Topologically protected quantum transport in locally exfoliated bismuth at room temperature

Topologically Protected Photovoltaics in Bi Nanoribbons

Photovoltaic efficiency in solar cells is hindered by many unwanted effects. Radiative channels (emission of photons) sometimes mediated by nonradiative ones (emission of phonons) are principally responsible for the decrease in exciton population before charge separation can take place. One such mechanism is electron-hole recombination at surfaces or defects where the in-gap edge states serve as the nonradiative channels. In topological insulators (TIs), which are rarely explored from an optoelectronics standpoint, we show that their characteristic surface states constitute a nonradiative decay channel that can be exploited to generate a protected photovoltaic current. Focusing on two-dimensional TIs, and specifically for illustration purposes on a Bi(111) monolayer, we obtain the transition rates from the bulk excitons to the edge states. By breaking the appropriate symmetries of the system, one can induce an edge charge accumulation and edge currents under illumination, demonstrating the potential of TI nanoribbons for photovoltaics.

Wet-Chemical Synthesis of Elemental 2D Materials

Wet-chemical synthesis refers to the bottom-up chemical synthesis in solution, which is among the most popular synthetic approaches towards functional two-dimensional (2D) materials. It offers several advantages, including cost-effectiveness, high yields,, precious control over the production process. As an emerging family of 2D materials, elemental 2D materials (Xenes) have shown great potential in various applications such as electronics, catalysts, biochemistry,, sensing technologies due to their exceptional/exotic properties such as large surface area, tunable band gap,, high carrier mobility. In this review, we provide a comprehensive overview of the current state-of-the-art in wet-chemical synthesis of Xenes including tellurene, bismuthene, antimonene, phosphorene,, arsenene. The current solvent compositions, process parameters utilized in wet-chemical synthesis, their effects on the thickness, stability of the resulting Xenes are also presented. Key factors considered involves ligands, precursors, surfactants, reaction time, temperature. Finally, we highlight recent advances, existing challenges in the current application of wet-chemical synthesis for Xenes production, provide perspectives on future improvement.

Engineering topological states in a two-dimensional honeycomb lattice

In this work, we use first-principles calculations to determine the interplay between spin-orbit coupling (SOC) and magnetism which can not only generate a quantum anomalous Hall state but can also result in topologically trivial states although some honeycomb systems host large band gaps. By employing tight-binding model analysis, we have summarized two types of topologically trivial states: one is due to the coexistence of quadratic non-Dirac and linear Dirac bands in the same spin channel that act together destructively in magnetic materials (such as, CrBr3, CrCl3, and VBr3 monolayers); the other one is caused by the destructive coupling effect between two different spin channels due to small magnetic spin splitting in heavy-metal-based materials, such as, BaTe(111)-supported plumbene. Further investigations reveal that topologically nontrivial states can be realized by removing the Dirac band dispersion of the magnetic monolayers for the former case (such as in alkali metal doped CrBr3), while separating the two different spin channels from each other by enhancing the magnetic spin splitting for the latter case (such as in half-iodinated silicene). Thus, our work provides a theoretical guideline to manipulate the topological states in a two-dimensional honeycomb lattice.

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.

Chemistry of two-dimensional pnictogens: emerging post-graphene materials for advanced applications

