Realization of Symmetry-Enforced Two-Dimensional Dirac Fermions in Nonsymmorphic α-Bismuthene

Ferroelectric Semimetals with α-Bi/SnSe van der Waals Heterostructures and Their Topological Currents

We show that proximity effects can be utilized to engineer van der Waals heterostructures (vdWHs) displaying semimetallic spin-ferroelectricity locking, where ferroelectricity and semimetallic spin states are confined to different layers, but are correlated by means of proximity effects. Our findings are supported by first principles calculations involving α-Bi/SnSe bilayers. We show that such systems support ferroelectrically switchable nonlinear anomalous Hall effect originating from large Berry curvature dipoles as well as direct and inverse spin Hall effects with giant bulk spin-charge interconversion efficiencies. The giant efficiencies are consequences of the proximity-induced semimetallic nature of low energy electron states, which are shown to behave as two-dimensional pseudo-Weyl fermions by means of symmetry analysis and first principles calculations as well as direct angle-resolved photoemission spectroscopy measurements.

Realization of a two-dimensional Weyl semimetal and topological Fermi strings

A two-dimensional (2D) Weyl semimetal, akin to a spinful variant of graphene, represents a topological matter characterized by Weyl fermion-like quasiparticles in low dimensions. The spinful linear band structure in two dimensions gives rise to distinctive topological properties, accompanied by the emergence of Fermi string edge states. We report the experimental realization of a 2D Weyl semimetal, bismuthene monolayer grown on SnS(Se) substrates. Using spin and angle-resolved photoemission and scanning tunneling spectroscopies, we directly observe spin-polarized Weyl cones, Weyl nodes, and Fermi strings, providing consistent evidence of their inherent topological characteristics. Our work opens the door for the experimental study of Weyl fermions in low-dimensional materials.

Photoinduced Electronic and Spin Topological Phase Transitions in Monolayer Bismuth

Ultrathin bismuth exhibits rich physics including strong spin-orbit coupling, ferroelectricity, nontrivial topology, and light-induced structural dynamics. We use ab initio calculations to show that light can induce structural transitions to four transient phases in bismuth monolayers. These light-induced phases exhibit nontrivial topological character, which we illustrate using the recently introduced concept of spin bands and spin-resolved Wilson loops. Specifically, we find that the topology changes via the closing of the electron and spin band gaps during photoinduced structural phase transitions, leading to distinct edge states. Our study provides strategies to tailor electronic and spin topology via ultrafast control of photoexcited carriers and associated structural dynamics.

Giant and Nonanalytic Negative Piezoelectric Response in Elemental Group-Va Ferroelectric Monolayers

Materials with negative longitudinal piezoelectric response have been a focus of recent research. So far, reported examples are mostly three-dimensional bulk materials, either compounds with strong ionic bonds or layered materials with van der Waals interlayer gaps. Here, we report the first example in two-dimensional elemental materials-the class of group-Va monolayers. From first-principles calculations, we show that these materials possess giant negative longitudinal piezoelectric coefficient e_{11}. Importantly, its physical mechanism is also distinct from all previous proposals, connected with the special buckling driven polarization in these elemental systems. As a result, the usually positive internal strain contribution to piezoelectricity becomes negative and even dominates over the clamped ion contribution in Bi monolayers. Based on this new mechanism, we also find several 2D crystal structures that may support negative longitudinal piezoelectricity. As another consequence, piezoelectric response in Bi monolayers exhibits a significant nonanalytic behavior, namely, the e_{11} coefficient takes sizably different values (differed by ∼18%) under tensile and compressive strains, a phenomenon not known before and helpful for the development of novel electromechanical devices.

