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

Quantum spin Hall insulators in functionalized arsenene (AsX, X = F, OH and CH3) monolayers with pronounced light absorption

The search for new two-dimensional topological insulators (2D-TIs) with large band gaps is of great interest and importance. Our first-principles calculations predicted three candidates for 2D-TIs, arsenene functionalized with F, OH and CH3 groups (AsX, X = F, OH and CH3), which preserved large bulk band gaps from 100 to 160 meV (up to 260 meV) derived from the spin-orbit coupling (SOC) within the px,y orbitals. This picture is similar to what was reported for an AsH monolayer with a band gap of 193 meV. Ab initio molecular dynamic (AIMD) simulations demonstrated the thermal stabilities of the AsX monolayers even at 500 K. The nontrivial topological phase was confirmed by the topological invariant Z2 and topological edge state. The topological electronic bandgap of the AsF monolayer can be effectively modulated by biaxial tensile strain and vertical external electric field. In addition, pronounced light absorption in the near-infrared and visible range of the solar spectrum was expected for the AsX (X = H, F) monolayers from the adsorption peaks at 0.45-1.6 eV, which is attractive for light harvesting. The nontrivial quantum spin Hall (QSH) insulators AsX could be promising candidates for practical room-temperature applications in dissipationless transport devices and photovoltaics.

A new structure of two-dimensional allotropes of group V elements

The elemental two-dimensional (2D) materials such as graphene, silicene, germanene, and black phosphorus have attracted considerable attention due to their fascinating physical properties. Structurally they possess the honeycomb or distorted honeycomb lattices, which are composed of six-atom rings. Here we find a new structure of 2D allotropes of group V elements composed of eight-atom rings, which we name as the octagonal tiling (OT) structure. First-principles calculations indicate that these allotropes are dynamically stable and are also thermally stable at temperatures up to 600 K. These allotropes are semiconductors with band gaps ranging from 0.3 to 2.0 eV, thus they are potentially useful in near- and mid-infrared optoelectronic devices. OT-Bi is also a 2D topological insulator (TI) with a band gap of 0.33 eV, which is the largest among the reported elemental 2D TIs, and this gap can be increased further by applying compressive strains.

Experimental Observation of Topological Edge States at the Surface Step Edge of the Topological Insulator ZrTe_{5}

We report an atomic-scale characterization of ZrTe_{5} by using scanning tunneling microscopy. We observe a bulk band gap of ∼80  meV with topological edge states at the step edge and, thus, demonstrate that ZrTe_{5} is a two-dimensional topological insulator. We also find that an applied magnetic field induces an energetic splitting of the topological edge states, which can be attributed to a strong link between the topological edge states and bulk topology. The relatively large band gap makes ZrTe_{5} a potential candidate for future fundamental studies and device applications.

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.

Engineering Electronic Structure of a Two-Dimensional Topological Insulator Bi(111) Bilayer on Sb Nanofilms by Quantum Confinement Effect

We report on the fabrication of a two-dimensional topological insulator Bi(111) bilayer on Sb nanofilms via a sequential molecular beam epitaxy growth technique. Our angle-resolved photoemission measurements demonstrate the evolution of the electronic band structure of the heterostructure as a function of the film thickness and reveal the existence of a two-dimensional spinful massless electron gas within the top Bi bilayer. Interestingly, our first-principles calculation extrapolating the observed band structure shows that, by tuning down the thickness of the supporting Sb films into the quantum dimension regime, a pair of isolated topological edge states emerges in a partial energy gap at 0.32 eV above the Fermi level as a consequence of quantum confinement effect. Our results and methodology of fabricating nanoscale heterostructures establish the Bi bilayer/Sb heterostructure as a platform of great potential for both ultra-low-energy-cost electronics and surface-based spintronics.