The layered allotropes of group 15 (P, As, Sb and Bi), also called two-dimensional (2D) pnictogens, have emerged as one of the most promising families of post-graphene 2D-materials. This is mainly due to the great variety of properties they exhibit, including layer-dependent bandgap, high charge-carrier mobility and current on/off ratios, strong spin-orbit coupling, wide allotropic diversity and pronounced chemical reactivity. These are key ingredients for exciting applications in (opto)electronics, heterogeneous catalysis, nanomedicine or energy storage and conversion, to name a few. However, there are still many challenges to overcome in order to fully understand their properties and bring them to real applications. As a matter of fact, due to their strong interlayer interactions, the mechanical exfoliation (top-down) of heavy pnictogens (Sb & Bi) is unsatisfactory, requiring the development of new methodologies for the isolation of single layers and the scalable production of high-quality flakes. Moreover, due to their pronounced chemical reactivity, it is necessary to develop passivation strategies, thus preventing environmental degradation, as in the case of bP, or controlling surface oxidation, with the corresponding modification of the interfacial and electronic properties. In this Feature Article we will discuss, among others, the most important contributions carried out in our group, including new liquid phase exfoliation (LPE) processes, bottom-up colloidal approaches, the preparation of intercalation compounds, innovative non-covalent and covalent functionalization protocols or novel concepts for potential applications in catalysis, electronics, photonics, biomedicine or energy storage and conversion. The past years have seen the birth of the chemistry of pnictogens at the nanoscale, and this review intends to highlight the importance of the chemical approach in the successful development of routes to synthesise, passivate, modify, or process these materials, paving the way for their use in applications of great societal impact.

Polarization-Induced Phase Transitions in Ultra-Thin InGaN-Based Double Quantum Wells

We investigate the phase transitions and the properties of the topological insulator in InGaN/GaN and InN/InGaN double quantum wells grown along the [0001] direction. We apply a realistic model based on the nonlinear theory of elasticity and piezoelectricity and the eight-band k·p method with relativistic and nonrelativistic linear-wave-vector terms. In this approach, the effective spin−orbit interaction in InN is negative, which represents the worst-case scenario for obtaining the topological insulator in InGaN-based structures. Despite this rigorous assumption, we demonstrate that the topological insulator can occur in InGaN/GaN and InN/InGaN double quantum wells when the widths of individual quantum wells are two and three monolayers (MLs), and three and three MLs. In these structures, when the interwell barrier is sufficiently thin, we can observe the topological phase transition from the normal insulator to the topological insulator via the Weyl semimetal, and the nontopological phase transition from the topological insulator to the nonlocal topological semimetal. We find that in InGaN/GaN double quantum wells, the bulk energy gap in the topological insulator phase is much smaller for the structures with both quantum well widths of 3 MLs than in the case when the quantum well widths are two and three MLs, whereas in InN/InGaN double quantum wells, the opposite is true. In InN/InGaN structures with both quantum wells being three MLs and a two ML interwell barrier, the bulk energy gap for the topological insulator can reach about 1.2 meV. We also show that the topological insulator phase rapidly deteriorates with increasing width of the interwell barrier due to a decrease in the bulk energy gap and reduction in the window of In content between the normal insulator and the nonlocal topological semimetal. For InN/InGaN double quantum wells with the width of the interwell barrier above five or six MLs, the topological insulator phase does not appear. In these structures, we find two novel phase transitions, namely the nontopological phase transition from the normal insulator to the nonlocal normal semimetal and the topological phase transition from the nonlocal normal semimetal to the nonlocal topological semimetal via the buried Weyl semimetal. These results can guide future investigations towards achieving a topological insulator in InGaN-based nanostructures.

Atomically Thin Quantum Spin Hall Insulators

Atomically thin topological materials are attracting growing attention for their potential to radically transform classical and quantum electronic device concepts. Among them is the quantum spin Hall (QSH) insulator-a 2D state of matter that arises from interplay of topological band inversion and strong spin-orbit coupling, with large tunable bulk bandgaps up to 800 meV and gapless, 1D edge states. Reviewing recent advances in materials science and engineering alongside theoretical description, the QSH materials library is surveyed with focus on the prospects for QSH-based device applications. In particular, theoretical predictions of nontrivial superconducting pairing in the QSH state toward Majorana-based topological quantum computing are discussed, which are the next frontier in QSH materials research.

Thermoelectric power generation efficiency of zigzag monolayer nanoribbon of bismuth

The thermoelectric power generation efficiency of a bismuth monolayer nanoribbon has been studied theoretically. We calculate the conductance of such a structure using the multi-orbital tight-binding model and also recursive Green's function method, in the presence of a substrate and on-site potential. For the case of the [Formula: see text] substrate-supported bismuth nanoribbon and by proper selection of on-site potential, a boxcar shape conductance in terms of energy has been obtained. Using the Landauer-Büttiker formalism in the non-linear response regime, we calculate heat and charge currents at low temperatures. By calculation of the electrical output power and power conversion thermoelectric efficiency, we have illustrated that such a structure can operate at high thermoelectric efficiency and also a considerable power generation rate.

