be realized in a realistic material, i.e., quasi-2D α-FeSi2, by strain switching. The realization of tunable nodal line types occurs because quasi-2D α-FeSi2 has special opposite-pocket-behaving bands around the Fermi level. The results presented herein reflect that α-FeSi2 is a valuable candidate for spintronics application by utilization of type I, type II, and hybrid-type topological nodal line semimetals in a single material tuned by mechanical strain.

High thermoelectric efficiency of LaX (X = Sb, Bi) two dimensional topological insulators

Topological insulators with novel surfaces or edge states are the topological nature sequel of bulk electronic wave functions of these materials. The observed signatures in the electronic structure of topological insulators can make them excellent candidates for thermoelectric materials. Low dimensional materials such as phosphorene and Bi₂Te₃ nanowire have been confirmed to be desirable for the design of devices with high thermoelectric performance. So in this work, the phonon modes, formation energy and cohesive energy of LaX (X  =  Sb, Bi) monolayers are first calculated and investigated. Then the band order of these monolayers is investigated by the band structure calculations and the topological phase of these monolayers is proved by using the calculation of Z ₂ topological invariant. The energy band gap and the band inversion strength of these monolayers are evaluated under in-plane strains. Also, the effect of different temperatures and in-plane strains on the thermoelectric performance of LaX monolayers is studied. The results show the high thermoelectric efficiency and d-p topological band inversion of these monolayers under compressive strains.

Emergence of a spin-valley Dirac semimetal in a strained group-VA monolayer

The combination of Dirac and Valley physics in one single-layer system is a very interesting topic and has received widespread attention in materials science and condensed matter physics. Using density-functional theoretical calculations, we predict that a two-dimensional (2D) cyanided group-VA monolayer, MAs(CN)₂ (M = Sb, Bi), can turn into the spin-valley Dirac point (svDP) state under external strains. In sharp contrast to the symmetry protected 2D Dirac semimetal (DSM), the Dirac Fermions in svDP materials are spin non-degenerate due to strong spin-splitting under SOC. Remarkably, the Dirac fermions in inequivalent valleys can host opposite Berry curvature and spin moment, leading to the Dirac spin-valley Hall effect with dissipationless transport. We also find that the svDP of MAs(CN)₂ is a critical state of topological phase transition between the trivial and nontrivial states. An effective tight-binding model is used to unveil the physics of svDP and topological phase transition under strain. These results will provide a route towards the integration of spin-valley indexes in 2D Dirac materials and design multipurpose and controllable devices in valleytronics.

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.

All-optical signal processing in few-layer bismuthene coated microfiber: towards applications in optical fiber systems

Two-dimensional (2D) bismuthene can find its wide potential applications due to its appealing optical and electronic properties. Especially, bismuthene exhibits layer-count dependent direct bandgaps and strong light-matter interaction, enabling its applications in all-optical signal processing area that can overcome the bottle-neck in existing electrical signal processing. However, light-bismuthene interaction based on main stream optical fiber systems and its application in all-optical signal processing is relatively less investigated. In this work, few-layer bismuthene, synthesized with facile solution processing method, is coated onto a piece of microfiber. The experimental results show that this device can operate as an optical Kerr switcher and a four-wave-mixing-based wavelength converter under different configuration. The results including wavelength applicability, information bandwidth, eye diagrams in combination with bit-error rate (BER) performance and stability measurements confirm its feasibility in optical fiber systems. To the best of our knowledge, it is first prototypic device reported in this work for bismuthene in all-optical signal processing optical fiber systems.

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.

Oxygen-functionalized TlTe buckled honeycomb from first-principles study

A sizable band gap is crucial for the applications of topological insulators at room temperature. By first-principles calculations, we found that oxygen-functionalized TlTe buckled honeycomb, namely TlTeO, possessed quantum spin Hall (QSH) state with a sizable band gap of 0.17 eV, which owns potential applications at the room temperature. The QSH phase of TlTeO arose from the SOC-induced p-p band gap opening. In addition, the QSH phase was further confirmed by the topological invariant Z2 and gapless edge state in the bulk gap. Significantly, the QSH phase is robustly against the external strain and possesses more than 75% oxygen coverage, making the QSH effect of TlTeO easy to be achieved experimentally. Thus, the oxygen-functionalized TlTeO film is a fine candidate material for the topological device design and fabrication.

