Single Dirac cone topological surface state and unusual thermoelectric property of compounds from a new topological insulator family

Unraveling the topological phase in Zintl semiconductors RbZn4X3(X = P, As) through band engineering

We report the topological phase transition (TPT) in compounds of relatively less explored Zintl family RbZn4X3(X = P, As) viafirst-principlescalculation. These intermetallic compounds have already been experimentally synthesized in aKCu4S3-typetetragonal structure (P4/mmm) and reported to have a topologically trivial semimetallic nature with a direct band gap. We thoroughly studied the electronic structure, stability of RbZn4X3(X = P, As) and demonstrated the TPTs in these materials with external applied pressure and epitaxial strain. The dynamical and mechanical stabilities of these compounds are verified through phonon dispersion and Born stability criteria at ambient and TPT pressure/strain. A topologically non-trivial phase in RbZn4P3(RbZn4As3) is observed at 45 GPa (38 GPa) of hydrostatic pressure and 10% (8%) of epitaxial strain. This non-trivial phase is identified by band inversion betweenZn-sandP/As-pzorbitalsin the bulk band structure of these materials which is further confirmed using the surface density of states and Fermi arc contour in(001)-plane. The ℤ2topological invariants (ν0; ν1ν2ν3) for these materials are calculated using the product of parities of all filled bands (Kane and Mele model) and the evolution of Wannier charge centers (Wilson loop method). The change in values of (ν0; ν1ν2ν3) from (0; 000) to (1; 000), at the particular values of pressure and strain, is another signature of the TPT in these materials.

Phase diagram for the quasi-binary thallium(I) selenide-bismuth(III) telluride system

The phase diagram for the quasi-binary Tl2Se-Bi2Te3 system has been established based on the results of phase studies by differential thermal analysis (DTA) and X-ray diffraction (XRD). The diagram for the title system presented in this paper has been compared with that previously published by other authors. As a result of the research, a significant correction of the former phase diagram was made, because it was found that the components of the studied system formed three new chemical compounds. Obtained phase diagram has been compared with other thallium(I)-bismuth(III) chalcogenide systems.

Surface properties of 1T-TaS2 and contrasting its electron-phonon coupling with TlBiTe2 from helium atom scattering

We present a detailed helium atom scattering study of the charge-density wave (CDW) system and transition metal dichalcogenide 1T-TaS2. In terms of energy dissipation, we determine the electron-phonon (e-ph) coupling, a quantity that is at the heart of conventional superconductivity and may even "drive" phase transitions such as CDWs. The e-ph coupling of TaS2 in the commensurate CDW phase (λ = 0.59 ± 0.12) is compared with measurements of the topo-logical insulator TlBiTe2 (λ = 0.09 ± 0.01). Furthermore, by means of elastic He diffraction and resonance/interference effects in He scattering, the thermal expansion of the surface lattice, the surface step height, and the three-dimensional atom-surface interaction potential are determined including the electronic corrugation of 1T-TaS2. The linear thermal expansion coefficient is similar to that of other transition-metal dichalcogenides. The He-TaS2 interaction is best described by a corrugated Morse potential with a relatively large well depth and supports a large number of bound states, comparable to the surface of Bi2Se3, and the surface electronic corrugation of 1T-TaS2 is similar to the ones found for semimetal surfaces.

Ag2 Q-Based (Q = S, Se, Te) Silver Chalcogenide Thermoelectric Materials

Thermoelectric technology provides a promising solution to sustainable energy utilization and scalable power supply. Recently, Ag₂ Q-based (Q = S, Se, Te) silver chalcogenides have come forth as potential thermoelectric materials that are endowed with complex crystal structures, high carrier mobility coupled with low lattice thermal conductivity, and even exceptional plasticity. This review presents the latest advances in this material family, from binary compounds to ternary and quaternary alloys, covering the understanding of multi-scale structures and peculiar properties, the optimization of thermoelectric performance, and the rational design of new materials. The "composition-phase structure-thermoelectric/mechanical properties" correlation is emphasized. Flexible and hetero-shaped thermoelectric prototypes based on Ag₂ Q materials are also demonstrated. Several key problems and challenges are put forward concerning further understanding and optimization of Ag₂ Q-based thermoelectric chalcogenides.

