sd(2) Graphene: Kagome band in a hexagonal lattice

Chiral Honeycomb Lattices of Nonplanar π-Conjugated Supramolecules with Protected Dirac and Flat Bands

The honeycomb lattice is a fundamental two-dimensional (2D) network that gives rise to surprisingly rich electronic properties. While its expansion to 2D supramolecular assembly is conceptually appealing, its realization is not straightforward because of weak intermolecular coupling and the strong influence of a supporting substrate. Here, we show that the application of a triptycene derivative with phenazine moieties, Trip-Phz, solves this problem due to its strong intermolecular π-π pancake bonding and nonplanar geometry. Our scanning tunneling microscopy (STM) measurements demonstrate that Trip-Phz molecules self-assemble on a Ag(111) surface to form chiral and commensurate honeycomb lattices. Electronically, the network can be viewed as a hybrid of honeycomb and kagome lattices. The Dirac and flat bands predicted by a simple tight-binding model are reproduced by total density functional theory (DFT) calculations, highlighting the protection of the molecular bands from the Ag(111) substrate. The present work offers a rational route for creating chiral 2D supramolecules that can simultaneously accommodate pristine Dirac and flat bands.

Electronic Lieb lattice signatures embedded in two-dimensional polymers with a square lattice

Exotic band features, such as Dirac cones and flat bands, arise directly from the lattice symmetry of materials. The Lieb lattice is one of the most intriguing topologies, because it possesses both Dirac cones and flat bands which intersect at the Fermi level. However, the synthesis of Lieb lattice materials remains a challenging task. Here, we explore two-dimensional polymers (2DPs) derived from zinc-phthalocyanine (ZnPc) building blocks with a square lattice (sql) as potential electronic Lieb lattice materials. By systematically varying the linker length (ZnPc-xP), we found that some ZnPc-xP exhibit a characteristic Lieb lattice band structure. Interestingly though, fes bands are also observed in ZnPc-xP. The coexistence of fes and Lieb in sql 2DPs challenges the conventional perception of the structure-electronic structure relationship. In addition, we show that manipulation of the Fermi level, achieved by electron removal or atom substitution, effectively preserves the unique characteristics of Lieb bands. The Lieb Dirac bands of ZnPc-4P shows a non-zero Chern number. Our discoveries provide a fresh perspective on 2DPs and redefine the search for Lieb lattice materials into a well-defined chemical synthesis task.

Carbon Kagome nanotubes-quasi-one-dimensional nanostructures with flat bands

In recent years, a number of bulk materials and heterostructures have been explored due their connections with exotic materials phenomena emanating from flat band physics and strong electronic correlation. The possibility of realizing such fascinating material properties in simple realistic nanostructures is particularly exciting, especially as the investigation of exotic states of electronic matter in wire-like geometries is relatively unexplored in the literature. Motivated by these considerations, we introduce in this work carbon Kagome nanotubes (CKNTs)-a new allotrope of carbon formed by rolling up Kagome graphene, and investigate this material using specialized first principles calculations. We identify two principal varieties of CKNTs-armchair and zigzag, and find both varieties to be stable at room temperature, based on ab initio molecular dynamics simulations. CKNTs are metallic and feature dispersionless states (i.e., flat bands) near the Fermi level throughout their Brillouin zone, along with an associated singular peak in the electronic density of states. We calculate the mechanical and electronic response of CKNTs to torsional and axial strains, and show that CKNTs appear to be more mechanically compliant than conventional carbon nanotubes (CNTs). Additionally, we find that the electronic properties of CKNTs undergo significant electronic transitions-with emergent partial flat bands and tilted Dirac points-when twisted. We develop a relatively simple tight-binding model that can explain many of these electronic features. We also discuss possible routes for the synthesis of CKNTs. Overall, CKNTs appear to be unique and striking examples of realistic elemental quasi-one-dimensional materials that may display fascinating material properties due to strong electronic correlation. Distorted CKNTs may provide an interesting nanomaterial platform where flat band physics and chirality induced anomalous transport effects may be studied together.