Quantum fluctuation in thermopower at the topological phase transition in CaSrX (X: Si, Ge, Sn, Pb) studied from first principles theory

The present density functional calculations propose the compounds CaSrX (X: Si, Ge, Sn, Pb) as strong topological insulators, with appreciable thermoelectric properties. Emergence of Dirac semi-metallic states has been observed in CaSrX (X: Si, Ge, Sn, Pb), which is induced by uni-axial strain along 'b' axis. CaSrSi and CaSrGe evolved as normal semiconductors with uni-axial strain. The trivial and non-trivial topological phases are evaluated by band inversion and Z ₂ topological invariants. A comprehensive analysis of thermopower, electrical conductivity scaled by relaxation time at these Dirac semi-metallic states exposes the highly oscillating behaviour, which gives insight to quantum oscillations driven by uni-axial strain. Further the thermoelectric properties at strong topological insulating states and normal insulating states have been summarized, which reveals the potential thermoelectric properties of these materials.

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.

Non-Dirac Chern insulators with large band gaps and spin-polarized edge states

Based on first-principles calculations and k·p models, we demonstrate that PbC/MnSe heterostructures are a non-Dirac type of Chern insulator with very large band gaps (244 meV) and exotically half-metallic edge states, providing the possibilities of realizing very robust, completely spin polarized, and dissipationless spintronic devices from the heterostructures. The achieved extraordinarily large nontrivial band gap can be ascribed to the contribution of the non-Dirac type electrons (composed of px and py) and the very strong atomic spin-orbit coupling (SOC) interaction of the heavy Pb element in the system. Surprisingly, the band structures are found to be sensitive to the different exchange and correlation functionals adopted in the first-principles calculations. Chern insulators with various mechanisms are acquired from them. These discoveries show that the predicted nontrivial topology in PbC/MnSe heterostructures is robust and can be observed in experiments at high temperatures. The system has great potential to have attractive applications in future spintronics.

Bismuth oxide film: a promising room-temperature quantum spin Hall insulator

Two-dimensional (2D) bismuth films have attracted extensive attention due to their nontrivial band topology and tunable electronic properties for achieving dissipationless transport devices. The experimental observation of quantum transport properties, however, are rather challenging, limiting their potential application in nanodevices. Here, we predict, based on first-principles calculations, an alternative 2D bismuth oxide, BiO, as an excellent topological insulator (TI), whose intrinsic bulk gap reaches up to 0.28 eV. Its nontrivial topology is confirmed by topological invariant Z ₂ and time-reversal symmetry protected helical edge states. The appearance of topological phase is robust against mechanical strain and different levels of oxygen coverage in BiO. Since the BiO is naturally stable against surface oxidization and degradation, these results enrich the topological materials and present an alternative way to design topotronics devices at room temperature.

Structural and electronic properties of hydrogenated GaBi and InBi honeycomb monolayers with point defects

First-principles calculations are carried out to systematically investigate the structural and electronic properties of point defects in hydrogenated GaBi and InBi monolayers, including vacancies, antisites and Stone-Wales (SW) defects. Our results imply that the perfect H2-Ga(In)Bi is a semiconductor with a bandgap of 0.241 eV (0.265 eV) at the Γ point. The system turns into a metal by introducing a Ga(In) vacancy, substituting a Bi with a Ga(In) atom or substituting an In with a Bi atom. Other defect configurations can tune the bandgap value in the range from 0.09 eV to 0.3 eV. In particular, the exchange of neighboring Ga(In) and Bi increases the bandgap, meanwhile the spin splitting effect is preserved. All SW defects decrease the bandgap. The lowest formation energy of defects occurs when substituting a Ga(In) with a Bi atom and the values of SW defects vary from 0.98 eV to 1.77 eV.

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.

First-principles prediction of a giant-gap quantum spin Hall insulator in Pb thin film

The quantum spin Hall (QSH) effect is promising for achieving dissipationless transport devices due to the robust gapless states inside the insulating bulk gap. However, QSH insulators currently suffer from requiring extremely high vacuums or low temperatures. Here, using first-principles calculations, we predict cyanogen-decorated plumbene (PbCN) to be a new QSH phase, with a large gap of 0.92 eV, that is robust and tunable under external strain. The band topology mainly stems from s-p_xy band inversion related to the lattice symmetry, while the strong spin-orbit coupling (SOC) of the Pb atoms only opens a large gap. When halogen atoms are incorporated into PbCN, the resulting inversion-asymmetric PbF_x(CN)_1-x can host the QSH effect, accompanied by the presence of a sizable Rashba spin splitting at the top of the valence band. Furthermore, the Te(111)-terminated BaTe surface is proposed to be an ideal substrate for experimental realization of these monolayers, without destroying their nontrivial topology. These findings provide an ideal platform to enrich topological quantum phenomena and expand the potential applications in high-temperature spintronics.

Recent progress in 2D group-VA semiconductors: from theory to experiment

This review provides recent theoretical and experimental progress in the fundamental properties, electronic modulations, fabrications and applications of 2D group-VA materials.