Early-Stage Growth Mechanism and Synthesis Conditions-Dependent Morphology of Nanocrystalline Bi Films Electrodeposited from Perchlorate Electrolyte

Bi nanocrystalline films were formed from perchlorate electrolyte (PE) on Cu substrate via electrochemical deposition with different duration and current densities. The microstructural, morphological properties, and elemental composition were studied using scanning electron microscopy (SEM), atomic force microscopy (AFM), and energy-dispersive X-ray microanalysis (EDX). The optimal range of current densities for Bi electrodeposition in PE using polarization measurements was demonstrated. For the first time, it was shown and explained why, with a deposition duration of 1 s, co-deposition of Pb and Bi occurs. The correlation between synthesis conditions and chemical composition and microstructure for Bi films was discussed. The analysis of the microstructure evolution revealed the changing mechanism of the films’ growth from pillar-like (for Pb-rich phase) to layered granular form (for Bi) with deposition duration rising. This abnormal behavior is explained by the appearance of a strong Bi growth texture and coalescence effects. The investigations of porosity showed that Bi films have a closely-packed microstructure. The main stages and the growth mechanism of Bi films in the galvanostatic regime in PE with a deposition duration of 1–30 s are proposed.

Relative Abundance of Z 2 Topological Order in Exfoliable Two-Dimensional Insulators

Quantum spin Hall insulators make up a class of two-dimensional materials with a finite electronic band gap in the bulk and gapless helical edge states. In the presence of time-reversal symmetry,Z 2 topological order distinguishes the topological phase from the ordinary insulating one. Some of the phenomena that can be hosted in these materials, from one-dimensional low-dissipation electronic transport to spin filtering, could be promising for many technological applications in the fields of electronics, spintronics, and topological quantum computing. Nevertheless, the rarity of two-dimensional materials that can exhibit nontrivial [Formula: see text] topological order at room temperature hinders development. Here, we screen a comprehensive database we recently identified of 1825 monolayers that can be exfoliated from experimentally known compounds to search for novel quantum spin Hall insulators. Using density-functional and many-body perturbation theory simulations, we identify 13 monolayers that are candidates for quantum spin Hall insulators including high-performing materials such as AsCuLi2 and (platinum) jacutingaite (Pt2HgSe3). We also identify monolayer Pd2HgSe3 (palladium jacutingaite) as a novel Kane-Mele quantum spin Hall insulator and compare it with platinum jacutingaite. A handful of promising materials are mechanically stable and exhibitZ 2 topological order, either unperturbed or driven by small amounts of strain. Such screening highlights a relative abundance ofZ 2 topological order of around 1% and provides an optimal set of candidates for experimental efforts.

The Optimal Electronic Structure for High-Mobility 2D Semiconductors: Exceptionally High Hole Mobility in 2D Antimony

Two-dimensional (2D) semiconductors have very attractive properties for many applications such as photoelectrochemistry. However, a significant challenge that limits their further developments is the relatively low electron/hole mobility at room temperature. Here using the Boltzmann transport theory with the scattering rates calculated from first-principles that allow us to accurately determine the mobility, we discover an exceptionally high intrinsic mobility of holes in monolayer antimony (Sb), which is ∼1330 cm² V^-1 s^-1 at room temperature, much higher than the common 2D semiconductors including MoS₂, InSe, and black phosphorus in monolayer form, and is the highest among 2D materials with a band gap of >1 eV reported so far. Its high mobility and the moderate band gap make it very promising for many applications. By comparing the 2D Sb with other 2D materials in the same group, we find that the high mobility is closely related with its electronic structure, which has a sharp and deep valence band valley, and, importantly, located at the Γ point. This electronic structure not only gives rise to a high velocity for charge carriers but also leads to a small density of states for accepting the scattered carriers, particularly by eliminating the valley-valley and peak-valley scatterings that are found to be significant for other materials. This type of electronic structure thus can be used as a target feature to design/discover high-mobility 2D semiconductors. Our work provides a promising material to overcome the mobility issue and also suggests a simple and general principle for high-mobility semiconductor design/discovery.