Investigations on structural, electronic and optical properties of ZnO in two-dimensional configurations by first-principles calculations

The electronic structures and optical properties of two-dimensional (2D) ZnO monolayers in a series of configurations were systematically investigated by first-principles calculations with HubbardUevaluated by the linear response approach. Three types of 2D ZnO monolayers, as planer hexagonal-honeycomb (Plan), double-layer honeycomb (Dlhc), and corrugated tetragonal (Tile) structures, show a mechanical and dynamical stability, while the Dlhc-ZnO is the most energetically stable configuration and Plan-ZnO is the second one. Each 2D ZnO monolayer behaves as a semiconductor with that Plan-, Dlhc-ZnO have a direct band gap of 1.81 eV and 1.85 eV at theΓpoint, respectively, while Tile-ZnO has an indirect band gap of 2.03 eV. Interestingly, the 2D ZnO monolayers all show a typical near-free-electron character for the bottom conduction band with a small effective mass, leading to a tremendous optical absorption in the whole visible and ultraviolet window, and this origination was further confirmed by the transition dipole moment. Our investigations suggest a potential candidate in the photoelectric field and provide a theoretical guidance for the exploration of wide-band-gap 2D semiconductors.

Sumanene Monolayer of Pure Carbon: A Two-Dimensional Kagome-Analogy Lattice with Desirable Band Gap, Ultrahigh Carrier Mobility, and Strong Exciton Binding Energy

The design and synthesis of novel two-dimensional (2D) materials that possess robust structural stability and unusual physical properties may open up enormous opportunities for device and engineering applications. Herein, a 2D sumanene lattice that can be regarded as a derivative of the conventional Kagome lattice is proposed. The tight-binding analysis demonstrates sumanene lattice contains two sets of Dirac cones and two sets of flat bands near the Fermi surface, distinctively different from the Kagome lattice. Using first-principles calculations, two possible routines for the realization of stable 2D sumanene monolayers (named α phase and β phase) are theoretically suggested, and an α-sumanene monolayer can be experimentally synthesized with chemical vapor deposition using C₂₁ H₁₂ as a precursor. Small binding energies on Au(111) surface (e.g., -37.86 eV Å^-2 for α phase) signify the possibility of their peel-off after growing on the noble metal substrate. Importantly, the GW plus Bethe-Salpeter equation calculations demonstrate both monolayers have moderate band gaps (1.94 eV for α) and ultrahigh carrier mobilities (3.4 × 10⁴ cm²  V^-1  s^-1 for α). In particular, the α-sumanene monolayer possesses a strong exciton binding energy of 0.73 eV, suggesting potential applications in optics.

A generic dual d-band model for interlayer ferromagnetic coupling in a transition-metal doped MnBi2Te4 family of materials

Realization of ferromagnetic (FM) interlayer coupling in magnetic topological insulators (TIs) of the MnBi₂Te₄ family of materials (MBTs) may pave the way for realizing the high-temperature quantum anomalous Hall effect (high-T QAHE). Here we propose a generic dual d-band (DDB) model to elucidate the energy difference (ΔE = E_AFM - E_FM) between the AFM and FM coupling in transition-metal (TM)-doped MBTs, where the valence of TMs splits into d-t_2g and d-e_g sub-bands. Remarkably, the DDB shows that ΔE is universally determined by the relative position of the dopant (X) and Mn d-e_g/t_2g bands, . If ΔE_d > 0, then ΔE > 0 and the desired FM coupling is favored. This surprisingly simple rule is confirmed by first-principles calculations of hole-type 3d and 4d TM dopants. Significantly, by applying the DDB model, we predict the high-T QAHE in the V-doped Mn₂Bi₂Te₅, where the Curie temperature is enhanced by doubling of the MnTe layer, while the topological order mitigated by doping can be restored by strain.

Topological band transition between hexagonal and triangular lattices with (px,py) orbitals

By combining tight-binding modelling with density functional theory based first-principles calculations, we investigate the band evolution of two-dimensional (2D) hexagonal lattices with (p_x,p_y) orbitals, focusing on the electronic structures and topological phase transitions. The (p_x,p_y)-orbital hexagonal lattice model possesses two flat bands encompassing two linearly dispersive Dirac bands. Breaking the A/B sublattice symmetry could transform the model into two triangular lattices, each featuring a flat band and a dispersive band. Inclusion of the spin-orbit coupling and magnetization may give rise to quantum spin Hall and quantum anomalous Hall (QAH) states. As a proof of concept, we demonstrate that half-hydrogenated stanene is encoded by a triangular lattice with (p_x,p_y) orbitals, which exhibits ferromagnetism and QAH effect with a topological gap of ∼0.15 eV, feasible for experimental observation. These results provide insights into the structure-property relationships involving the orbital degree of freedom, which may shed light on future design and preparation of 2D topological materials for novel electronic/spintronic and quantum computing devices.