Coordination Programming of Two-Dimensional Metal Complex Frameworks

Since the discovery of graphene, two-dimensional materials with atomic thickness have attracted much attention because of their characteristic physical and chemical properties. Recently, coordination nanosheets (CONASHs) came into the world as new series of two-dimensional frameworks, which can show various functions based on metal complexes formed by numerous combinations of metal ions and ligands. This Feature Article provides an overview of recent progress in synthesizing CONASHs and in elucidating their intriguing electrical, sensing, and catalytic properties. We also review recent theoretical studies on the prediction of the unique electronic structures, magnetism, and catalytic ability of materials based on CONASHs. Future prospects for applying CONASHs to novel applications are also discussed.

Surface Landau levels and spin states in bismuth (111) ultrathin films

The development of next-generation electronics is much dependent on the discovery of materials with exceptional surface-state spin and valley properties. Because of that, bismuth has attracted a renewed interest in recent years. However, despite extensive studies, the intrinsic electronic transport properties of Bi surfaces are largely undetermined due to the strong interference from the bulk. Here we report the unambiguous determination of the surface-state Landau levels in Bi (111) ultrathin films using scanning tunnelling microscopy under magnetic fields perpendicular to the surface. The Landau levels of the electron-like and the hole-like carriers are accurately characterized and well described by the band structure of the Bi (111) surface from density functional theory calculations. Some specific surface spin states with a large g-factor are identified. Our findings shed light on the exploiting surface-state properties of Bi for their applications in spintronics and valleytronics.

Predicting a new phase (T'') of two-dimensional transition metal di-chalcogenides and strain-controlled topological phase transition

Single layered transition metal dichalcogenides have attracted tremendous research interest due to their structural phase diversities. By using a global optimization approach, we have discovered a new phase of transition metal dichalcogenides (labelled as T''), which is confirmed to be energetically, dynamically and kinetically stable by our first-principles calculations. The new T'' MoS2 phase exhibits an intrinsic quantum spin Hall (QSH) effect with a nontrivial gap as large as 0.42 eV, suggesting that a two-dimensional (2D) topological insulator can be achieved at room temperature. Most interestingly, there is a topological phase transition simply driven by a small tensile strain of up to 2%. Furthermore, all the known MX2 (M = Mo or W; X = S, Se or Te) monolayers in the new T'' phase unambiguously display similar band topologies and strain controlled topological phase transitions. Our findings greatly enrich the 2D families of transition metal dichalcogenides and offer a feasible way to control the electronic states of 2D topological insulators for the fabrication of high-speed spintronics devices.

Topological modification of the electronic structure by Bi-bilayers lying deep inside bulk Bi₂Se₃

We observe the modified surface states of an epitaxial thin film of a homologous series of (Bi2)m(Bi2Se3)n, as a topological insulator (TI), by angle-resolved photoemission spectroscopy measurements. A thin film with m : n  =  1 : 3 (Bi8Se9) has been grown with Bi2 bilayers embedded every other three quintuple layers (QLs) of Bi2Se3. Despite the reduced dimension of continuous QLs due to the Bi2 heterolayers, we find that the topological surface states stem from the inverted Bi and Se states and the topologically nontrivial structures are mainly based on the prototype of 3D TI Bi2Se3 without affecting the overall topological order.

Topologically nontrivial bismuth(111) thin films

Using high-resolution angle-resolved photoemission spectroscopy (ARPES), the topological property of the three-dimensional Bi(111) films grown on the Bi₂Te₃(111) substrate were studied. Very different from the bulk Bi, we found another surface band near the point besides the two well-known surface bands on the 30 nm films. With this new surface band, the bulk valence band and the bulk conduction band can be connected by the surface states in the Bi(111)/Bi₂Te₃ films. Our band mapping revealed odd number of Fermi crossings of the surface bands, which provided new experimental evidences that Bi(111)/Bi₂Te₃ films of a certain thickness can be topologically nontrivial in three dimension.