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.

Unrestricted Electron Bunching at the Helical Edge

A quantum magnetic impurity of spin S at the edge of a two-dimensional time reversal invariant topological insulator may give rise to backscattering. We study here the shot noise associated with the backscattering current for arbitrary S. Our full analytical solution reveals that for S>1/2 the Fano factor may be arbitrarily large, reflecting bunching of large batches of electrons. By contrast, we rigorously prove that for S=1/2 the Fano factor is bounded between 1 and 2, generalizing earlier studies.

Topological electronic structure and Rashba effect in Bi thin layers: theoretical predictions and experiments

The goal of the present review is to cross-compare theoretical predictions with selected experimental results on bismuth thin films exhibiting topological properties and a strong Rashba effect. The theoretical prediction that a single free-standing Bi(1 1 1) bilayer is a topological insulator has triggered a large series of studies of ultrathin Bi(1 1 1) films grown on various substrates. Using selected examples we review theoretical predictions of atomic and electronic structure of Bi thin films exhibiting topological properties due to interaction with a substrate. We also survey experimental signatures of topological surface states and Rashba effect, as obtained mostly by angle- and spin-resolved photoelectron spectroscopy.

Optical properties of monolayer bismuthene in electric fields

Optical excitations of monolayer bismuthene present very rich and unique absorption spectra. The optical energy gap corresponding to the threshold frequency is not equal to an indirect energy gap, and it becomes zero under the critical electric field. The frequency, number, intensity, and form of the absorption structures are dramatically changed when an external electric field is applied. The prominent peaks and the observable shoulders, respectively, arise from the constant-energy loop and the band-edge states of parabolic dispersions. These directly reflect the unusual electronic properties, being very different from those in monolayer graphene. The novel optical properties of bismuthine that are easily manipulated by electric fields may find a lot of various applications in optoelectronics, either combined with or complementary to those graphene-based systems.

Observation of the quantum spin Hall effect up to 100 kelvin in a monolayer crystal

A variety of monolayer crystals have been proposed to be two-dimensional topological insulators exhibiting the quantum spin Hall effect (QSHE), possibly even at high temperatures. Here we report the observation of the QSHE in monolayer tungsten ditelluride (WTe₂) at temperatures up to 100 kelvin. In the short-edge limit, the monolayer exhibits the hallmark transport conductance, ~e²/h per edge, where e is the electron charge and h is Planck's constant. Moreover, a magnetic field suppresses the conductance, and the observed Zeeman-type gap indicates the existence of a Kramers degenerate point and the importance of time-reversal symmetry for protection from elastic backscattering. Our results establish the QSHE at temperatures much higher than in semiconductor heterostructures and allow for exploring topological phases in atomically thin crystals.

Bursting at the seams: Rippled monolayer bismuth on NbSe2

Bismuth, one of the heaviest semimetals in nature, ignited the interest of the materials physics community for its potential impact on topological quantum material systems that use its strong spin-orbit coupling and unique orbital hybridization. In particular, recent theoretical predictions of unique topological and superconducting properties of thin bismuth films and interfaces prompted intense research on the growth of submonolayers to a few monolayers of bismuth on different substrates. Similar to bulk rhombohedral bismuth, the initial growth of bismuth films on most substrates results in buckled bilayers that grow in either the (111) or (110) directions, with a lattice constant close to that of bulk Bi. By contrast, we show a new growth pattern for bismuth monolayers on NbSe₂. We find that the initial growth of Bi can form a strongly bonded commensurate layer, resulting in a compressively strained two-dimensional (2D) triangular lattice. We also observed unique pattern of 1D ripples and domain walls is observed. The single layer of bismuth also introduces strong marks on the electronic properties at the surface.

