Topological Complex Charge Conservation in Nontrivial Z2 × Z2 Domain Walls.

Localized topological modes such as solitons, Majorana Fermions, and skyrmions are attracting great interest as robust information carriers for future devices. Here, a novel conserved quantity for topological domain wall networks of a Z2 × Z2 order generated with spin-polarized current in Sr2VO3FeAs is discovered. Domain walls are mobilized by the scanning tunneling current, which also observes in atomic scale active dynamics of domain wall vertices including merge, bifurcation, pair creation, and annihilation. Within this dynamics, the product of the topological complex charges defined for domain wall vertices is conserved with a novel boundary-charge correspondence rule. These results may open an avenue toward topological electronics based on domain wall vertices in generic Z2 × Z2 systems.

Control over a Wide Phase Diagram of 2D Correlated Electrons by Surface Doping; K/1T-TaS2.

We demonstrate the systematic tuning of a trivial insulator into a Mott insulator and a Mott insulator into a correlated metallic and a pseudogap state, which emerge in a quasi-two-dimensional electronic system of 1T-TaS2 through strong electron correlation. The band structure evolution is investigated upon surface doping by alkali adsorbates for two distinct phases occurring at around 220 and 10 K by angle-resolved photoelectron spectroscopy. We find contrasting behaviors upon doping that corroborate the fundamental difference of two electronic states: while the antibonding state of the spin-singlet insulator at 10 K is partially occupied to produce an emerging Mott insulating state, the presumed Mott insulating state at 220 K evolves into a correlated metallic state and then a pseudogap state. The work indicates that surface doping onto correlated 2D materials can be a powerful tool to systematically engineer a wide range of correlated electronic phases.

Topological quantum devices: a review.

The introduction of the concept of topology into condensed matter physics has greatly deepened our fundamental understanding of transport properties of electrons as well as all other forms of quasi particles in solid materials. It has also fostered a paradigm shift from conventional electronic/optoelectronic devices to novel quantum devices based on topology-enabled quantum device functionalities that transfer energy and information with unprecedented precision, robustness, and efficiency. In this article, the recent research progress in topological quantum devices is reviewed. We first outline the topological spintronic devices underlined by the spin-momentum locking property of topology. We then highlight the topological electronic devices based on quantized electron and dissipationless spin conductivity protected by topology. Finally, we discuss quantum optoelectronic devices with topology-redefined photoexcitation and emission. The field of topological quantum devices is only in its infancy, we envision many significant advances in the near future.

Realizing a Superconducting Square-Lattice Bismuth Monolayer.

Interplay of crystal symmetry, strong spin-orbit coupling (SOC), and many-body interactions in low-dimensional materials provides a fertile ground for the discovery of unconventional electronic and magnetic properties and versatile functionalities. Two-dimensional (2D) allotropes of group 15 elements are appealing due to their structures and controllability over symmetries and topology under strong SOC. Here, we report the heteroepitaxial growth of a proximity-induced superconducting 2D square-lattice bismuth monolayer on superconducting Pb films. The square lattice of monolayer bismuth films in a C4 symmetry together with a stripey moiré structure is clearly resolved by our scanning tunneling microscopy, and its atomic structure is revealed by density functional theory (DFT) calculations. A Rashba-type spin-split Dirac band is predicted by DFT calculations to exist at the Fermi level and becomes superconducting through the proximity effect from the Pb substrate. We suggest the possibility of a topological superconducting state in this system with magnetic dopants/field. This work introduces an intriguing material platform with 2D Dirac bands, strong SOC, topological superconductivity, and the moiré superstructure.

Tunable Mott Dirac and Kagome Bands Engineered on 1T-TaS2.

Strongly interacting electrons in hexagonal and kagome lattices exhibit rich phase diagrams of exotic quantum states, including superconductivity and correlated topological orders. However, material realizations of these electronic states have been scarce in nature or by design. Here, we theoretically propose an approach to realize artificial lattices by metal adsorption on a 2D Mott insulator 1T-TaS2. Alkali, alkaline-earth, and group 13 metal atoms are deposited in (√3 × âˆš3)R30° and 2 × 2 TaS2 superstructures of honeycomb- and kagome-lattice symmetries exhibiting Dirac and kagome bands, respectively. The strong electron correlation of 1T-TaS2 drives the honeycomb and kagome systems into correlated topological phases described by Kane-Mele-Hubbard and kagome-Hubbard models. We further show that the 2/3 or 3/4 band filling of Mott Dirac and flat bands can be achieved with a proper concentration of Mg adsorbates. Our proposal may be readily implemented in experiments, offering an attractive condensed-matter platform to exploit the interplay of correlated topological order and superconductivity.