Floquet anomalous Hall effect in ferromagnetic multiorbital tight-binding models

In this work, we study the band structures and intrinsic anomalous Hall conductivity (AHC) of the ferromagnetic multiorbital tight-binding (TB) model derived from the transition metal compound Sr₂RuO₄under periodic driving of monochromatic polarized light. Within the framework of the Floquet theory, we adopt the continued fraction technique to attain the effective Hamiltonian valid in the weak-driving and low-frequency regimes, and the related Green's functions which are further employed for the transport calculations based on the Kubo formalism. The high-frequency circularly and linearly polarized light has limited impacts on the band structures, while the low-frequency light with the photon energy smaller than the bandwidth of the system opens up bandgaps at the edges of the Floquet-Brillouin zone since the transitions between Floquet sidebands become significant. For intrinsic AHC, the left-handed circularly polarized (LCP) light plays a distinct role on AHC compared to the right-handed circularly polarized (RCP) light. Furthermore, it reveals that the roles of LCP and RCP light can be interchanged by altering the incident plane of light. Finally, the intrinsic AHC with the interplay between the short-range disorder and circularly polarized light is also investigated.

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.

Γ valley transition metal dichalcogenide moiré bands

The valence band maxima of most group VI transition metal dichalcogenide thin films remain at the Γ point all of the way from bulk to bilayer. In this paper, we develop a continuum theory of the moiré minibands that are formed in the valence bands of Γ-valley homobilayers by a small relative twist. Our effective theory is benchmarked against large-scale ab initio electronic structure calculations that account for lattice relaxation. As a consequence of an emergent [Formula: see text] symmetry, we find that low-energy Γ-valley moiré holes differ qualitatively from their K-valley counterparts addressed previously; in energetic order, the first three bands realize 1) a single-orbital model on a honeycomb lattice, 2) a two-orbital model on a honeycomb lattice, and 3) a single-orbital model on a kagome lattice.

Half-Dirac semimetals and the quantum anomalous Hall effect in Kagome Cd2N3 lattices

Half-Dirac semimetals (HDSs), which possess 100% spin-polarizations for Dirac materials, are highly desirable for exploring various topological phases of matter as low-dimensionality opens unprecedented opportunities for manipulating the quantum state of low-cost electronic nanodevices. The search for high-temperature HDSs is still a current hotspot and yet challenging experimentally. Herein based on first-principles calculations, we propose the realization of Half Dirac semimetals (HDS) in two-dimensional (2D) Kagome transition-metal nitride Cd₂N₃, which is robust against strain engineering. Monte Carlo simulations reveal that Cd₂N₃ possesses a Curie temperature reaching up to T _C = 225 K, which is much higher than that of the reported monolayers CrI₃ (T _C = 45 K) and Cr₂Ge₂Te₆ (T _C = 20 K). The band crossings in Cd₂N₃ are gapped out by the spin-orbit coupling, which brings about the quantum anomalous Hall (QAH) effect with a sizeable band gap of E _g = 4.9 meV, characterized by the nonzero Chern number (C = 1) and chiral edge states. A tight-binding model is further used to clarify the origin of HDSs and nontrivial electronic properties. The results suggest monolayer transition-metal nitrides as a promising platform to explore fascinating physical phenomena associated with novel 2D emergent HDSs and QAH insulators toward realistic spintronics devices, thus stimulating experimental interest.

Quantum Phase Engineering of Two-Dimensional Post-Transition Metals by Substrates: Toward a Room-Temperature Quantum Anomalous Hall Insulator

We propose a new strategy to engineer topological and magnetic properties of two-dimensional (2D) hexagonal lattices consisting of post-transition metals. Our first-principles calculations demonstrate that substrates serve as templates to form 2D lattices with high thermodynamic stability, where their topological properties as well as magnetic properties sensitively change as a function of lattice constants, i.e., the system undergoes a first-order phase transition from nonmagnetic to ferromagnetic state above a critical lattice constant. Consequently, substrates can be used to explore versatile magnetic, electronic, and quantum topological properties. We establish phase diagrams of versatile quantum phases in terms of exchange coupling and spin-orbit coupling effectively tuned by the lattice constants. We further reveal the first room-temperature quantum anomalous Hall (QAH) effect, i.e., Sn on 2√3 × 2√3 graphane is a QAH insulator with a large spin-orbit coupling gap of ∼0.2 eV and a Curie temperature of ∼380 K by using the 2D anisotropic Heisenberg model.