1D Electronic Flat Bands in Untwisted Moiré Superlattices

After the preparation of 2D electronic flat band (EFB) in van der Waals (vdW) superlattices, recent measurements suggest the existence of 1D electronic flat bands (1D-EFBs) in twisted vdW bilayers. However, the realization of 1D-EFBs is experimentally elusive in untwisted 2D layers, which is desired considering their fabrication and scalability. Herein, the discovery of 1D-EFBs is reported in an untwisted in situ-grown two atomic-layer Bi(110) superlattice self-aligned on an SnSe(001) substrate using scanning probe microscopy measurements and density functional theory calculations. While the Bi-Bi dimers of Bi zigzag (ZZ) chains are buckled, the epitaxial lattice mismatch between the Bi and SnSe layers induces two 1D buckling reversal regions (BRRs) extending along the ZZ direction in each Bi(110)-11 × 11 supercell. A series of 1D-EFBs arises spatially following BRRs that isolate electronic states along the armchair (AC) direction and localize electrons in 1D extended states along ZZ due to quantum interference at a topological node. This work provides a generalized strategy for engineering 1D-EFBs in utilizing lattice mismatch between untwisted rectangular vdW layers.

InBi: A Ferroelastic Monolayer with Strain Tunable Spin-Orbit Dirac Points and Carrier Self-Doping Effect

Semimetallic two-dimensional (2D) Dirac materials beyond graphene, especially 2D materials with robust Dirac points against the spin-orbit coupling (SOC), are still highly sought. Herein, we theoretically demonstrate the InBi monolayer as a long-sought 2D Dirac material whose exotic Dirac Fermionic states cannot be gapped out by SOC. The InBi monolayer with the litharge crystal structure possesses not only 4-fold band degeneracy, linear energy dispersion, and ultrahigh Fermi velocity in the order of 10⁵ m/s, but also spontaneous ferroelasticity that can lead to the orthorhombic lattice deformation and semimetallic electronic structure. Specifically, the symmetry protected spin-orbit Dirac points in 2D InBi are located at the Brillouin Zone (BZ) boundary and near the Fermi level in energy. More importantly, with coexisting spin-orbit Dirac points and spontaneous ferroelasticity, the InBi monolayer exhibits an additional advantage for engineering Dirac Fermionic states by ferroelastic (FE) strain. Energy levels of Dirac points are strongly coupled to FE strain, and the semimetallic electronic structure of the InBi monolayer is also susceptible to the FE strain induced carrier self-doping effect. Depending on the strain orientation within the InBi monolayer, electron and hole Fermi pockets will develop along the two planar directions, leading to the characteristic transport coefficients (as evidenced by our transport simulations based on Boltzmann formalism) for future experimental detection. FE strain tunable Dirac Fermionic states together with the carrier self-doping effect will benefit future development of ultrathin electronic devices with both high carrier mobility and controllable charge conductivities.

Realization of unpinned two-dimensional dirac states in antimony atomic layers

Two-dimensional (2D) Dirac states with linear dispersion have been observed in graphene and on the surface of topological insulators. 2D Dirac states discovered so far are exclusively pinned at high-symmetry points of the Brillouin zone, for example, surface Dirac states at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\overline{{{\Gamma }}}$$\end{document}Γ¯ in topological insulators Bi₂Se(Te)₃ and Dirac cones at K and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$K^{\prime}$$\end{document}K′ points in graphene. The low-energy dispersion of those Dirac states are isotropic due to the constraints of crystal symmetries. In this work, we report the observation of novel 2D Dirac states in antimony atomic layers with phosphorene structure. The Dirac states in the antimony films are located at generic momentum points. This unpinned nature enables versatile ways such as lattice strains to control the locations of the Dirac points in momentum space. In addition, dispersions around the unpinned Dirac points are highly anisotropic due to the reduced symmetry of generic momentum points. The exotic properties of unpinned Dirac states make antimony atomic layers a new type of 2D Dirac semimetals that are distinct from graphene.

In graphene and on the surfaces of many topological insulators, the Dirac cones are pinned to high symmetry points in reciprocal space. Here, the authors report that the Dirac cones in atomically-thin Sb layers occur at generic reciprocal-space points which can be tuned by lattice strain.