An implementation of spin-orbit coupling for band structure calculations with Gaussian basis sets: Two-dimensional topological crystals of Sb and Bi

We present an implementation of spin-orbit coupling (SOC) for density functional theory band structure calculations that makes use of Gaussian basis sets. It is based on the explicit evaluation of SOC matrix elements, both the radial and angular parts. For all-electron basis sets, where the full nodal structure is present in the basis elements, the results are in good agreement with well-established implementations such as VASP. For more practical pseudopotential basis sets, which lack nodal structure, an ad-hoc increase of the effective nuclear potential helps to capture all relevant band structure variations induced by SOC. In this work, the non-relativistic or scalar-relativistic Kohn-Sham Hamiltonian is obtained from the CRYSTAL code and the SOC term is added a posteriori. As an example, we apply this method to the Bi(111) monolayer, a paradigmatic 2D topological insulator, and to mono- and multilayer Sb(111) (also known as antimonene), the former being a trivial semiconductor and the latter a topological semimetal featuring topologically protected surface states.

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

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

Recent Progress on Antimonene: A New Bidimensional Material

Antimonene, defined in sensu stricto as a single layer of antimony atoms, is recently the focus of numerous theoretical works predicting a variety of interesting properties and is quickly attracting the attention of the scientific community. However, what places antimonene in a different category from other 2D crystals is its strong spin-orbit coupling and a drastic evolution of its properties from the monolayer to the few-layer system. The recent isolation of this novel 2D material pushes the interest for antimonene even further. Here, a review of both theoretical predictions and experimental results is compiled. First, an account of the calculations anticipating an electronic band structure suitable for optoelectronics and thermoelectric applications in monolayer form and a topological semimetal in few-layer form is given. Second, the different approaches to produce antimonene-mechanical and liquid phase exfoliation, and epitaxial growth methods-are reviewed. In addition, this work also reports the main characterization techniques used to study this exotic material. This review provides insights for further exploring the appealing properties of antimonene and puts forward the opportunities and challenges for future applications from (opto)electronic device fabrication to biomedicine.

Effect of Amidogen Functionalization on Quantum Spin Hall Effect in Bi/Sb(111) Films

Knowledge about chemical functionalization is of fundamental importance to design novel two-dimensional topological insulators. Despite theoretical predictions of quantum spin Hall effect (QSH) insulator via chemical functionalization, it is quite challenging to obtain a high-quality sample, in which the toxicity is also an important factor that cannot be ignored. Herein, using first-principles calculations, we predict an intrinsic QSH effect in amidogen-functionalized Bi/Sb(111) films (SbNH₂ and BiNH₂), characterized by nontrivial Z₂ invariant and helical edge states. The bulk gaps derived from p_x,y orbitals reaches up to 0.39 and 0.83 eV for SbNH₂ and BiNH₂ films, respectively. The topological properties are robust against strain engineering, electric field, and rotation angle of amidogen, accompanied with sizable bulk gaps. Besides, the topological phases are preserved with different arrangements of amidogen. The H-terminated SiC(111) is verified as a good candidate substrate for supporting the films without destroying their QSH effect. These results have substantial implications for theoretical and experimental studies of functionalized Bi/Sb films, which also provide a promising platform for realizing practical application in dissipationless transport devices at room temperature.

Bismuthene on a SiC substrate: A candidate for a high-temperature quantum spin Hall material

Quantum spin Hall materials hold the promise of revolutionary devices with dissipationless spin currents but have required cryogenic temperatures owing to small energy gaps. Here we show theoretically that a room-temperature regime with a large energy gap may be achievable within a paradigm that exploits the atomic spin-orbit coupling. The concept is based on a substrate-supported monolayer of a high-atomic number element and is experimentally realized as a bismuth honeycomb lattice on top of the insulating silicon carbide substrate SiC(0001). Using scanning tunneling spectroscopy, we detect a gap of ~0.8 electron volt and conductive edge states consistent with theory. Our combined theoretical and experimental results demonstrate a concept for a quantum spin Hall wide-gap scenario, where the chemical potential resides in the global system gap, ensuring robust edge conductance.