B5N5 monolayer: a room-temperature light element antiferromagnetic insulator

We demonstrate theoretically that an intrinsic antiferromagnetic phase exists in monolayer materials consisting of non-magnetic light atoms, and propose that B5N5 with a decorated bounce lattice is a thermodynamically stable two-dimensional antiferromagnetic insulator by performing state-of-the-art density functional theory calculations. The antiferromagnetic phase originates from spontaneous symmetry breaking at the nearly flat bands in the vicinity of the Fermi energy. The flat bands are formed by purely s-p z orbitals and are spin degenerate. A perpendicular electric field can remove the spin degeneracy and a prototype controllable dual spin filter with 100% spin polarization is proposed. Our proposal offers a possible two-dimensional atomically thick antiferromagnetic insulator.

High-temperature and multichannel quantum anomalous Hall effect in pristine and alkali-metal-doped CrBr3 monolayers

The realization of the high-temperature and multichannel quantum anomalous Hall effect (QAHE) has been a central research area in the development of low-power-consumption electronics and quantum computing. Recently discovered two-dimensional (2D) ferromagnetic (FM) materials provide unprecedented opportunities for the exploration of the high-temperature QAHE. Based on first-principles approaches, we first reveal that a FM CrBr₃ monolayer harbors topologically nontrivial conduction bands with a high Chern number of C = 2. Then, we reveal that the interesting conduction bands can be moved downwards to the Fermi levels by electron and alkali-metal-doping; meanwhile, the QAHE characteristics can be preserved. Most strikingly, the Na-doped CrBr₃ system possesses a higher Chern number of C = -4 with a transition temperature of ∼54 K, which is attributed to the constructive coupling effect of the quadratic non-Dirac and linear Dirac band dispersions. The present study, together with recent achievements in the field of 2D FM materials, provides an experimentally achievable guide for realizing the high-temperature and multichannel QAHE based purely on 2D FM systems.

Flat Band and Hole-induced Ferromagnetism in a Novel Carbon Monolayer

In recent experiments, superconductivity and correlated insulating states were observed in twisted bilayer graphene (TBG) with small magic angles, which highlights the importance of the flat bands near Fermi energy. However, the moiré pattern of TBG consists of more than ten thousand carbon atoms that is not easy to handle with conventional methods. By density functional theory calculations, we obtain a flat band at E_F in a novel carbon monolayer coined as cyclicgraphdiyne with the unit cell of eighteen atoms. By doping holes into cyclicgraphdiyne to make the flat band partially occupied, we find that cyclicgraphdiyne with 1/8, 1/4, 3/8 and 1/2 hole doping concentration shows ferromagnetism (half-metal) while the case without doping is nonmagnetic, indicating a hole-induced nonmagnetic-ferromagnetic transition. The calculated conductivity of cyclicgraphdiyne with 1/8, 1/4 and 3/8 hole doping concentration is much higher than that without doping or with 1/2 hole doping. These results make cyclicgraphdiyne really attractive. By studying several carbon monolayers, we find that a perfect flat band may occur in the lattices with both separated or corner-connected triangular motifs with only including nearest-neighboring hopping of electrons, and the dispersion of flat band can be tuned by next-nearest-neighboring hopping. Our results shed insightful light on the formation of flat band in TBG. The present study also poses an alternative way to manipulate magnetism through doping flat band in carbon materials.

Chern and Z2 topological insulating phases in perovskite-derived 4d and 5d oxide buckled honeycomb lattices

Based on density functional theory calculations including a Coulomb repulsion parameter U, we explore the topological properties of (LaXO₃)₂/(LaAlO₃)₄ (111) with X = 4d and 5d cations. The metastable ferromagnetic phases of LaTcO₃ and LaPtO₃ with preserved P321 symmetry emerge as Chern insulators (CI) with C = 2 and 1 and band gaps of 41 and 38 meV at the lateral lattice constant of LaAlO₃, respectively. Berry curvatures, spin textures as well as edge states provide additional insight into the nature of the CI states. While for X = Tc the CI phase is further stabilized under tensile strain, for X = Pd and Pt a site disproportionation takes place when increasing the lateral lattice constant from a_LAO to a_LNO. The CI phase of X = Pt shows a strong dependence on the Hubbard U parameter with sign reversal for higher values associated with the change of band gap opening mechanism. Parallels to the previously studied (X₂O₃)₁/(Al₂O₃)₅ (0001) honeycomb corundum layers are discussed. Additionally, non-magnetic systems with X = Mo and W are identified as potential candidates for Z₂ topological insulators at a_LAO with band gaps of 26 and 60 meV, respectively. The computed edge states and Z₂ invariants underpin the non-trivial topological properties.