Comprehensive Insight into p-Type Bi2Te3-Based Thermoelectrics near Room Temperature

Bi2Te3 is a well-recognized material for its unique properties in diverse thermoelectric applications near room temperature. The considerable efforts on Bi2Te3-based alloys have been extremely extensive in recent years, and thus the latest breakthroughs in high-performance p-type (Bi, Sb)2Te3 alloys are comprehensively reviewed to further implement applications. Effective strategies to further improve the thermoelectric performance are summarized from the perspective of enhancing the power factor and minimizing the lattice thermal conductivity. Furthermore, the surface states of topological insulators are investigated to provide a possibility of advancing (Bi, Sb)2Te3 thermoelectrics. Finally, future challenges and outlooks are overviewed. This review will provide potential guidance toward designing and developing high-efficient Bi2Te3-based and other thermoelectrics.

Pressure induced topological and topological crystalline insulators

Research on topological and topological crystalline insulators (TCIs) is one of the most intense and exciting topics due to its fascinating fundamental science and potential technological applications. Pressure (strain) is one potential pathway to induce the non-trivial topological phases in some topologically trivial (normal) insulating or semiconducting materials. In the last ten years, there have been substantial theoretical and experimental efforts from condensed-matter scientists to characterize and understand pressure-induced topological quantum phase transitions (TQPTs). In particular, a promising enhancement of the thermoelectric performance through pressure-induced TQPT has been recently realized; thus evidencing the importance of this subject in society. Since the pressure effect can be mimicked by chemical doping or substitution in many cases, these results have opened a new route to develop more efficient materials for harvesting green energy at ambient conditions. Therefore, a detailed understanding of the mechanism of pressure-induced TQPTs in various classes of materials with spin-orbit interaction is crucial to improve their properties for technological implementations. Hence, this review focuses on the emerging area of pressure-induced TQPTs to provide a comprehensive understanding of this subject from both theoretical and experimental points of view. In particular, it covers the Raman signatures of detecting the topological transitions (under pressure), some of the important pressure-induced topological and TCIs of the various classes of spin-orbit coupling materials, and provide future research directions in this interesting field.

First principle based investigation of topological insulating phase in half-Heusler family NaYO (Y= Ag, Au, and Cu)

The ternary half-Heusler compounds have shown great potential for realizing new 3D topological insulators. With band gap tuning and spin orbit coupling these compounds may undergo topological phase transitions. In present work, we explore the possibility of realizing a topological insulating phase in half-Heusler family NaYO (Y= Ag, Au, and Cu). We find that for NaAgO, external strain (∼19%) along with spin-orbit coupling (SOC), is required to achieve band-inversion at Γ high-symmetry point and leads to phase transition from trivial to non-trivial topological insulating phase. In case of NaAuO and NaCuO, non-trivial phase appears in their equilibrium lattice constant, hence only SOC is enough to achieve band-inversion leading to non-trivial topology. The non-centrosymmetric nature of crystal geometry leads to the formation of two twofold degenerate point nodes near the Fermi level.

Criteria for Realizing Room-Temperature Electrical Transport Applications of Topological Materials

The unusual electronic states found in topological materials can enable a new generation of devices and technologies, yet a long-standing challenge has been finding materials without deleterious parallel bulk conduction. This can arise either from defects or thermally activated carriers. Here, the criteria that materials need to meet to realize transport properties dominated by the topological states, a necessity for a topological device, are clarified. This is demonstrated for 3D topological insulators, 3D Dirac materials, and 1D quantum anomalous Hall insulators, though this can be applied to similar systems. The key parameters are electronic bandgap, dielectric constant, and carrier effective mass, which dictate under what circumstances (defect density, temperature, etc.) the unwanted bulk state will conduct in parallel to the topological states. As these are fundamentally determined by the basic atomic properties, simple chemical arguments can be used to navigate the phase space to ultimately find improved materials. This will enable rapid identification of new systems with improved properties, which is crucial to designing new material systems and push a new generation of topological technologies.