Thickness dependent band structure of-bismuthene grown on epitaxial graphene

Along with the great interest in two-dimensional elemental materials that has emerged in recent years, atomically thin layers of bismuth have attracted attention due to physical properties on account of a strong spin-orbit coupling. Thickness dependent electronic band structure must be explored over the whole Brillouin zone in order to further explore their topological electronic properties. The anisotropic band structures along zig-zag and armchair directions of α-bismuthene (α-Bi) were resolved using the two-dimensional mapping of angle-resolved photoemission spectra. An increase in the number of layers from 1- to 2-bilayers (BLs) shifts the top of a hole band onΓ¯-X¯1line to high wavenumber regions. Subsequently, an electron pocket onΓ¯-X¯1line and a hole pocket centred atΓ¯point appears in the 3 BL α-Bi. Gapless Dirac-cone features with a large anisotropy were clearly resolved onX¯2point in the 1-BL and 2-BL α-Bi, which can be attributed to the strong spin-orbit coupling and protection by the nonsymmorphic symmetry of the α-Bi lattice.

Electronic Structures of Polymorphic Layers of Borophane

The search for free-standing 2D materials has been one of the most important subjects in the field of studies on 2D materials and their applications. Recently, a free-standing monolayer of hydrogenated boron (HB) sheet has been synthesized by hydrogenation of borophene. The HB sheet is also called borophane, and its application is actively studied in many aspects. Here, we review recent studies on the electronic structures of polymorphic sheets of borophane. A hydrogenated boron sheet with a hexagonal boron frame was shown to have a semimetallic electronic structure by experimental and theoretical analyses. A tight-binding model that reproduces the electronic structure was given and it allows easy estimation of the properties of the material. Hydrogenated boron sheets with more complicated nonsymmorphic boron frames were also analyzed. Using the symmetry restrictions from the nonsymmorphic symmetry and the filling factor of hydrogenated boron sheets, the existence of a Dirac nodal line was suggested. These studies provide basic insights for research on and device applications of hydrogenated boron sheets.

Quantum Size Effects, Multiple Dirac Cones, and Edge States in Ultrathin Bi(110) Films

The presence of inherently strong spin-orbit coupling in bismuth, its unique layer-dependent band topology and high carrier mobility make it an interesting system for both fundamental studies and applications. Theoretically, it has been suggested that strong quantum size effects should be present in the Bi(110) films, with the possibility of Dirac Fermion states in the odd-bilayer (BL) films, originating from dangling p_z orbitals and quantum-spin hall (QSH) states in the even-bilayer films. However, the experimental verification of these claims has been lacking. Here, we study the electronic structure of Bi(110) films grown on a high-T_c superconductor, Bi₂Sr₂CaCu₂O_8+δ (Bi2212) using angle-resolved photoemission spectroscopy (ARPES). We observe an oscillatory behavior of electronic structure with the film thickness and identify the Dirac-states in the odd-bilayer films, consistent with the theoretical predictions. In the even-bilayer films, we find another Dirac state that was predicted to play a crucial role in the QSH effect. In the low thickness limit, we observe several extremely one-dimensional states, probably originating from the edge-states of Bi(110) islands. Our results provide a much needed experimental insight into the electronic and structural properties of Bi(110) films.

Robust Topological Nodal-Line Semimetals from Periodic Vacancies in Two-Dimensional Materials

A nodal-line semimetal (NLSM) is suppressed in the presence of spin-orbit coupling unless it is protected by a nonsymmorphic symmetry. We show that two-dimensional (2D) materials can realize robust NLSMs when vacancies are introduced on the lattice. As a case study we investigate borophene, a boron honeycomb-like sheet. While the Dirac cones of pristine borophene are shown to be gapped out by spin-orbit coupling and by magnetic exchange, robust nodal lines (NLs) emerge in the spectrum when selected atoms are removed. We propose an effective 2D model and a symmetry analysis to demonstrate that these NLs are topological and protected by a nonsymmorphic glide plane. Our findings offer a paradigm shift to the design of NLSMs: instead of searching for nonsymmorphic materials, robust NLSMs may be realized simply by removing atoms from ordinary symmorphic crystals.