Possible realization of the high-temperature and multichannel quantum anomalous Hall effect in graphene/CrBr3 heterostructures under pressure

The recent studies of magno-assisted tunnelling in ferromagnetic van der Waals heterostructures formed by graphene and ultrathin CrBr₃ films (D. Ghazaryan et al., Nat. Electron., 2018, 1, 344) offer broader opportunities for exploration of novel quantum phenomena, especially for realizing the graphene-based quantum anomalous Hall effect (QAHE). Based on first-principles approaches, we reveal that three types of graphene/CrBr₃ (Gr/CrBr₃) heterostructures exhibit metallic band behavior due to strong charge-transfer at the interfaces of these heterosystems. Remarkably, the pressure-induced QAHE can be achieved in Gr/CrBr₃ and CrBr₃/Gr/CrBr₃ systems. Further low energy k·p model analyses show that the nontrivial topological properties are mainly attributed to the Rashba spin-orbit coupling (SOC), but not to the intrinsic SOC of graphene. Moreover, a multichannel device prototype is proposed in the superlattices composed of Gr/CrBr₃ and normal insulator (such as hexagonal boron nitride) layers. Our work provides an experimentally feasible scheme for realizing the high-temperature and multichannel QAHE in graphene-based heterostructures.

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

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

Topological Dirac states in transition-metal monolayers on graphyne

Realizing topological Dirac states in two-dimensional (2D) magnetic materials is particularly important to spintronics. Here, we propose that such states can be obtained in a transition-metal (Hf) monolayer grown on a 2D substrate with hexagonal hollow geometry (graphyne). We find that the significant orbital hybridizations between Hf and C atoms can induce sizable magnetism and bring three Dirac cones at/around each high-symmetry K(K') point in the Brillouin zone. One Dirac cone is formed by pure spin-up electrons from the dz2 orbital of Hf, and the remaining two are formed by crossover between spin-up electrons from the dz2 orbital and spin-down electrons from the hybridization of the dxy/x2-y2 orbitals of Hf atoms and the pz orbital of C atoms. We also find that the spin-orbit coupling effect can open sizable band gaps for the Dirac cones. The Berry curvature calculations further show the nontrivial topological nature of the system with a negative Chern number C = -3, which is mainly attributed to the Dirac states. Molecular dynamics simulations confirm the system's thermodynamic stability approaching room temperature. The results provide a new avenue for realizing the high-temperature quantum anomalous Hall effect based on 2D transition-metals.

Scanning tunneling microscopy investigations of unoccupied surface states in two-dimensional semiconducting β-√3 × √3-Bi/Si(111) surface

Two-dimensional surface structures often host a surface state in the bulk gap, which plays a crucial role in the surface electron transport. The diversity of in-gap surface states extends the category of two-dimensional systems and gives us more choices in material applications. In this article, we investigated the surface states of β-√3 × √3-Bi/Si(111) surface by scanning tunneling microscopy. Two nearly free electron states in the bulk gap of silicon were found in the unoccupied states. Combined with first-principles calculations, these two states were verified to be the Bi-contributed surface states and electron-accumulation-induced quantum well states. Due to the spin-orbit coupling of Bi atoms, Bi-contributed surface states exhibit free-electron Rashba splitting. The in-gap surface states with spin splitting can possibly be used for spin polarized electronics applications.

Two-dimensional Au-1,3,5 triethynylbenzene organometallic lattice: Structure, half-metallicity, and gas sensing

On the basis of first-principles calculations, we investigated the structural and electronic properties of the two-dimensional (2D) Au-1,3,5 triethynylbenzene (Au-TEB) framework, which has been recently synthesized by homocoupling reactions in experiments. Featured by the C-Au-C linkage, the 2D Au-TEB network has a kagome lattice by Au atoms and a hexagonal lattice by organic molecules within the same metal-organic framework (MOF), which exhibits intrinsic half-metallicity with one spin channel metallic and the other spin channel fully insulating with a large energy gap of 2.8 eV. Two branches of kagome bands are located near the Fermi level, with each branch including one flat band and two Dirac bands, which originates from the out-of-plane d_xz and d_yz orbitals of Au and may lead to many exotic topological quantum phases. We further studied the adsorption of F atoms, Cl atoms, and small gas molecules including O₂, CO, NO₂, and NH₃ on the Au-TEB network, aiming to exploit its potential applications in gas sensors. Detailed analyses on adsorption geometry, energy, molecular orbital interaction, and electronic structure modification suggest the great potential of Au-TEP as a promising alternative for gas sensing. We expect these results to expand the universe of low-dimensional half-metallic MOF structures and shed new light on their practical applications in nanoelectronics/spintronics.