Functionalized Thallium Antimony Films as Excellent Candidates for Large-Gap Quantum Spin Hall Insulator

Group III-V films are of great importance for their potential application in spintronics and quantum computing. Search for two-dimensional III-V films with a nontrivial large-gap are quite crucial for the realization of dissipationless transport edge channels using quantum spin Hall (QSH) effects. Here we use first-principles calculations to predict a class of large-gap QSH insulators in functionalized TlSb monolayers (TlSbX2; (X = H, F, Cl, Br, I)), with sizable bulk gaps as large as 0.22~0.40 eV. The QSH state is identified by Z2 topological invariant together with helical edge states induced by spin-orbit coupling (SOC). Noticeably, the inverted band gap in the nontrivial states can be effectively tuned by the electric field and strain. Additionally, these films on BN substrate also maintain a nontrivial QSH state, which harbors a Dirac cone lying within the band gap. These findings may shed new light in future design and fabrication of QSH insulators based on two-dimensional honeycomb lattices in spintronics.

Prediction of topological phase transition in X2–SiGe monolayers

Quantum spin Hall (QSH) insulators exhibit a bulk insulting gap and metallic edge states characterized by nontrivial topology.

Local currents in a 2D topological insulator

Symmetry protected edge states in 2D topological insulators are interesting both from the fundamental point of view as well as from the point of view of potential applications in nanoelectronics as perfectly conducting 1D channels and functional elements of circuits. Here using a simple tight-binding model and the Landauer-Büttiker formalism we explore local current distributions in a 2D topological insulator focusing on effects of non-magnetic impurities and vacancies as well as finite size effects. For an isolated edge state, we show that the local conductance decays into the bulk in an oscillatory fashion as explained by the complex band structure of the bulk topological insulator. We demonstrate that although the net conductance of the edge state is topologically protected, impurity scattering leads to intricate local current patterns. In the case of vacancies we observe vortex currents of certain chirality, originating from the scattering of current-carrying electrons into states localized at the edges of hollow regions. For finite size strips of a topological insulator we predict the formation of an oscillatory band gap in the spectrum of the edge states, the emergence of Friedel oscillations caused by an open channel for backscattering from an impurity and antiresonances in conductance when the Fermi energy matches the energy of the localized state created by an impurity.

Strain-driven band inversion and topological aspects in Antimonene

Searching for the two-dimensional (2D) topological insulators (TIs) with large bulk band gaps is the key to achieve room-temperature quantum spin Hall effect (QSHE). Using first-principles calculations, we demonstrated that the recently-proposed antimonene [Zhang et al., Angew. Chem. Int. Ed. 54, 3112–3115 (2015)] can be tuned to a 2D TI by reducing the buckling height of the lattice which can be realized under tensile strain. The strain-driven band inversion in the vicinity of the Fermi level is responsible for the quantum phase transition. The buckled configuration of antimonene enables it to endure large tensile strain up to 18% and the resulted bulk band gap can be as large as 270 meV. The tunable bulk band gap makes antimonene a promising candidate material for achieving quantum spin Hall effect (QSH) at high temperatures which meets the requirement of future electronic devices with low power consumption.

Communication: Surface stability and topological surface states of cleaved Bi2Se3: First-principles studies

Through systematic first principles calculations within the nonlocal van der Waals functional, we investigated the structure stability and topological surface state properties of various surface cleaves in the topological insulator Bi2Se3 Our results reveal that under Bi-rich conditions, the Bi bilayer-covered surface and the Se-terminated surface with a Bi bilayer under the first quintuple layer are even more stable than the generic Bi2Se3. The surface state bands are changed by different surface terminations, causing the formation of new Dirac states. We may distinguish various surfaces by using scanning tunneling microscopy experimentally.

Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles

Both spin and orbital degrees of freedom contribute to the magnetic moment of isolated atoms. However, when inserted in crystals, atomic orbital moments are quenched because of the lack of rotational symmetry that protects them when isolated. Thus, the dominant contribution to the magnetization of magnetic materials comes from electronic spin. Here we show that nanoislands of quantum spin Hall insulators can host robust orbital edge magnetism whenever their highest occupied Kramers doublet is singly occupied, upgrading the spin edge current into a charge current. The resulting orbital magnetization scales linearly with size, outweighing the spin contribution for islands of a few nm in size. This linear scaling is specific of the Dirac edge states and very different from Schrodinger electrons in quantum rings. By modeling Bi(111) flakes, whose edge states have been recently observed, we show that orbital magnetization is robust with respect to disorder, thermal agitation, shape of the island, and crystallographic direction of the edges, reflecting its topological protection.

Low-Energy Electron Potentiometry: Contactless Imaging of Charge Transport on the Nanoscale

Charge transport measurements form an essential tool in condensed matter physics. The usual approach is to contact a sample by two or four probes, measure the resistance and derive the resistivity, assuming homogeneity within the sample. A more thorough understanding, however, requires knowledge of local resistivity variations. Spatially resolved information is particularly important when studying novel materials like topological insulators, where the current is localized at the edges, or quasi-two-dimensional (2D) systems, where small-scale variations can determine global properties. Here, we demonstrate a new method to determine spatially-resolved voltage maps of current-carrying samples. This technique is based on low-energy electron microscopy (LEEM) and is therefore quick and non-invasive. It makes use of resonance-induced contrast, which strongly depends on the local potential. We demonstrate our method using single to triple layer graphene. However, it is straightforwardly extendable to other quasi-2D systems, most prominently to the upcoming class of layered van der Waals materials.

Low-temperature growth of bismuth thin films with (111) facet on highly oriented pyrolytic graphite

The epitaxial growth of artificial two-dimensional metals at interfaces plays a key role in fabricating heterostructures for nanoelectronics. Here, we present the growth of bismuth nanostructures on highly oriented pyrolytic graphite (HOPG) under ultrahigh vacuum (UHV) conditions, which was investigated thoroughly by a combination of scanning tunneling microscopy (STM), ultraviolet photoemission spectroscopy (UPS), X-ray photoelectron spectroscopy (XPS), and low energy electron diffraction (LEED). It was found that (111)-oriented bilayers are formed on as-cleaved high-quality HOPG at 140 K, which opens the possibility of making Bi(111) thin films on a semimetal, and this is a notable step forward from the earlier studies, which show that only Bi(110) facets could be formed at ultrathin thickness at room temperature. XPS investigation of both C 1s and Bi 4f reflects the rather weak bonding between the Bi film and the HOPG substrate and suggests a quasi layer-by-layer growth mode of Bi nanostructures on HOPG at low temperature. Moreover, the evolution of the valence band of the interface is recorded by UPS, and a transition from quantum well states to bulk-like features is observed at varying film thickness. Unlike semimetallic bulk bismuth, ultrathin Bi(111) films are expected to be topological insulators. Our study may therefore pave the way for the generation of high quality Bi nanostructures to be used in spin electronics.

One-dimensional edge states with giant spin splitting in a bismuth thin film

To realize a one-dimensional (1D) system with strong spin-orbit coupling is a big challenge in modern physics, since the electrons in such a system are predicted to exhibit exotic properties unexpected from the 2D or 3D counterparts, while it was difficult to realize genuine physical properties inherent to the 1D system. We demonstrate the first experimental result that directly determines the purely 1D band structure by performing spin-resolved angle-resolved photoemission spectroscopy of Bi islands on a silicon surface that contains a metallic 1D edge structure with unexpectedly large Rashba-type spin-orbit coupling suggestive of the nontopological nature. We have also found a sizable out-of-plane spin polarization of the 1D edge state, consistent with our first-principles band calculations. Our result provides a new platform to realize exotic quantum phenomena at the 1D edge of the strong spin-orbit-coupling systems.