Two-dimensional topological insulators of Pb/Sb honeycombs on a Ge(111) semiconductor surface

Based on first-principles hybrid functional calculations, we demonstrate the formation of two-dimensional (2D) topological insulators (TIs) of Pb/Sb honeycombs on Ge(111) semiconductor surface.

Strain induced band inversion and topological phase transition in methyl-decorated stanene film

The researches for new quantum spin Hall (QSH) insulators with large bulk energy gap are of much significance for their practical applications at room temperature in electronic devices with low-energy consumption. By means of first-principles calculations, we proposed that methyl-decorated stanene (SnCH₃) film can be tuned into QSH insulator under critical tensile strain of 6%. The nonzero topological invariant and helical edge states further confirm the nontrivial nature in stretched SnCH₃ film. The topological phase transition originates from the s-p_xy type band inversion at the Γ point with the strain increased. The spin-orbital coupling (SOC) induces a large band gap of ~0.24 eV, indicating that SnCH₃ film under strain is a quite promising material to achieve QSH effect. The proper substrate, h-BN, finally is presented to support the SnCH₃ film with nontrivial topology preserved.

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.

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.

First-principles prediction on bismuthylene monolayer as a promising quantum spin Hall insulator

Two-dimensional (2D) large band-gap topological insulators (TIs) with highly stable structures are imperative for achieving dissipationless transport devices. However, to date, only very few materials have been experimentally observed to host the quantum spin Hall (QSH) effect at low temperature, thus obstructing their potential application in practice. Using first-principles calculations, herein, we predicted a new 2D TI in the porous allotrope of a bismuth monolayer, i.e. bismuthylene, its geometrical stability was confirmed via phonon spectrum and molecular dynamics simulations. Analysis of the electronic structures reveals that bismuthylene is a native QSH state with a band gap as large as 0.28 eV at the Γ point, which is smaller than that (0.50 eV) of the buckled Bi (111) and suitable for room temperature applications. Notably, it has a much lower energy than flattened Bi and a higher energy than buckled Bi (111)…” [corrected] and flattened Bi films; thus, bismuthylene is feasible for experimental realization. Interestingly, the topological properties can be retained under strains within the range of -6%-3% and electrical fields up to 0.8 eV Å^-1. A heterostructure was constructed by sandwiching bismuthylene between BN sheets, and the non-trivial topology of bismuthylene was retained with a sizable band gap. These findings provide a platform to design a large-gap QSH insulator based on the 2D bismuthylene films, which show potential applications in spintronic devices.

Antimonene Oxides: Emerging Tunable Direct Bandgap Semiconductor and Novel Topological Insulator

Highly stable antimonene, as the cousin of phosphorene from group-VA, has opened up exciting realms in the two-dimensional (2D) materials family. However, pristine antimonene is an indirect band gap semiconductor, which greatly restricts its applications for optoelectronics devices. Identifying suitable materials, both responsive to incident photons and efficient for carrier transfer, is urgently needed for ultrathin devices. Herein, by means of first-principles computations we found that it is rather feasible to realize a new class of 2D materials with a direct bandgap and high carrier mobility, namely antimonene oxides with different content of oxygen. Moreover, these tunable direct bandgaps cover a wide range from 0 to 2.28 eV, which are crucial for solar cell and photodetector applications. Especially, the antimonene oxide (18Sb-18O) is a 2D topological insulator with a sizable global bandgap of 177 meV, which has a nontrivial Z₂ topological invariant in the bulk and the topological states on the edge. Our findings not only introduce new vitality into 2D group-VA materials family and enrich available candidate materials in this field but also highlight the potential of these 2D semiconductors as appealing ultrathin materials for future flexible electronics and optoelectronics devices.

Two-Dimensional Topological Insulators: Progress and Prospects

Two-dimensional topological insulators (2D TIs) are a remarkable class of atomically thin layered materials that exhibit unique symmetry-protected helical metallic edge states with an insulating interior. Recent years have seen a tremendous surge in research of this intriguing new state of quantum matter. In this Perspective, we summarize major milestones and the most significant progress in the latest developments of material discovery and property characterization in 2D TI research. We categorize the large number and rich variety of theoretically proposed 2D TIs based on the distinct mechanisms of topological phase transitions, and we systematically analyze and compare their structural, chemical, and physical characteristics. We assess the current status and challenges of experimental synthesis and potential device applications of 2D TIs and discuss prospects of exciting new opportunities for future research and development of this fascinating class of materials.

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.