Interacting Dirac materials

We investigate the extent to which the class of Dirac materials in two-dimensions provides general statements about the behavior of both fermionic and bosonic Dirac quasiparticles in the interacting regime. For both quasiparticle types, we find common features for the interaction induced renormalization of the conical Dirac spectrum. We perform the perturbative renormalization analysis and compute the self-energy for both quasiparticle types with different interactions and collate previous results from the literature whenever necessary. Guided by the systematic presentation of our results in table1, we conclude that long-range interactions generically lead to an increase of the slope of the single-particle Dirac cone, whereas short-range interactions lead to a decrease. The quasiparticle statistics does not qualitatively impact the self-energy correction for long-range repulsion but does affect the behavior of short-range coupled systems, giving rise to different thermal power-law contributions. The possibility of a universal description of the Dirac materials based on these features is also mentioned.

A topological semimetal Li2CrN2 sheet as a promising hydrogen storage material

An ideal electrode for electrochemical storage of hydrogen needs to be conductive for electrons. The robust conductivity protected by topology in topological quantum materials just meets this requirement. However, such a study is still lacking so far. Herein, for the first time, we explore the performance of hydrogen storage in a topological quantum material Li₂CrN₂ sheet, and have found that the interaction between H₂ and the sheet is mainly attributed to the polarization mechanism, resulting in a gravimetric capacity of 4.77% that is higher than the value of the Li decorated MoS₂ (4.4%), Li-decorated phosphorene (4.4%) and Li substituted BHNH sheet (3.16%). The hydrogen adsorption energy is found to be in the range of 0.16-0.33 eV, which is in the required energy window for balancing the adsorption stability and fast kinetics, and the releasing temperature is in the range of 160-270 K, desirable for practical operations. This study is of significance for fuel cell applications going beyond the conventional materials for hydrogen storage.

Conversion of a conventional superconductor into a topological superconductor by topological proximity effect

Realization of topological superconductors (TSCs) hosting Majorana fermions is a central challenge in condensed-matter physics. One approach is to use the superconducting proximity effect (SPE) in heterostructures, where a topological insulator contacted with a superconductor hosts an effective p-wave pairing by the penetration of Cooper pairs across the interface. However, this approach suffers a difficulty in accessing the topological interface buried deep beneath the surface. Here, we propose an alternative approach to realize topological superconductivity without SPE. In a Pb(111) thin film grown on TlBiSe₂, we discover that the Dirac-cone state of substrate TlBiSe₂ migrates to the top surface of Pb film and obtains an energy gap below the superconducting transition temperature of Pb. This suggests that a Bardeen-Cooper-Schrieffer superconductor is converted into a TSC by the topological proximity effect. Our discovery opens a route to manipulate topological superconducting properties of materials.

Realizing topological superconductivity is essential for applicable fault-tolerant quantum computation. Here, Trang et al. report migration of Dirac-cone from TlBiSe₂ substrate to top surface of superconducting Pb film due to topological proximity effect, suggesting realization of topological superconductivity.

Thermoelectrics of Nanowires

The field of thermoelectric research has undergone a renaissance and boom in the past two and a half decades, largely fueled by the prospect of engineering electronic and phononic properties in nanostructures, among which semiconductor nanowires (NWs) have served both as an important platform to investigate fundamental thermoelectric transport phenomena and as a promising route for high thermoelectric performance for diverse applications. In this Review, we provide a comprehensive look at various aspects of thermoelectrics of NWs. We start with a brief introduction of basic thermoelectric phenomena, followed by synthetic methods for thermoelectric NWs and a summary of their thermoelectric figures of merit (ZT). We then focus our discussion on charge and heat transport, which dictate thermoelectric power factor and thermal conductivity, respectively. For charge transport, we cover the basic principles governing the power factor and then review several strategies using NWs to enhance it, including earlier theoretical and experimental work on quantum confinement effects and semimetal-to-semiconductor transition, surface engineering and complex heterostructures to enhance the carrier mobility and power factor, and the recent emergence of topological insulator NWs. For phonon transport, we broadly categorize the work on thermal conductivity of NWs into five different effects: classic size effect, acoustic softening, surface roughness, complex NW morphology, and dimensional crossover. Finally, we discuss the integration of NWs for device applications for thermoelectric power generation and cooling. We conclude our review with some outlooks for future research.

