Modular Design with 2D Topological-Insulator Building Blocks

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Modular Design with 2D Topological-Insulator Building Blocks: Optimized Synthesis and Crystal Growth, Crystal and Electronic Structures of BiTeI (x = 2, 3) x

Alexander Zeugner, Martin Kaiser, Peer Schmidt, Tatiana V. Menshchikova, Igor P. Rusinov, Anton V. Markelov, Wouter Van den Broek, Evgueni V. Chulkov, Thomas Doert, Michael Ruck, and Anna Isaeva Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.6b05038 • Publication Date (Web): 09 Jan 2017 Downloaded from http://pubs.acs.org on January 9, 2017

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Chemistry of Materials

Modular Design with 2D Topological-Insulator Building Blocks: Optimized Synthesis and Crystal Growth, Crystal and Electronic Structures of BixTeI (x = 2, 3) Alexander Zeugner1, Martin Kaiser1, Peer Schmidt2, Tatiana V. Menshchikova3, Igor P. Rusinov3,4, Anton V. Markelov5, Wouter Van den Broek6, Evgueni V. Chulkov3,4,7,8,9, Thomas Doert1, Michael Ruck1, Anna Isaeva1* 1

Technische Universität Dresden, Department of Chemistry and Food Chemistry, Helmholtzstraße 10, 01069 Dresden, Germany 2 Brandenburgische Technische Universität (BTU) Cottbus–Senftenberg, Department of Applied Chemistry, Universitätsplatz 1, 01968 Senftenberg, Germany 3

Tomsk State University, pr. Lenina, 36, 634050 Tomsk, Russia

4

St. Petersburg State University, Universitetskaya nab., 7/9, 199034 St. Petersburg, Russia

5

SuperOx, Odintsovskii district, 143082 Moscow region, Russia

6

Humboldt Universität zu Berlin, Department of Physics, Newtonstraße 15, 12489 Berlin, Germany

7

Donostia International Physics Center (DIPC), Paseo de Manuel Lardizabal, 4, 20018 San Sebastián/Donostia, Basque Country, Spain

8

Departamento de Física de Materiales, Facultad de Ciencias Químicas, UPV/EHU, 20080 San Sebastián/Donostia, Basque Country, Spain

9

Centro de Física de Materiales CFM–MPC, Centro Mixto CSIC–UPV/EHU, 20080 San Sebastián/Donostia, Basque Country, Spain

ABSTRACT: Structural engineering of topological bulk materials is systematically explored on the example of incorporation of the buckled bismuth layer [Bi2], which is a 2D topological insulator per se, into the layered BiTeI host structure. The previously known bismuth telluride iodides, BiTeI and Bi2TeI, offer physical properties relevant for spintronics. Herewith a new cousin, Bi3TeI (sp.gr. R3m, a = 440.12(2) pm, c = 3223.1(2) pm), joins the ranks and expands this structural family. Bi3TeI = [Bi2][BiTeI] represents a stack with strictly alternating building blocks. Conditions for reproducible synthesis and crystal-growth of Bi2TeI and Bi3TeI are ascertained; thus yielding platelet-like crystals on the mm size scale and enabling direct measurements. The crystal structures of Bi2TeI and Bi3TeI are examined by X-ray diffraction and electron microscopy. DFT calculations predict metallic properties of Bi3TeI and an unconventional surface state residing on various surface terminations. This state emerges as a result of complex hybridization of atomic states due to their strong intermixing. Our study does not support the existence of new stacking variants BixTeI with x > 3; instead it indicates a possible homogeneity range of Bi3TeI. The series BiTeI – Bi2TeI – Bi3TeI illustrates the influence of structural modifications on topological properties.