Two-Dimensional Large Gap Topological Insulators with Tunable Rashba Spin-Orbit Coupling in Group-IV films

The coexistence of nontrivial topology and giant Rashba splitting, however, has rare been observed in two-dimensional (2D) films, limiting severely its potential applications at room temperature. Here, we through first-principles calculations to propose a series of inversion-asymmetric group-IV films, ABZ₂ (A ≠ B = Si, Ge, Sn, Pb; Z = F, Cl, Br), whose stability are confirmed by phonon spectrum calculations. The analyses of electronic structures reveal that they are intrinsic 2D TIs with a bulk gap as large as 0.74 eV, except for GeSiF₂, SnSiCl₂, GeSiCl₂ and GeSiBr₂ monolayers which can transform from normal to topological phases under appropriate tensile strain of 4, 4, 5, and 4%, respectively. The nontrivial topology is identified by Z₂ topological invariant together with helical edge states, as well as the berry curvature of these systems. Another prominent intriguing feature is the giant Rashba spin splitting with a magnitude reaching 0.15 eV, the largest value reported in 2D films so far. The tunability of Rashba SOC and band topology can be realized through achievable compressive/tensile strains (−4 ~ 6%). Also, the BaTe semiconductor is an ideal substrate for growing ABZ₂ films without destroying their nontrivial topology.

Searching for large-gap quantum spin hall insulators: boron-nitride/(Pb, Sn)/α-Al2O3 sandwich structures

Topological insulators hold great potential for efficient information processing and storage. Using density functional theory calculations, we predict that a honeycomb lead monolayer can be stabilized on an Al₂O₃ (0001) substrate to become topologically non-trivial with a sizeable band gap (∼0.27 eV). Furthermore, we propose to use a hexagonal boron-nitride (h-BN) monolayer as a protection for the topological states of Pb/Al₂O₃ and Sn/Al₂O₃. Our findings suggest new possibilities for designing and protecting two-dimensional TIs for practical applications.

Topological insulating states in 2D transition metal dichalcogenides induced by defects and strain

First-principles calculations and extensive analyses reveal that the H phase of two-dimensional (2D) transition metal dichalcogenides (TMDs) can be tuned to topological insulators by introducing square-octagon (4-8) defects and by applying equi-biaxial tensile strain simultaneously. The 2D structure composed of hexagonal rings with 4-8 defects, named sho-TMD, is dynamically and thermally stable. The critical equi-biaxial tensile strain for the topological phase transition is 4%, 6%, and 4% for sho-MoS₂, sho-MoSe₂ and sho-WS₂, respectively, and the corresponding nontrivial band gap induced by the spin-orbit coupling is 2, 8, and 22 meV, implying the possibility of observing the helical conducting edge states that are free of backscattering in experiment. It is equally interesting that the size of the energy band gap of the H-phase can be flexibly tuned by changing the concentration of 4-8 defects while the feature of the quasi-direct band gap semiconductor remains. These findings add additional traits to the TMD family, and provide a new strategy for engineering the electronic structure and the band topology of 2D TMDs for applications in nanoelectronics and spintronics.

Films based on group IV–V–VI elements for the design of a large-gap quantum spin Hall insulator with tunable Rashba splitting

Rashba spin–orbit coupling (SOC) in topological insulators (TIs) has recently attracted significant interest due to its potential applications in spintronics.

Theoretical design of a new family of two-dimensional topological insulators

A new family of two-dimensional topological insulators, hydrogenated monolayer of Pb₂XY (X = Ga/In and Y = Sb/Bi), has been predicted in our study.

Elemental two-dimensional nanosheets beyond graphene

The recent progress of elemental two-dimensional nanosheets, beyond graphene, has been summarized with the focus on their preparation and applications.

Large-Area Dry Transfer of Single-Crystalline Epitaxial Bismuth Thin Films

We report the first direct dry transfer of a single-crystalline thin film grown by molecular beam epitaxy. A double cantilever beam fracture technique was used to transfer epitaxial bismuth thin films grown on silicon (111) to silicon strips coated with epoxy. The transferred bismuth films retained electrical, optical, and structural properties comparable to the as-grown epitaxial films. Additionally, we isolated the bismuth thin films on freestanding flexible cured-epoxy post-transfer. The adhesion energy at the bismuth/silicon interface was measured to be ∼1 J/m², comparable to that of exfoliated and wet transferred graphene. This low adhesion energy and ease of transfer is unexpected for an epitaxially grown film and may enable the study of bismuth's unique electronic and spintronic properties on arbitrary substrates. Moreover, this method suggests a route to integrate other group-V epitaxial films (i.e., phosphorus) with arbitrary substrates, as well as potentially to isolate bismuthene, the atomic thin-film limit of bismuth.