Resolving the one-dimensional singularity edge states of Bi(1 1 1) thin films

We report our investigation on the electronic properties of the step edges on a Bi(1 1 1) surface in epitiaxially grown thin films, using scanning tunneling microscopy and spectroscopy. Our results show three differential conductance peaks including the previously reported peak in the spectra recorded at the step edges. Our analysis indicates that all of the three peaks can be ascribed to the van Hove singularities and thus to the band extrema of the one-dimensional edge bands, according to the quasiparticle interference and the Fourier transform patterns. These edge states show an overall penetration length of about 5 nm, but they also show different spatial distributions perpendicular to the edge. The well-determined band extrema may provide information for establishing a better model to describe the electronic topology of the step edge in the Bi(1 1 1) films.

Stability of topological properties of bismuth (1 1 1) bilayer

We investigate the electronic and transport properties of the bismuth (1 1 1) bilayer in the context of the stability of its topological properties against different perturbations. The effects of spin-orbit coupling variations, geometry relaxation and interaction with a substrate are considered. The transport properties are studied in the presence of Anderson disorder. Band structure calculations are performed within the multi-orbital tight-binding model and density functional theory methods. A band inversion process in the bismuth (1 1 1) infinite bilayer and an evolution of the edge state dispersion in ribbons as a function of spin-orbit coupling strength are analyzed. A significant change in the orbital composition of the conduction and valence bands is observed during a topological phase transition. The topological edge states are shown to be weakly affected by the effect of ribbon geometry relaxation. The interaction with a substrate is considered for narrow ribbons on top of another bismuth (1 1 1) bilayer. This corresponds to a weakly interacting case and the effect is similar to an external perpendicular electric field. Robust quantized conductance is observed when the Fermi energy lies within the energy gap, where only two counter-propagating edge states are present. For energies where the Fermi level crosses more in-gap states, scattering is possible between the channels lying close in the k-space. When the energy of the edge states overlaps the valence states, no topological protection is observed.

Controlling the growth of Bi(110) and Bi(111) films on an insulating substrate

We demonstrate the controlled growth of Bi(110) and Bi(111) films on an α-Al₂O₃(0001) substrate by surface x-ray diffraction and x-ray reflectivity using synchrotron radiation. At temperatures as low as 40 K, unanticipated pseudo-cubic Bi(110) films are grown with thicknesses ranging from a few to tens of nanometers. The roughness at the film-vacuum as well as the film-substrate interface, can be reduced by mild heating, where a crystallographic orientation transition of Bi(110) towards Bi(111) is observed at 400 K. From 450 K onwards high quality ultrasmooth Bi(111) films form. Growth around the transition temperature results in the growth of competing Bi(110) and Bi(111) domains.

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.

A new kind of 2D topological insulators BiCN with a giant gap and its substrate effects

Based on DFT calculation, we predict that BiCN, i.e., bilayer Bi films passivated with -CN group, is a novel 2D Bi-based material with highly thermodynamic stability, and demonstrate that it is also a new kind of 2D TI with a giant SOC gap (~1 eV) by direct calculation of the topological invariant Z₂ and obvious exhibition of the helical edge states. Monolayer h-BN and MoS₂ are identified as good candidate substrates for supporting the nontrivial topological insulating phase of the 2D TI films, since the two substrates can stabilize and weakly interact with BiCN via van der Waals interaction and thus hardly affect the electronic properties, especially the band topology. The topological properties are robust against the strain and electric field. This may provide a promising platform for realization of novel topological phases.

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.

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.

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.

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.

Magnetoresistance in the Spin-Orbit Kondo State of Elemental Bismuth

Materials with strong spin-orbit coupling, which competes with other particle-particle interactions and external perturbations, offer a promising route to explore novel phases of quantum matter. Using LDA + DMFT we reveal the complex interplay between local, multi-orbital Coulomb and spin-orbit interaction in elemental bismuth. Our theory quantifies the role played by collective dynamical fluctuations in the spin-orbit Kondo state. The correlated electronic structure we derive is promising in the sense that it leads to results that might explain why moderate magnetic fields can generate Dirac valleys and directional-selective magnetoresistance responses within spin-orbit Kondo metals.