Double Kagome Bands in a Two-Dimensional Phosphorus Carbide P2C3

The interesting properties of Kagome bands, consisting of Dirac bands and a flat band, have attracted extensive attention. However, materials with only one Kagome band around the Fermi level cannot possess physical properties of Dirac Fermions and strong correlated Fermions simultaneously. Here, we propose a new type of band structure, double Kagome bands, which can realize coexistence of the two kinds of Fermions. Moreover, the new band structure is found to exist in a new two-dimensional material, phosphorus carbide P₂C₃. The carbide material shows good stability and unusual electronic properties. Strong magnetism appears in the structure by hole doping of the flat band, which results in spin splitting of the Dirac bands. The edge states induced by Dirac and flat bands coexist on the Fermi level, indicating outstanding transport characteristics. In addition, a possible route to experimentally grow P₂C₃ on some suitable substrates such as the Ag(111) surface is also discussed.

Quantum anomalous/valley Hall effect and tunable quantum state in hydrogenated arsenene decorated with a transition metal

The quantum anomalous Hall (QAH) effect is superior to the quantum spin Hall (QSH) effect, which can avoid the inelastic scattering of two edge electrons located on one side of a topological nontrivial material, and thus it has attracted both theoretical and experimental interest. Here, we systematically investigate the lattice structures, and electronic and magnetic properties of hydrogenated arsenene decorated with certain transition metals (Cr, Mo and Cu) based on density-functional theory. A unique QAH effect in Mo@AsH is predicted, whose Chern number (C = 1) indicates only one chiral edge channel located on its one side. Then, we prove that this QAH effect realization is closely related with band inversion, which is the competitive result between its spin-orbit coupling (SOC) strength and exchange field. The quantum state of Mo@AsH can also be tuned by an external strain, similar to SOC, and it is noted that its increased topological gap of about 35 meV under 5.0% tensile strain, is large enough to realize the QAH effect at room-temperature. Additionally, the quantum valley Hall effect in Cu@AsH contributed by the inequality of AB sublattices is also found. Our results reveal the physical mechanism to realize the QAH effect in TM@AsH and provide a platform for electrically controllable topological states, which are highly desirable for nanoelectronics and spintronics.

Quantum anomalous Hall effect in a stable 1T-YN2 monolayer with a large nontrivial bandgap and a high Chern number

The quantum anomalous Hall (QAH) effect is a topologically nontrivial phase, characterized by a non-zero Chern number defined in the bulk and chiral edge states in the boundary. Using first-principles calculations, we demonstrate the presence of the QAH effect in a 1T-YN2 monolayer, which was recently predicted to be a Dirac half metal without spin-orbit coupling (SOC). We show that the inclusion of SOC opens up a large nontrivial bandgap of nearly 0.1 eV in the electronic band structure. This results in the nontrivial bulk topology, which is confirmed by the calculation of Berry curvature, anomalous Hall conductance and the presence of chiral edge states. Remarkably, a QAH phase of high Chern number C = 3 is found, and there are three corresponding gapless chiral edge states emerging inside the bulk gap. Different substrates are also chosen to study the possible experimental realization of the 1T-YN2 monolayer, while retaining its nontrivial topological properties. Our results open a new avenue in searching for QAH insulators with high temperature and high Chern numbers, which can have nontrivial practical applications.

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

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

Nontrivial topology and topological phase transition in two-dimensional monolayer Tl

Topological insulating material with dissipationless edge states is a rising star in spintronics.