Enhanced Berry Curvature Dipole and Persistent Spin Texture in the Bi(110) Monolayer.

Nonvanishing Berry curvature dipole (BCD) and persistent spin texture (PST) are intriguing physical manifestations of electronic states in noncentrosymmetric 2D materials. The former induces a nonlinear Hall conductivity while the latter offers a coherent spin current. Based on density-functional-theory (DFT) calculations, we demonstrate the coexistence of both phenomena in a Bi(110) monolayer with a distorted phosphorene structure. Both effects are concurrently enhanced due to the strong spin-orbit coupling of Bi while the structural distortion creates internal in-plane ferroelectricity with inversion asymmetry. We further succeed in fabricating a Bi(110) monolayer in the desired phosphorene structure on the NbSe2 substrate. Detailed atomic and electronic structures of the Bi(110)/NbSe2 heterostructure are characterized by scanning tunneling microscopy/spectroscopy and angle-resolved-photoemission spectroscopy. These results are consistent with DFT calculations which indicate the large BCD and PST are retained. Our results suggest the Bi(110)/NbSe2 heterostructure as a promising platform to exploit nonlinear Hall and coherent spin transport properties together.

Distinguishing a Mott Insulator from a Trivial Insulator with Atomic Adsorbates.

In an electronic system with various interactions intertwined, revealing the origin of its many-body ground state is challenging and a direct experimental way to verify the correlated nature of an insulator has been lacking. Here we demonstrate a way to unambiguously distinguish a paradigmatic correlated insulator, a Mott insulator, from a trivial band insulator based on their distinct chemical behavior for a surface adsorbate using 1T-TaS_{2}, which has been debated between a spin-frustrated Mott insulator or a spin-singlet trivial insulator. We start from the observation of different sizes of spectral gaps on different surface terminations and show that potassium adatoms on these two surface layers behave in totally different ways. This can be straightforwardly understood from distinct properties of Mott and band insulators due to the fundamental difference of the half- and full-filled orbitals involved, respectively. This work not only solves an outstanding problem in this particularly interesting material but also provides a simple touchstone to identify the correlated ground state of electrons experimentally.

Honeycomb-Lattice Mott Insulator on Tantalum Disulphide.

Effects of electron many-body interactions amplify in an electronic system with a narrow bandwidth opening a way to exotic physics. A narrow band in a two-dimensional (2D) honeycomb lattice is particularly intriguing as combined with Dirac bands and topological properties but the material realization of a strongly interacting honeycomb lattice described by the Kane-Mele-Hubbard model has not been identified. Here we report a novel approach to realize a 2D honeycomb-lattice narrow-band system with strongly interacting 5d electrons. We engineer a well-known triangular lattice 2D Mott insulator 1T-TaS_{2} into a honeycomb lattice utilizing an adsorbate superstructure. Potassium (K) adatoms at an optimum coverage deplete one-third of the unpaired d electrons and the remaining electrons form a honeycomb lattice with a very small hopping. Ab initio calculations show extremely narrow Z_{2} topological bands mimicking the Kane-Mele model. Electron spectroscopy detects an order of magnitude bigger charge gap confirming the substantial electron correlation as confirmed by dynamical mean field theory. It could be the first artificial Mott insulator with a finite spin Chern number.

1D topological phases in transition-metal monochalcogenide nanowires.

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

A 2D nonsymmorphic Dirac semimetal in a chemically modified group-VA monolayer with a black phosphorene structure.

A symmetry-protected 2D Dirac semimetal has attracted intense interest for its intriguing material properties. Here, we report a 2D nonsymmorphic Dirac semimetal state in a chemically modified group-VA 2D puckered structure. Based on first-principles calculations, we demonstrate the existence of 2D Dirac fermions in a one-side modified phosphorene structure in two different types: one with a Dirac nodal line (DNL) structure for light elements with negligible spin-orbit coupling (SOC) and the other having an hourglass band protected by a nonsymmorphic symmetry for heavy elements with strong SOC. In the absence of SOC, the DNL exhibits an anisotropic behavior and unique electronic properties, such as constant density of states. The Dirac node is protected from gap opening by the nonsymmorphic space group symmetry. In the presence of SOC, the DNL states split and form an hourglass-shaped dispersion due to the broken inversion symmetry and the Rashba SOC interaction. Moreover, around certain high symmetry points in the Brillouin zone, the spin orientation is enforced to be along a specific direction. We construct an effective tight-binding model to characterize the 2D nonsymmorphic Dirac states. Our result provides a promising material platform for exploring the intriguing properties of essential nodal-line and nodal-point fermions in 2D systems.