Strain-Tuned Topological Insulator and Rashba-Induced Anisotropic Momentum-Locked Dirac Cones in Two-Dimensional SeTe Monolayers

Rashba spin-orbit coupling (SOC) in topological insulators (TIs) is a very interesting phenomenon and has received extensive attention in two-dimensional (2D) materials. However, the coexistence of Rashba SOC and band topology, especially for materials with a square lattice, is still lacking. Here, by using first-principles calculations, we propose for the first time a SeTe monolayer as a 2D candidate with these novel properties. We find that the square lattice exhibits anisotropic band dispersions near the Fermi level and a Rashba effect related to large SOC and inversion asymmetry, which leads to a Dirac semimetal state. Another prominent feature is that SeTe can achieve a topological state under a tensile strain of only 1%, characterized by the Z₂ invariant and helical edge states. Our findings demonstrate that SeTe is a promising material for novel electronic and spintronics applications.

High-Throughput Screening and Automated Processing toward Novel Topological Insulators

The bottleneck of current studies on topological insulators is to identify better materials that can be fabricated into devices more feasibly. To search for novel topological materials, we developed a high-throughput framework that can be utilized to screen for candidates with known crystal structures and further showcase topological properties based on automated construction of Wannier functions. We have applied our methods to ternary compounds of Bi, Sb, and nitrides as a representative sample. The topological properties are characterized by the surface states, verified by auxiliary evaluation of the Z₂ topological invariant. We successfully identified seven topological insulators. Our work paves the way to design novel topological materials.

Thermoelectric properties and thermal stability of layered chalcogenides, TlScQ2, Q = Se, Te

A few thallium based layered chalcogenides of α-NaFeO₂ structure-type are known for their excellent thermoelectric properties and interesting topological insulator nature. TlScQ₂ belongs to this structural category. In the present work, we have studied the electronic structure, electrical and thermal transport properties and thermal stability of the title compounds within the temperature range 2-600 K. Density functional theory (DFT) predicts a metallic nature for TlScTe₂ and a semiconducting nature for TlScSe₂. DFT calculations also show significant lowering of energies of frontier bands upon inclusion of spin-orbit coupling contribution in the calculation. The electronic structure also shows the simultaneous occurrence of holes and electron pockets for the telluride. Experiments reveal that the telluride shows a semi-metallic behaviour whereas the selenide is a semiconductor. The thermoelectric properties for both the materials were also investigated. Both these materials possess very low thermal conductivity which is an attractive feature for thermoelectrics. However, they lack thermal stability and decompose upon warming above room temperature, as evidenced from high temperature powder X-ray diffraction and thermal analysis.

Gigantic negative magnetoresistance in the bulk of a disordered topological insulator

With the recent discovery of Weyl semimetals, the phenomenon of negative magnetoresistance (MR) is attracting renewed interest. Large negative MR is usually related to magnetism, but the chiral anomaly in Weyl semimetals is a rare exception. Here we report a mechanism for large negative MR which is also unrelated to magnetism but is related to disorder. In the nearly bulk-insulating topological insulator TlBi_0.15Sb_0.85Te₂, we observed gigantic negative MR reaching 98% in 14 T at 10 K, which is unprecedented in a nonmagnetic system. Supported by numerical simulations, we argue that this phenomenon is likely due to the Zeeman effect on a barely percolating current path formed in the disordered bulk. Since disorder can also lead to non-saturating linear MR in Ag_2+δSe, the present finding suggests that disorder engineering in narrow-gap systems is useful for realizing gigantic MR in both positive and negative directions.

Large negative magnetoresistance is usually related to magnetism and the exceptions are rare. Here, Breunig et al. report a large negative magnetoresistance in a topological insulator, TlBi_0.15Sb_0.85Te₂, which is likely due to the Zeeman effect on a barely percolating current path formed in the disordered bulk.