Antimony oxide nanostructures in the monolayer limit: self-assembly of van der Waals-bonded molecular building blocks

Antimony oxide nanostructures have been identified as candidates for a range of electronic and optoelectronic applications. Here we demonstrate the growth of 2-dimensional antimony oxide nanostructures on various substrates, including highly oriented pyrolytic graphite (HOPG), MoS₂ and α-Bi(110) nanoislands. Using scanning tunneling microscopy (STM) we show that the nanostructures formed are exclusively highly crystalline α-Sb₂O₃(111) monolayers with a lattice constant of 796 pm ± 7 pm. The nanostructures are triangular with lateral dimensions of up to ∼30 nm. Even though elemental antimony nanostructures are grown simultaneously mixed phases are not observed and both materials exhibit their own distinct growth modes. Moiré patterns are also observed and simulated, allowing confirmation of the atomic unit cell and an understanding of the orientation of the Sb₂O₃ structures with respect to the supporting materials. As in the bulk, the Sb₂O₃ nanostructures are formed from Sb₄O₆ molecules that are weakly interacting through van der Waals forces. This allows physical modification of the nanostructures with the STM tip. Scanning tunnelling spectroscopy reveals a wide band gap of at least 3.5 eV. Finally, we show that possible alternative structures that have unit cells comparable to those observed can be excluded based on our DFT calculations. The considered structures are a 2 × 2 reconstruction of β-Sb with one vacancy per unit cell and a van der Waals solid composed of Sb₄ clusters. Previous reports have predominantly demonstrated Sb₂O₃ structures with much larger thicknesses.

Polymorphism in Post-Dichalcogenide Two-Dimensional Materials

Two-dimensional (2D) materials exhibit a wide range of atomic structures, compositions, and associated versatility of properties. Furthermore, for a given composition, a variety of different crystal structures (i.e., polymorphs) can be observed. Polymorphism in 2D materials presents a fertile landscape for designing novel architectures and imparting new functionalities. The objective of this Review is to identify the polymorphs of emerging 2D materials, describe their polymorph-dependent properties, and outline methods used for polymorph control. Since traditional 2D materials (e.g., graphene, hexagonal boron nitride, and transition metal dichalcogenides) have already been studied extensively, the focus here is on polymorphism in post-dichalcogenide 2D materials including group III, IV, and V elemental 2D materials, layered group III, IV, and V metal chalcogenides, and 2D transition metal halides. In addition to providing a comprehensive survey of recent experimental and theoretical literature, this Review identifies the most promising opportunities for future research including how 2D polymorph engineering can provide a pathway to materials by design.

Anisotropic thermoelectric effect and field-effect devices in epitaxial bismuthene on Si (111)

This experimental study reveals intriguing thermoelectric effects and devices in epitaxial bismuthene, two-dimensional (2D) bismuth with thickness ⩽30 nm, on Si (111). Bismuthene exhibits interesting anisotropic Seebeck coefficients varying 2-5 times along different crystal orientations, implying the existence of a puckered atomic structure like black phosphorus. An absolute value of Seebeck coefficient up to 237 μV K^-1 sets a record for elemental Bi ever measured to the best of our knowledge. Electrical conductivity of bismuthene can reach up to 4.6 × 10⁴ S m^-1, which is sensitive to thickness and magnetic field. Along with a desired low thermal conductivity ∼1.97 W m^-1 K that is 20% of its bulk form, the first experimental zT value at room temperature for bismuthene was measured ∼10^-2, which is much higher than many other VA Xenes and comparable to its bulk compounds. Above results suggest a mixed buckled and puckered Bi atomic structure for epitaxial 2D bismuth on Si (111). Our work paves the way to explore potential applications, such as heat flux sensor, energy converting devices and so on for bismuthene.

Universal Approach to Magnetic Second-Order Topological Insulator

We propose a universal practical approach to realize magnetic second-order topological insulator (SOTI) materials, based on properly breaking the time reversal symmetry in conventional (first-order) topological insulators. The approach works for both three dimensions (3D) and two dimensions (2D), and is particularly suitable for 2D, where it can be achieved by coupling a quantum spin Hall insulator with a magnetic substrate. Using first-principles calculations, we predict bismuthene on EuO(111) surface as the first realistic system for a two-dimensional magnetic SOTI. We explicitly demonstrate the existence of the protected corner states. Benefitting from the large spin-orbit coupling and sizable magnetic proximity effect, these corner states are located in a boundary gap ∼83  meV, and hence can be readily probed in experiment. By controlling the magnetic phase transition, a topological phase transition between a first-order TI and a SOTI can be simultaneously achieved in the system. The effect of symmetry breaking, the connection with filling anomaly, and the experimental detection are discussed.