Intrinsic quantum anomalous hall effect in a two-dimensional anilato-based lattice.

Using first-principles calculations, we predict an intrinsic quantum anomalous Hall (QAH) state in a monolayer anilato-based metal-organic framework M2(C6O4X2)3 (M = Mn and Tc, X = F, Cl, Br and I). The spin-orbit coupling of M d orbitals opens a nontrivial band gap up to 18 meV at the Dirac point. The electron counting rule is used to explain the intrinsic nature of the QAH state. The calculated nonzero Chern number, gapless edge states and quantized Hall conductance all confirm the nontrivial topological properties in the anilato-based lattice. Our findings provide an organic materials platform for the realization of the QAH effect without the need for magnetic and charge doping, which are highly desirable for the development of low-energy-consumption spintronic devices.

Alloy Engineering of Topological Semimetal Phase Transition in MgTa_{2-x}Nb_{x}N_{3}.

Dirac, triple-point, and Weyl fermions represent three topological semimetal phases, characterized with a descending degree of band degeneracy, which have been realized separately in specific crystalline materials with different lattice symmetries. Here we demonstrate an alloy engineering approach to realize all three types of fermions in one single material system of MgTa_{2-x}Nb_{x}N_{3}. Based on symmetry analysis and first-principles calculations, we map out a phase diagram of topological order in the parameter space of alloy concentration and crystalline symmetry, where the intrinsic MgTa_{2}N_{3} with the highest symmetry hosts the Dirac semimetal phase, which transforms into the triple-point and then the Weyl semimetal phases with increasing Nb concentration that lowers the crystalline symmetries. Therefore, alloy engineering affords a unique approach for the experimental investigation of topological transitions of semimetallic phases manifesting different fermionic behaviors.

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 (px, py and pz). The essential mechanism can be understood by the fact while in 3D, the pz 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 px-py 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.

Topological Electride Y2C.

Two-dimensional (2D) electrides are layered ionic crystals in which anionic electrons are confined in the interlayer space. Here, we report a discovery of nontrivial [Formula: see text] topology in the electronic structures of 2D electride Y2C. Based on first-principles calculations, we found a topological [Formula: see text] invariant of (1; 111) for the bulk band and topologically protected surface states in the surfaces of Y2C, signifying its nontrivial electronic topology. We suggest a spin-resolved angle-resolved photoemission spectroscopy (ARPES) measurement to detect the unique helical spin texture of the spin-polarized topological surface state, which will provide characteristic evidence for the nontrivial electronic topology of Y2C. Furthermore, the coexistence of 2D surface electride states and topological surface state enables us to explain the outstanding discrepancy between the recent ARPES experiments and theoretical calculations. Our findings establish a preliminary link between the electride in chemistry and the band topology in condensed-matter physics, which are expected to inspire further interdisciplinary research between these fields.

Nanostructured topological state in bismuth nanotube arrays: inverting bonding-antibonding levels of molecular orbitals.

We demonstrate a new class of nanostructured topological materials that exhibit a topological quantum phase arising from nanoscale structural motifs. Based on first-principles calculations, we show that an array of bismuth nanotubes (Bi-NTs), a superlattice of Bi-NTs with periodicity in the order of tube diameter, behaves as a nanostructured two-dimensional (2D) quantum spin Hall (QSH) insulator, as confirmed from the calculated band topology and 1D helical edge states. The underpinning mechanism of the QSH phase in the Bi-NT array is revealed to be inversion of bonding-antibonding levels of molecular orbitals of constituent nanostructural elements in place of atomic-orbital band inversion in conventional QSH insulators. The quantized edge conductance of the QSH phase in a Bi-NT array can be more easily isolated from bulk contributions and their properties can be highly tuned by tube size, representing distinctive advantages of nanostructured topological phases. Our finding opens a new avenue for topological materials by extending topological phases into nanomaterials with molecular-orbital-band inversion.

Atomically Abrupt Topological p-n Junction.