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.

Systematic pseudopotentials from reference eigenvalue sets for DFT calculations: Pseudopotential files

We present in this article a pseudopotential (PP) database for DFT calculations in the context of the SIESTA code [1-3]. Comprehensive optimized PPs in two formats (psf files and input files for ATM program) are provided for 20 chemical elements for LDA and GGA exchange-correlation potentials. Our data represents a validated database of PPs for SIESTA DFT calculations. Extensive transferability tests guarantee the usefulness of these PPs.

Strain and the optoelectronic properties of nonplanar phosphorene monolayers

Phosphorene is a new 2D atomic material, and we document a drastic reduction of its electronic gap when under a conical shape. Furthermore, geometry determines the properties of 2D materials, and we introduce discrete differential geometry to study them. This geometry arises from particle/atomic positions; it is not based on a parametric continuum, and it applies across broad disciplinary lines.

Lattice kirigami, ultralight metamaterials, polydisperse aggregates, ceramic nanolattices, and 2D atomic materials share an inherent structural discreteness, and their material properties evolve with their shape. To exemplify the intimate relation among material properties and the local geometry, we explore the properties of phosphorene––a new 2D atomic material––in a conical structure, and document a decrease of the semiconducting gap that is directly linked to its nonplanar shape. This geometrical effect occurs regardless of phosphorene allotrope considered, and it provides a unique optical vehicle to single out local structural defects on this 2D material. We also classify other 2D atomic materials in terms of their crystalline unit cells, and propose means to obtain the local geometry directly from their diverse 2D structures while bypassing common descriptions of shape that are based from a parametric continuum.

Surface superconductivity in thin cylindrical Bi nanowire

The physical origin and the nature of superconductivity in nanostructured Bi remains puzzling. Here, we report transport measurements of individual cylindrical single-crystal Bi nanowires, 20 and 32 nm in diameter. In contrast to nonsuperconducting Bi nanoribbons with two flat surfaces, cylindrical Bi nanowires show superconductivity below 1.3 K. However, their superconducting critical magnetic fields decrease with their diameter, which is the opposite of the expected behavior for thin superconducting wires. Quasiperiodic oscillations of magnetoresistance were observed in perpendicular fields but were not seen in the parallel orientation. These results can be understood by a model of surface superconductivity with an enhanced surface-to-bulk volume in small diameter wires, where the superconductivity originates from the strained surface states of the nanowires due to the surface curvature-induced stress.

Topological states modulation of Bi and Sb thin films by atomic adsorption

Based on first-principles calculations, we systematically investigated the topological surface states of Bi and Sb thin films of 1–5 bilayers in (111) orientation without and with H(F) adsorption, respectively.

Magnetotransport in atomic-size bismuth contacts

We report low-temperature transport experiments on atomic-size contacts of bismuth that are fabricated using the mechanically controlled break-junction technique at low temperatures. We observe stable contacts with conductance values at fractions of one conductance quantum G0 = 2e(2)/h, as is expected for systems with long Fermi wavelength. We defer two preferred conductance scales: the lower one is in the order of 0.015 G0 and can be attributed to single-atom Bi contact, while the higher one amounts to 0.15 G0, as indicated by the appearance of multiples of this value in the conductance histogram. Rich magneto-transport behaviour with significant changes in the magneto-conductance is found in the whole conductance range. Although for the pristine samples and large contacts with G > 5 G0, indications for Shubnikov-de Haas oscillations are present, the smallest contacts show pronounced conductance fluctuations that decay rapidly when a magnetic field is applied. Moreover, large variations are observed when a finite bias voltage is applied. These findings are interpreted as the transition from the diffusive to the ballistic and the ultra-quantum regime when lowering the contact size.

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.