A novel quasi-one-dimensional topological insulator in bismuth iodide β-Bi4I4

Recent progress in the field of topological states of matter has largely been initiated by the discovery of bismuth and antimony chalcogenide bulk topological insulators (TIs; refs ,,,), followed by closely related ternary compounds and predictions of several weak TIs (refs ,,). However, both the conceptual richness of Z2 classification of TIs as well as their structural and compositional diversity are far from being fully exploited. Here, a new Z2 topological insulator is theoretically predicted and experimentally confirmed in the β-phase of quasi-one-dimensional bismuth iodide Bi4I4. The electronic structure of β-Bi4I4, characterized by Z2 invariants (1;110), is in proximity of both the weak TI phase (0;001) and the trivial insulator phase (0;000). Our angle-resolved photoemission spectroscopy measurements performed on the (001) surface reveal a highly anisotropic band-crossing feature located at the  point of the surface Brillouin zone and showing no dispersion with the photon energy, thus being fully consistent with the theoretical prediction.

rGO-Wrapped flowerlike Bi2Se3 nanocomposite: synthesis, experimental and simulation-based investigation on cold cathode applications

Bi₂Se₃ nanoflowers (NFs) – reduced graphene oxide (rGO) nanocomposite (BG) synthesized via cost-effective, ecofriendly and easy hydrothermal route: smart cold cathode for future display device.

Optically detecting the edge-state of a three-dimensional topological insulator under ambient conditions by ultrafast infrared photoluminescence spectroscopy

Ultrafast infrared photoluminescence spectroscopy was applied to a three-dimensional topological insulator TlBiSe2 under ambient conditions. The dynamics of the luminescence exhibited bulk-insulating and gapless characteristics bounded by the bulk band gap energy. The existence of the topologically protected surface state and the picosecond-order relaxation time of the surface carriers, which was distinguishable from the bulk response, were observed. Our results provide a practical method applicable to topological insulators under ambient conditions for device applications.

Emergence of topological and topological crystalline phases in TlBiS2 and TlSbS2

Using first-principles calculations, we investigate the band structure evolution and topological phase transitions in TlBiS₂ and TlSbS₂ under hydrostatic pressure as well as uniaxial and biaxial strain. The phase transitions are identified by parity analysis and by calculating the surface states. Zero, one, and four Dirac cones are found for the (111) surfaces of both TlBiS₂ and TlSbS₂ when the pressure grows, which confirms trivial-nontrivial-trivial phase transitions. The Dirac cones at the points are anisotropic with large out-of-plane component. TlBiS₂ shows normal, topological, and topological crystalline insulator phases under hydrostatic pressure, thus being the first compound to exhibit a phase transition from a topological to a topological crystalline insulator.

Synthesis and characterization of 3D topological insulators: a case TlBi(S1-x Se x )2

In this article, practical methods for synthesizing Tl-based ternary III-V-VI2 chalcogenide TlBi(S[Formula: see text]Se x )2 are described in detail, along with characterization by x-ray diffraction and charge transport properties. The TlBi(S[Formula: see text]Se x )2 system is interesting because it shows a topological phase transition, where a topologically nontrivial phase changes to a trivial phase without changing the crystal structure qualitatively. In addition, Dirac semimetals whose bulk band structure shows a Dirac-like dispersion are considered to exist near the topological phase transition. The technique shown here is also generally applicable for other chalcogenide topological insulators, and will be useful for studying topological insulators and related materials.

Turning a band insulator into an exotic superconductor

Understanding exotic, non-s-wave-like states of Cooper pairs is important and may lead to new superconductors with higher critical temperatures and novel properties. Their existence is known to be possible but has always been thought to be associated with non-traditional mechanisms of superconductivity where electronic correlations play an important role. Here we use a first principles linear response calculation to show that in doped Bi₂Se₃ an unconventional p-wave-like state can be favoured via a conventional phonon-mediated mechanism, as driven by an unusual, almost singular behaviour of the electron–phonon interaction at long wavelengths. This may provide a new platform for our understanding of superconductivity phenomena in doped band insulators.

Most superconductors that exhibit exotic pairing symmetries are derived from host materials that are Mott insulators. Xiangang Wan and Sergey Savrasov show that it may be possible to realize an exotic p-wave superconductor in doped Bi₂Se₃, which is a topological band insulator.