Topological insulators (TI's) are a new class of quantum matter with extraordinary surface electronic states, which bear great potential for spintronics and error-tolerant quantum computing. In order to put a TI into any practical use, these materials need to be fabricated into devices whose basic units are often p-n junctions. Interesting electronic properties of a 'topological' p-n junction were proposed theoretically such as the junction electronic state and the spin rectification. However, the fabrication of a lateral topological p-n junction has been challenging because of materials, process, and fundamental reasons. Here, we demonstrate an innovative approach to realize a p-n junction of topological surface states (TSS's) of a three-dimensional (3D) topological insulator (TI) with an atomically abrupt interface. When a ultrathin Sb film is grown on a 3D TI of Bi2Se3 with a typical n-type TSS, the surface develops a strongly p-type TSS through the substantial hybridization between the 2D Sb film and the Bi2Se3 surface. Thus, the Bi2Se3 surface covered partially with Sb films bifurcates into areas of n- and p-type TSS's as separated by atomic step edges with a lateral electronic junction of as short as 2 nm. This approach opens a different avenue toward various electronic and spintronic devices based on well-defined topological p-n junctions with the scalability down to atomic dimensions.

Bending strain engineering in quantum spin hall system for controlling spin currents.

Quantum spin Hall system can exhibit exotic spin transport phenomena, mediated by its topological edge states. Here the concept of bending strain engineering to tune the spin transport properties of a quantum spin Hall system is demonstrated. We show that bending strain can be used to control the spin orientation of counter-propagating edge states of a quantum spin system to generate a non-zero spin current. This physics mechanism can be applied to effectively tune the spin current and pure spin current decoupled from charge current in a quantum spin Hall system by control of its bending curvature. Furthermore, the curved quantum spin Hall system can be achieved by the concept of topological nanomechanical architecture in a controllable way, as demonstrated by the material example of Bi/Cl/Si(111) nanofilm. This concept of bending strain engineering of spins via topological nanomechanical architecture affords a promising route towards the realization of topological nano-mechanospintronics.

Quantum Spin Hall Effect and Tunable Spin Transport in As-Graphane.

Tunable spin transport in nanodevices is highly desirable to spintronics. Here, we predict existence of quantum spin Hall effects and tunable spin transport in As-graphane, based on first-principle density functional theory and tight binding calculations. Monolayer As-graphane is constituted by using As adsorbing on graphane with honeycomb H vacancies. Owing to the surface strain, monolayer As-graphane nanoribbons will self-bend toward the graphane side. The naturally curved As-graphane nanoribbons then exhibit unique spin transport properties, distinctively different from the flat ones, which is a two-dimensional topological insulator. Under external stress, one can realize tunable spin transport in curved As-graphane nanoribon arrays. Such intriguing mechanical bending induced spin flips can offer promising applications in the future nanospintronics devices.

Large-Gap Quantum Spin Hall State in MXenes: d-Band Topological Order in a Triangular Lattice.

MXenes are a large family of two-dimensional (2D) early transition metal carbides that have shown great potential for a host of applications ranging from electrodes in supercapacitors and batteries to sensors to reinforcements in polymers. Here, on the basis of first-principles calculations, we predict that Mo2MC2O2 (M = Ti, Zr, or Hf), belonging to a recently discovered new class of MXenes with double transition metal elements in an ordered structure, are robust quantum spin Hall (QSH) insulators. A tight-binding (TB) model based on the dz2-, dxy-, and dx2-y2-orbital basis in a triangular lattice is also constructed to describe the QSH states in Mo2MC2O2. It shows that the atomic spin-orbit coupling (SOC) strength of M totally contributes to the topological gap at the Γ point, a useful feature advantageous over the usual cases where the topological gap is much smaller than the atomic SOC strength based on the classic Kane-Mele (KM) or Bernevig-Hughes-Zhang (BHZ) model. Consequently, Mo2MC2O2 show sizable gaps from 0.1 to 0.2 eV with different M atoms, sufficiently large for realizing room-temperature QSH effects. Another advantage of Mo2MC2O2 MXenes lies in their oxygen-covered surfaces which make them antioxidative and stable upon exposure to air.

Topological phase transition and quantum spin Hall edge states of antimony few layers.

While two-dimensional (2D) topological insulators (TI's) initiated the field of topological materials, only very few materials were discovered to date and the direct access to their quantum spin Hall edge states has been challenging due to material issues. Here, we introduce a new 2D TI material, Sb few layer films. Electronic structures of ultrathin Sb islands grown on Bi2Te2Se are investigated by scanning tunneling microscopy. The maps of local density of states clearly identify robust edge electronic states over the thickness of three bilayers in clear contrast to thinner islands. This indicates that topological edge states emerge through a 2D topological phase transition predicted between three and four bilayer films in recent theory. The non-trivial phase transition and edge states are confirmed for epitaxial films by extensive density-functional-theory calculations. This work provides an important material platform to exploit microscopic aspects of the quantum spin Hall phase and its quantum phase transition.