Self-texturizing electronic properties of a 2-dimensional GdAu2 layer on Au(111): the role of out-of-plane atomic displacement

Here, we show that the electronic properties of a surface-supported 2-dimensional (2D) layer structure can self-texturize at nanoscale. The local electronic properties are determined by structural relaxation processes through variable adsorption stacking configurations. We demonstrate that the spatially modulated layer-buckling, which arises from the lattice mismatch and the layer/substrate coupling at the GdAu₂/Au(111) interface, is sufficient to locally open an energy gap of ∼0.5 eV at the Fermi level in an otherwise metallic layer. Additionally, this out-of-plane displacement of the Gd atoms patterns the character of the hybridized Gd-d states and shifts the center of mass of the Gd 4f multiplet proportionally to the lattice distortion. These findings demonstrate the close correlation between the electronic properties of the 2D-layer and its planarity. We demonstrate that the resulting template shows different chemical reactivities which may find important applications.

Prediction of topological crystalline insulators and topological phase transitions in two-dimensional PbTe films

Topological phases, especially topological crystalline insulators (TCIs), have been intensively explored and observed experimentally in three-dimensional (3D) materials. However, two-dimensional (2D) films are explored much less than 3D TCIs, and even 2D topological insulators. Based on ab initio calculations, here we investigate the electronic and topological properties of 2D PbTe(001) few-layer films. The monolayer and trilayer PbTe are both intrinsic 2D TCIs with a large band gap reaching 0.27 eV, indicating a high possibility for room-temperature observation of quantized conductance. The origin of the TCI phase can be attributed to the p_x,y-p_z band inversion, which is determined by the competition of orbital hybridization and the quantum confinement effect. We also observe a semimetal-TCI-normal insulator transition under biaxial strains, whereas a uniaxial strain leads to Z₂ nontrivial states. In particular, the TCI phase of a PbTe monolayer remains when epitaxially grown on a NaI semiconductor substrate. Our findings on the controllable quantum states with sizable band gaps present an ideal platform for realizing future topological quantum devices with ultralow dissipation.

An sd2 hybridized transition-metal monolayer with a hexagonal lattice: reconstruction between the Dirac and kagome bands

Graphene-like two-dimensional materials have garnered tremendous interest as emerging device materials due to their remarkable properties. However, their applications in spintronics have been limited by the lack of intrinsic magnetism. Here, we perform an ab initio simulation on the structural and electronic properties of several transition-metal (TM) monolayers (TM = Cr, Mo and W) with a honeycomb lattice on a 1/3 monolayer Cl-covered Si(111) surface. Due to the template effect from the halogenated Si substrate, the TM-layers will be maintained in an expanded lattice which is nearly 60% larger than that of the freestanding case. All these isolated TM-layers exhibit ferromagnetic coupling with kagome band structures related to sd² hybridization and a strong interfacial interaction may destroy the topological bands. Interestingly, the W-monolayer on the Cl-covered Si substrate shows a half-metallic behavior. A Dirac point formed at the K point in the spin-down channel is located exactly at the Fermi level which is crucial for the realization of a quantum spin Hall state. Moreover, the reconstruction process between the Dirac and kagome bands is discussed in detail, providing an interesting platform to study the interplay between massless Dirac fermions and heavy fermions.

Tunable Dirac cones in two-dimensional covalent organic materials: C2N6S3 and its analogs

C₂N₆S₃ sustains a biaxial tensile strain up to 24% and its Fermi velocity can be tuned by biaxial strain.

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).

Coexisting Honeycomb and Kagome Characteristics in the Electronic Band Structure of Molecular Graphene

We uncover the electronic structure of molecular graphene produced by adsorbed CO molecules on a copper (111) surface by means of first-principles calculations. Our results show that the band structure is fundamentally different from that of conventional graphene, and the unique features of the electronic states arise from coexisting honeycomb and Kagome symmetries. Furthermore, the Dirac cone does not appear at the K-point but at the Γ-point in the reciprocal space and is accompanied by a third, almost flat band. Calculations of the surface structure with Kekulé distortion show a gap opening at the Dirac point in agreement with experiments. Simple tight-binding models are used to support the first-principles results and to explain the physical characteristics behind the electronic band structures.

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.

Intrinsic Two-Dimensional Organic Topological Insulators in Metal-Dicyanoanthracene Lattices

We predict theoretical existence of intrinsic two-dimensional organic topological insulator (OTI) states in Cu-dicyanoanthracene (DCA) lattice, a system that has also been grown experimentally on Cu substrate, based on first-principle density functional theory calculations. The pz-orbital Kagome bands having a Dirac point lying exactly at the Fermi level are found in the freestanding Cu-DCA lattice. The tight-binding model analysis, the calculated Chern numbers, and the semi-infinite Dirac edge states within the spin-orbit coupling gaps all confirm its intrinsic topological properties. The intrinsic TI states are found to originate from a proper number of electrons filling of the hybridized bands from Cu atomic and DCA molecular orbitals based on which similar lattices containing noble metal atoms (Au and Cu) and those molecules with two CN groups (DCA and cyanogens) are all predicted to be intrinsic OTIs.