Spin-orbit coupling and weak antilocalization in the thermoelectric material β-K₂Bi₈Se₁₃

We have studied the effect of spin-orbital coupling (SOC) on the electronic transport properties of the thermoelectric material β-K₂Bi₈Se₁₃ via magnetoresistance measurements. We found that the strong SOC in this material results in the weak antilocalization (WAL) effect, which can be described well by a three-dimensional weak localization model. The phase coherence length extracted from theoretical fitting exhibits a power-law temperature dependence, with an exponent around 2.1, indicating that the electron dephasing is governed by electron-transverse phonon interactions. As in topological insulators, the WAL effect in β-K₂Bi₈Se₁₃ can be quenched by magnetic impurities (Mn) but is robust against non-magnetic impurities (Te). Although our magnetotransport studies provide no evidence for topological surface states, our analyses suggest that SOC plays an important role in determining the thermoelectric properties of β-K₂Bi₈Se₁₃.

Band structure engineering in topological insulator based heterostructures

The ability to engineer an electronic band structure of topological insulators would allow the production of topological materials with tailor-made properties. Using ab initio calculations, we show a promising way to control the conducting surface state in topological insulator based heterostructures representing an insulator ultrathin films on the topological insulator substrates. Because of a specific relation between work functions and band gaps of the topological insulator substrate and the insulator ultrathin film overlayer, a sizable shift of the Dirac point occurs resulting in a significant increase in the number of the topological surface state charge carriers as compared to that of the substrate itself. Such an effect can also be realized by applying the external electric field that allows a gradual tuning of the topological surface state. A simultaneous use of both approaches makes it possible to obtain a topological insulator based heterostructure with a highly tunable topological surface state.

Signatures of a pressure-induced topological quantum phase transition in BiTeI

We report the observation of two signatures of a pressure-induced topological quantum phase transition in the polar semiconductor BiTeI using x-ray powder diffraction and infrared spectroscopy. The x-ray data confirm that BiTeI remains in its ambient-pressure structure up to 8 GPa. The lattice parameter ratio c/a shows a minimum between 2.0-2.9 GPa, indicating an enhanced c-axis bonding through p(z) band crossing as expected during the transition. Over the same pressure range, the infrared spectra reveal a maximum in the optical spectral weight of the charge carriers, reflecting the closing and reopening of the semiconducting band gap. Both of these features are characteristics of a topological quantum phase transition and are consistent with a recent theoretical proposal.

Organic topological insulators in organometallic lattices

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

Topological phase diagrams of bulk and monolayer TiS2-x Tex

With the use of ab initio calculations, the topological phase diagrams of bulk and monolayer TiS(2-x) Te(x) are established. Whereas bulk TiS(2-x) Te(x) shows two strong topological phases [1;(000)] and [1;(001)] for 0.44<x<0.56 and 0.56<x<1, respectively, the monolayer is topologically nontrivial for 0.48<x<0.80. Because in the latter doping range the topologically nontrivial nature survives down to a monolayer, TiS(2-x) Te(x) is a unique system for studying topological phases in three and two dimensions simultaneously.

Spin polarization of gapped Dirac surface states near the topological phase transition in TlBi(S(1-x)Se(x))2

We performed systematic spin- and angle-resolved photoemission spectroscopy of TlBi(S(1-x)Se(x))(2) which undergoes a topological phase transition at x ~ 0.5. In TlBiSe(2) (x = 1.0), we revealed a helical spin texture of Dirac-cone surface states with an intrinsic in-plane spin polarization of ~0.8. The spin polarization still survives in the gapped surface states at x > 0.5, although it gradually weakens upon approaching x = 0.5 and vanishes in the nontopological phase. No evidence for the out-of-plane spin polarization was found, irrespective of x and momentum. The present results unambiguously indicate the topological origin of the gapped Dirac surface states, and also impose a constraint on models to explain the origin of mass acquisition of Dirac fermions.

Topological surface states with persistent high spin polarization across the Dirac point in Bi2Te2Se and Bi2Se2Te

Helical spin textures with marked spin polarizations of topological surface states have been unveiled for the first time by state-of-the-art spin- and angle-resolved photoemission spectroscopy for two promising topological insulators, Bi(2)Te(2)Se and Bi(2)Se(2)Te. Their highly spin-polarized natures are found to be persistent across the Dirac point in both compounds. This novel finding paves a pathway to extending the utilization of topological surface states of these compounds for future spintronic applications.