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.

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

One of the major obstacles to a wide application range of the quantum spin Hall (QSH) effect is the lack of suitable QSH insulators with a large bulk gap. By means of first-principles calculations including relativistic effects, we predict that methyl-functionalized bismuth, antimony, and lead bilayers (Me-Bi, Me-Sb, and Me-Pb) are 2D topological insulators (TIs) with protected Dirac type topological helical edge states, and thus suitable QSH systems. In addition to the explicitly obtained topological edge states, the nontrivial topological characteristic of these systems is confirmed by the calculated nontrivial Z2 topological invariant. The TI characteristics are intrinsic to the studied materials and are not subject to lateral quantum confinement at edges, as confirmed by explicit simulation of the corresponding nanoribbons. It is worthwhile to point out that the large nontrivial bulk gaps of 0.934 eV (Me-Bi), 0.386 eV (Me-Sb), and 0.964 eV (Me-Pb) are derived from the strong spin-orbit coupling within the p(x) and p(y) orbitals and would be large enough for room-temperature application. Moreover, we show that the topological properties in these three systems are robust against mechanical deformation. These novel 2D TIs with such giant topological energy gaps are promising platforms for topological phenomena and possible applications at high temperature.

Visualization of a ferromagnetic metallic edge state in manganite strips

Recently, broken symmetry effect induced edge states in two-dimensional electronic systems have attracted great attention. However, whether edge states may exist in strongly correlated oxides is not yet known. In this work, using perovskite manganites as prototype systems, we demonstrate that edge states do exist in strongly correlated oxides. Distinct appearance of ferromagnetic metallic phase is observed along the edge of manganite strips by magnetic force microscopy. The edge states have strong influence on the transport properties of the strips, leading to higher metal-insulator transition temperatures and lower resistivity in narrower strips. Model calculations show that the edge states are associated with the broken symmetry effect of the antiferromagnetic charge-ordered states in manganites. Besides providing a new understanding of the broken symmetry effect in complex oxides, our discoveries indicate that novel edge state physics may exist in strongly correlated oxides beyond the current two-dimensional electronic systems.

Topological properties determined by atomic buckling in self-assembled ultrathin Bi(110)

Topological insulators (TIs) are a new type of electronic materials in which the nontrivial insulating bulk band topology governs conducting boundary states with embedded spin-momentum locking. Such edge states are more robust in a two-dimensional (2D) TI against scattering by nonmagnetic impurities than in its three-dimensional (3D) variant, because in 2D the two helical edge states are protected from the only possible backscattering. This makes the 2D TI family a better candidate for coherent spin transport and related applications. While several 3D TIs are already synthesized experimentally, physical realization of 2D TI is so far limited to hybrid quantum wells with a tiny bandgap that does not survive temperatures above 10 K. Here, combining first-principles calculations and scanning tunneling microscopy/spectroscopy (STM/STS) experimental studies, we report nontrivial 2D TI phases in 2-monolayer (2-ML) and 4-ML Bi(110) films with large and tunable bandgaps determined by atomic buckling of Bi(110) films. The gapless edge states are experimentally detected within the insulating bulk gap at 77 K. The band topology of ultrathin Bi(110) films is sensitive to atomic buckling. Such buckling is sensitive to charge doping and could be controlled by choosing different substrates on which Bi(110) films are grown.

Formation of quantum spin Hall state on Si surface and energy gap scaling with strength of spin orbit coupling

For potential applications in spintronics and quantum computing, it is desirable to place a quantum spin Hall insulator [i.e., a 2D topological insulator (TI)] on a substrate while maintaining a large energy gap. Here, we demonstrate a unique approach to create the large-gap 2D TI state on a semiconductor surface, based on first-principles calculations and effective Hamiltonian analysis. We show that when heavy elements with strong spin orbit coupling (SOC) such as Bi and Pb atoms are deposited on a patterned H-Si(111) surface into a hexagonal lattice, they exhibit a 2D TI state with a large energy gap of ≥0.5 eV. The TI state arises from an intriguing substrate orbital filtering effect that selects a suitable orbital composition around the Fermi level, so that the system can be matched onto a four-band effective model Hamiltonian. Furthermore, it is found that within this model, the SOC gap does not increase monotonically with the increasing strength of SOC. These interesting results may shed new light in future design and fabrication of large-gap topological quantum states.