Formation of a quantum spin Hall state on a Ge(111) surface

Using first-principles density functional theory (DFT) hybrid functional calculations, we demonstrate the formation of a quantum spin Hall (QSH) state on a Ge(111) surface. We show that a 1/3 monolayer (ML) Cl-covered Ge(111) surface offers an ideal template for metal, such as Bi, deposition into a stable hexagonal overlayer 2D lattice, which we refer to as Bi@Cl-Ge(111). The band structure and band topology of Bi@Cl-Ge(111) are analyzed with respect to the effect of spin-orbit coupling (SOC). The Bi@Cl-Ge(111) exhibits a QSH state with a band gap of 0.54 eV. In contrast, the Au@Cl-Ge(111) is found to be a trivial semiconducting surface. The Ge(111) substrate acts as an orbital filter to critically select the orbital composition around the Fermi level. Our findings offer another possible system for experimental exploration of the growth of 2D topological materials on conventional semiconductor substrates, where the 2D overlayer is atomically bonded to, but electronically decoupled from, the underlying substrate, exhibiting an isolated topological quantum state inside the substrate band gap.

Formation of Ideal Rashba States on Layered Semiconductor Surfaces Steered by Strain Engineering

Spin splitting of Rashba states in two-dimensional electron system provides a promising mechanism of spin manipulation for spintronics applications. However, Rashba states realized experimentally to date are often outnumbered by spin-degenerated substrate states at the same energy range, hindering their practical applications. Here, by density functional theory calculation, we show that Au one monolayer film deposition on a layered semiconductor surface β-InSe(0001) can possess "ideal" Rashba states with large spin splitting, which are completely situated inside the large band gap of the substrate. The position of the Rashba bands can be tuned over a wide range with respect to the substrate band edges by experimentally accessible strain. Furthermore, our nonequilibrium Green's function transport calculation shows that this system may give rise to the long-sought strong current modulation when made into a device of Datta-Das transistor. Similar systems may be identified with other metal ultrathin films and layered semiconductor substrates to realize ideal Rashba states.

Two-Dimensional Rectangular and Honeycomb Lattices of NbN: Emergence of Piezoelectric and Photocatalytic Properties at Nanoscale

Using first-principles calculations, we predict that monolayered honeycomb and rectangular two-dimensional (2D) lattice forms of NbN are metastable and naturally derivable from different orientations of its rocksalt structure. While the rectangular form is shown to retain the metallic and superconducting (SC) properties of the bulk, spectacularly contrasting properties emerge in the honeycomb form of NbN: it exhibits (a) semiconducting electronic structure suitable for valleytronics and photocatalysis of water splitting, (b) piezoelectricity with a spontaneous polarization originating from a rare sd(2)-sp(2) type hybridization, and (c) a wide gap in its phonon spectrum making it suitable for use in hot carrier solar cells. Our work demonstrates how low coordination numbers and associated strong bonding stabilize 2D nanoforms of covalently bonded solids and introduce novel functionalities of technological importance.

Prediction of flatness-driven quantum spin Hall effect in functionalized germanene and stanene

We used first-principles calculations to predict a class of new QSH phases for f-Ge(Sn)X₂ films, which are useful for applications because of not only their sizable nontrivial bulk gaps, but also the tunability of the QSH states by chemical functionalization.

Highly Anisotropic Dirac Fermions in Square Graphynes

We predict a family of 2D carbon (C) allotropes, square graphynes (S-graphynes) that exhibit highly anisotropic Dirac fermions, using first-principle calculations within density functional theory. They have a square unit-cell containing two sizes of square C rings. The equal-energy contour of their 3D band structure shows a crescent shape, and the Dirac crescent has varying Fermi velocities from 0.6 × 10(5) to 7.2 × 10(5) m/s along different k directions. Near the Fermi level, the Dirac crescent can be nicely expressed by an extended 2D Dirac model Hamiltonian. Furthermore, tight-binding band fitting reveals that the Dirac crescent originates from the next-nearest-neighbor interactions between C atoms. S-graphynes may be used to build new 2D electronic devices taking advantages of their highly directional charge transport.

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.