Prediction of weak topological insulators in layered semiconductors

We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit cell as a prerequisite for forming weak topological insulators. Here, the single-layered KHgSb is the most suitable candidate for its large bulk energy gap of 0.24 eV. Its side surface hosts metallic surface states, forming two anisotropic Dirac cones. Although the stacking of even-layered structures leads to trivial insulators, the structures can host a quantum spin Hall layer with a large bulk gap, if an additional single layer exists as a stacking fault in the crystal. The reported honeycomb compounds can serve as prototypes to aid in the finding of new weak topological insulators in layered small-gap semiconductors.

Topological materials

Recently, topological insulator materials have been theoretically predicted and experimentally observed in both 2D and 3D systems. We first review the basic models and physical properties of topological insulators, using HgTe and Bi(2)Se(3) as prime examples. We then give a comprehensive survey of topological insulators which have been predicted so far, and discuss the current experimental status.

Experimental verification of PbBi2Te4 as a 3D topological insulator

The experimental evidence is presented of the topological insulator state in PbBi2Te4. A single surface Dirac cone is observed by angle-resolved photoemission spectroscopy with synchrotron radiation. Topological invariants Z2 are calculated from the ab initio band structure to be 1;(111). The observed two-dimensional isoenergy contours in the bulk energy gap are found to be the largest among the known three-dimensional topological insulators. This opens a pathway to achieving a sufficiently large spin current density in future spintronic devices.

A search model for topological insulators with high-throughput robustness descriptors

Topological insulators (TI) are becoming one of the most studied classes of novel materials because of their great potential for applications ranging from spintronics to quantum computers. To fully integrate TI materials in electronic devices, high-quality epitaxial single-crystalline phases with sufficiently large bulk bandgaps are necessary. Current efforts have relied mostly on costly and time-consuming trial-and-error procedures. Here we show that by defining a reliable and accessible descriptor , which represents the topological robustness or feasibility of the candidate, and by searching the quantum materials repository aflowlib.org, we have automatically discovered 28 TIs (some of them already known) in five different symmetry families. These include peculiar ternary halides, Cs{Sn,Pb,Ge}{Cl,Br,I}(3), which could have been hardly anticipated without high-throughput means. Our search model, by relying on the significance of repositories in materials development, opens new avenues for the discovery of more TIs in different and unexplored classes of systems.

Topological surface states in lead-based ternary telluride Pb(Bi(1-x)Sb(x))2Te4

We have performed angle-resolved photoemission spectroscopy on Pb(Bi(1-x)Sb(x))2Te4, which is a member of lead-based ternary tellurides and has been theoretically proposed as a candidate for a new class of three-dimensional topological insulators. In PbBi2Te4, we found a topological surface state with a hexagonally deformed Dirac-cone band dispersion, indicating that this material is a strong topological insulator with a single topological surface state at the Brillouin-zone center. Partial replacement of Bi with Sb causes a marked change in the Dirac carrier concentration, leading to the sign change of Dirac carriers from n type to p type. The Pb(Bi(1-x)Sb(x))2Te4 system with tunable Dirac carriers thus provides a new platform for investigating exotic topological phenomena.

Robustness of topological order and formation of quantum well states in topological insulators exposed to ambient environment

The physical property investigation (like transport measurements) and ultimate application of the topological insulators usually involve surfaces that are exposed to ambient environment (1 atm and room temperature). One critical issue is how the topological surface state will behave under such ambient conditions. We report high resolution angle-resolved photoemission measurements to directly probe the surface state of the prototypical topological insulators, Bi(2)Se(3) and Bi(2)Te(3), upon exposing to various environments. We find that the topological order is robust even when the surface is exposed to air at room temperature. However, the surface state is strongly modified after such an exposure. Particularly, we have observed the formation of two-dimensional quantum well states near the exposed surface of the topological insulators. These findings provide key information in understanding the surface properties of the topological insulators under ambient environment and in engineering the topological surface state for applications.