Topological insulator states in a honeycomb lattice of s-triazines

Two-dimensional (2D) graphitic carbon nitride materials have been drawing increasing attentions in energy conversion, environment protection and spintronic devices. Here, based on first-principles calculations, we demonstrate that the already-synthesized honeycomb lattice of s-triazines with a chemical formula of C6N6 (g-C6N6) has topologically nontrivial electronic states characterized by px,y-orbital band structures with a topological invariant of Z2 = 1, and stronger spin-orbital coupling (SOC) than both graphene and silicene. The band gaps opened in the px,y-orbital bands due to SOC are 5.50 meV (K points) and 8.27 eV (Γ point), respectively, implying that the quantum spin Hall effect (QSHE) could be achieved in this 2D graphitic carbon nitride material at a temperature lower than 95 K. This offers a viable approach for searching for 2D Topological Insulators (TIs) in metal-free organic materials.

Epitaxial growth of large-gap quantum spin Hall insulator on semiconductor surface

Formation of topological quantum phase on a conventional semiconductor surface is of both scientific and technological interest. Here, we demonstrate epitaxial growth of 2D topological insulator, i.e., quantum spin Hall state, on Si(111) surface with a large energy gap, based on first-principles calculations. We show that the Si(111) surface functionalized with one-third monolayer of halogen atoms [Si(111)-√3 x √3 -X (X = Cl, Br, I)] exhibiting a trigonal superstructure provides an ideal template for epitaxial growth of heavy metals, such as Bi, which self-assemble into a hexagonal lattice with high kinetic and thermodynamic stability. Most remarkably, the Bi overlayer is atomically bonded to but electronically decoupled from the underlying Si substrate, exhibiting isolated quantum spin Hall state with an energy gap as large as ∼ 0.8 eV. This surprising phenomenon originates from an intriguing substrate-orbital-filtering effect, which critically selects the orbital composition around the Fermi level, leading to different topological phases. In particular, the substrate-orbital-filtering effect converts the otherwise topologically trivial freestanding Bi lattice into a nontrivial phase; and the reverse is true for Au lattice. The underlying physical mechanism is generally applicable, opening a new and exciting avenue for exploration of large-gap topological surface/interface states.

Large-gap quantum spin Hall insulator in single layer bismuth monobromide Bi4Br4

Quantum spin Hall (QSH) insulators have gapless topological edge states inside the bulk band gap, which can serve as dissipationless spin current channels. The major challenge currently is to find suitable materials for this topological state. Here, we predict a new large-gap QSH insulator with bulk direct band gap of ∼ 0.18 eV, in single-layer Bi4Br4, which could be exfoliated from its three-dimensional bulk material due to the weakly bonded layered structure. The band gap of single-layer Bi4Br4 is tunable via strain engineering, and the QSH phase is robust against external strain. Moreover, because this material consists of special one-dimensional molecular chain as its basic building block, the single layer Bi4Br4 could be torn to ribbons with clean and atomically sharp edges. These nanoribbons, which have single-Dirac-cone edge states crossing the bulk band gap, are ideal wires for dissipationless transport. Our work thus provides a new promising material for experimental studies and practical applications of the QSH effect.

Evidence of topological two-dimensional metallic surface states in thin bismuth nanoribbons

Understanding the exotic quantum phenomena in bulk bismuth beyond its ultraquantum limit remains controversial and gives rise to renewed interest. The focus of the issues is whether these quantum properties have a conventional bulk nature or just the surface effect due to the significant spin-orbital interaction and in relation to the Bi-based topological insulators. Here, we present angular-dependent magnetoresistance (AMR) measurements on single-crystal bismuth nanoribbons of different thicknesses with magnetic fields up to 31 T. In thin nanoribbons with thickness of ∼40 nm, a two-fold rational symmetry of the low field AMR spectra and two sets of 1/2-shifted (i.e., γ = 1/2) Shubnikov-de Haas (SdH) quantum oscillations with exact two- dimensional (2D) character were obtained. However, when the thickness of the ribbon increases, a 3D bulk-like SdH oscillations with γ = 0 and a four-fold rotational symmetry of the AMR spectra appear. These results provided unambiguous transport evidence of the topological 2D metallic surface states in thinner nanoribbons with an insulating bulk. Our observations provide a promising pathway to understand the quantum phenomena in Bi arising from the surface states.

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

Based on first-principles and tight-binding calculations, we report that the topological edge states of zigzag Bi(111) nanoribbon can be significantly tuned by H edge adsorption. The Fermi velocity is increased by 1 order of magnitude, as the Dirac point is moved from the Brillouin zone boundary to the Brillouin zone center, and the real-space distribution of Dirac states are made twice more delocalized. These intriguing changes are explained by an orbital filtering effect of edge H atoms, which pushes certain components of the p orbital of edge Bi atoms out of the band gap regime that reshapes the topological edge states. In addition, the spin texture of the Dirac states is also modified, which is described by introducing an effective Hamiltonian. Our findings not only are of fundamental interest but also have practical implications in potential applications of topological insulators.

Organic topological insulators in organometallic lattices

Topological insulators are a recently discovered class of materials having insulating bulk electronic states but conducting boundary states distinguished by nontrivial topology. So far, several generations of topological insulators have been theoretically predicted and experimentally confirmed, all based on inorganic materials. Here, based on first-principles calculations, we predict a family of two-dimensional organic topological insulators made of organometallic lattices. Designed by assembling molecular building blocks of triphenyl-metal compounds with strong spin-orbit coupling into a hexagonal lattice, this new classes of organic topological insulators are shown to exhibit nontrivial topological edge states that are robust against significant lattice strain. We envision that organic topological insulators will greatly broaden the scientific and technological impact of topological insulators.

Prediction of a two-dimensional organic topological insulator

Topological insulators (TI) are a class of materials exhibiting unique quantum transport properties with potential applications in spintronics and quantum computing. To date, all of the experimentally confirmed TIs are inorganic materials. Recent theories predicted the possible existence of organic TIs (OTI) in two-dimensional (2D) organometallic frameworks. However, those theoretically proposed structures do not naturally exist and remain to be made in experiments. Here, we identify a recently experimentally made 2D organometallic framework, consisting of π-conjugated nickel-bis-dithiolene with a chemical formula Ni3C12S12, which exhibits nontrivial topological states in both a Dirac band and a flat band, therefore confirming the existence of OTI.

Topologically protected quantum transport in locally exfoliated bismuth at room temperature

We report electrical conductance measurements of Bi nanocontacts created by repeated tip-surface indentation using a scanning tunneling microscope at temperatures of 4 and 300 K. As a function of the elongation of the nanocontact, we measure robust, tens of nanometers long plateaus of conductance G0 = 2e2/h at room temperature. This observation can be accounted for by the mechanical exfoliation of a Bi(111) bilayer, a predicted quantum spin Hall (QSH) insulator, in the retracing process following a tip-surface contact. The formation of the bilayer is further supported by the additional observation of conductance steps below G0 before breakup at both temperatures. Our finding provides the first experimental evidence of the possibility of mechanical exfoliation of Bi bilayers, the existence of the QSH phase in a two-dimensional crystal, and, most importantly, the observation of the QSH phase at room temperature.