Emergence of non-centrosymmetric topological insulating phase in BiTeI under pressure

The spin-orbit interaction affects the electronic structure of solids in various ways. Topological insulators are one example in which the spin-orbit interaction leads the bulk bands to have a non-trivial topology, observable as gapless surface or edge states. Another example is the Rashba effect, which lifts the electron-spin degeneracy as a consequence of the spin-orbit interaction under broken inversion symmetry. It is of particular importance to know how these two effects, that is, the non-trivial topology of electronic states and the Rashba spin splitting, interplay with each other. Here we show through sophisticated first-principles calculations that BiTeI, a giant bulk Rashba semiconductor, turns into a topological insulator under a reasonable pressure. This material is shown to exhibit several unique features, such as a highly pressure-tunable giant Rashba spin splitting, an unusual pressure-induced quantum phase transition, and more importantly, the formation of strikingly different Dirac surface states at opposite sides of the material.

Topological Superconductivity in Cu(x)Bi(2)Se(3)

A topological superconductor (TSC) is characterized by the topologically protected gapless surface state that is essentially an Andreev bound state consisting of Majorana fermions. While a TSC has not yet been discovered, the doped topological insulator Cu(x)Bi(2)Se(3), which superconducts below ∼3 K, has been predicted to possess a topological superconducting state. We report that the point-contact spectra on the cleaved surface of superconducting Cu(x)Bi(2)Se(3) present a zero-bias conductance peak (ZBCP) which signifies unconventional superconductivity. Theoretical considerations of all possible superconducting states help us conclude that this ZBCP is due to Majorana fermions and gives evidence for a topological superconductivity in Cu(x)Bi(2)Se(3). In addition, we found an unusual pseudogap that develops below ∼20 K and coexists with the topological superconducting state.

Majorana modes at the ends of superconductor vortices in doped topological insulators

Recent experiments have observed bulk superconductivity in doped topological insulators. Here we ask whether vortex Majorana zero modes, previously predicted to occur when s-wave superconductivity is induced on the surface of topological insulators, survive in these doped systems with metallic normal states. Assuming inversion symmetry, we find that they do but only below a critical doping. The critical doping is tied to a topological phase transition of the vortex line, at which it supports gapless excitations along its length. The critical point depends only on the vortex orientation and a suitably defined SU(2) Berry phase of the normal state Fermi surface. By calculating this phase for available band structures we determine that superconducting p-doped Bi(2)Te(3), among others, supports vortex end Majorana modes. Surprisingly, superconductors derived from topologically trivial band structures can support Majorana modes too.

Direct measurement of the out-of-plane spin texture in the Dirac-cone surface state of a topological insulator

We have performed spin- and angle-resolved photoemission spectroscopy of Bi(2)Te(3) and present the first direct evidence for the existence of the out-of-plane spin component on the surface state of a topological insulator. We found that the magnitude of the out-of-plane spin polarization on a hexagonally deformed Fermi surface of Bi(2)Te(3) reaches maximally 25% of the in-plane counterpart, while such a sizable out-of-plane spin component does not exist in the more circular Fermi surface of TlBiSe(2), indicating that the hexagonal deformation of the Fermi surface is responsible for the deviation from the ideal helical spin texture. The observed out-of-plane polarization is much smaller than that expected from the existing theory, suggesting that an additional ingredient is necessary for correctly understanding the surface spin polarization in Bi(2)Te(3).

Topological magnetic insulators with corundum structure

Topological insulators are new states of quantum matter in which surface states residing in the bulk insulating gap are protected by time-reversal symmetry. When a proper kind of antiferromagnetic long-range order is established in a topological insulator, the system supports axionic excitations. In this Letter, we study theoretically the electronic states in a transition metal oxide of corundum structure, in which both spin-orbit interaction and electron-electron interaction play crucial roles. A tight-binding model analysis predicts that materials with this structure can be strong topological insulators. Because of the electron correlation, an antiferromagnetic order may develop, giving rise to a topological magnetic insulator phase with axionic excitations.

Three-dimensional topological insulators in I-III-VI2 and II-IV-V2 chalcopyrite semiconductors

Using first-principles calculations within density functional theory, we investigate the band topology of ternary chalcopyrites of composition I-III-VI2 and II-IV-V2. By exploiting adiabatic continuity of their band structures to the binary 3D-HgTe, combined with direct evaluation of the Z2 topological invariant, we show that a large number of chalcopyrites can realize the topological insulating phase in their native states. The ability to host room-temperature ferromagnetism in the same chalcopyrite family makes them appealing candidates for novel spintronics devices.