INTRODUCTION The advent of topological insulators let many bismuth-based materials that had been investigated before primarily in the context of their thermoelectric properties shine in new splendour.1–3 The classic concept of a topological insulator (TI) “protected” by the time-reversal symmetry postulates the existence of bulk semiconductors that host spin-resolved edge or surface states. These states enable surface spin transport resilient to backscattering thanks to spin–momentum locking.1,2 Just like the quantum Hall effect, this particular phenomenon is intimately connected with the symmetries of matter and hence is not limited to any particular class of

compounds with certain “chemical” markings. It became evident that topological phases are versatile and that topological robustness of the surface spin-polarized states against backscattering can also be realized through crystal lattice symmetries, e.g. mirror and glide planes4,5,6 in so called topological crystalline insulators (TCI) (SnTe7, Bi2Te38, Bi4Se39,10) and topological non-symmorphic crystalline insulators11 and superconductors12. Furthermore, signatures of 3D Dirac fermions were recently observed in Weyl semimetals13 opening up prospects for topological transport in bulk. These findings increase hopes that TI compounds should be widely accessible. Nevertheless, an ultimate confirmation of the topological properties can only be delivered

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experimentally which necessitates high-quality crystals and a high degree of control over a compound’s stoichiometry. The latter is complicated, for instance, by ubiquitous point defects in the famous 3D strong topological insulators Bi2Te3 and Bi2Se3. The resultant lack of insulating behavior in the bulk has been remedied by development of the first bulkinsulating 3D TI Bi2Te2Se (BTS)14 with compensated Se vacancies and Bi/Te antisite defects and, later on, of the outmost bulk-insulating Bi2–xSbxTe3–ySey (BSTS)15 material with tunable Dirac carriers. Besides Bi2X3 (X = Se, Te), numerous bismuth-rich chalcogenides have been reported which all share the same modular building principle: they are heterostructures stacked from building blocks of two types, i. e. buckled bismuth [Bi2] and quintuple [Bi2X3] (X = Se, Te) layers that exhibit an almost ideal geometrical match. Owing to this fact almost any arbitrary [Bi2]m[Bi2Te3]n composition with either ordered or random stacking sequence of these layers can be synthesized.16,17 Such structural flexibility, on the one hand, enables fine tuning of the electronic structure and multiple substitutions in bismuth chalcogenides, but, on the other hand, also accounts for their strong propensity to stacking disorder. It poses a major problem for synthesis of materials with predefined compositions. Due to the similarity of Bi–Bi, Bi–Te and Bi–I bonding distances, the advantages of modular structural design are also accessible for some bismuth iodides.18 In particular, layered BiTeI seems to be a promising host structure.19 BiTeI is the first Rashba material with giant splitting of bulk and surface states20–23 and may undergo a pressure-induced topological transition24–26. The latter is being intensively studied nowadays both theoretically and experimentally,27–29 and very recently a superconducting state in a high-pressure modification of BiTeI was reported30,31. Incorporation / intercalation into the van der Waals gaps in between 2∞[BiTe3/3I3/3] triple layers was studied mostly with respect to its thermoelectric performance32,33; and, most interestingly for the present discussion, it was shown that the buckled bismuth sheet can enter the BiTeI host structure to form the periodic Bi2TeI bulk structure34, which accomodates [Bi2] layers in every second van der Waals gap of the BiTeI host structure and also attains an inversion centre due to the flip of each second [BiTeI] triple layer. The effects of varying bismuth content on the thermoelectric performance of [Bi2]m[Bi2Te3]n heterostructures were in the focus of earlier studies, but the addition of bismuth is relevant for topological properties as well. The corrugated bismuth layer was theoretically35 and experimentally36,37 characterized as a 2D TI with a pair of helical edge states. From this viewpoint, [Bi2]m[Bi2X3]n are stacks of interacting topological fragments that account for various TI properties of the entire compound. For instance, in the series of the increasing number of [Bi2] layers per quintuple [Bi2X3] layer one goes from a 3D strong TI in Bi2Te3 to a 3D weak TI in BiTe = [Bi2][Bi2Te3]238 and likely in isostructural BiSe thin-film39, then to a topological semimetal in Bi4Se3 = [Bi2][Bi2Se3]9. One intriguing finding is that the listed bismuth tellurides also exhibit dual topological nature being simultaneously TCIs.8,9,38 The intuitive idea that the [Bi2] structural fragment may trigger topological properties in other materials but bismuth chalcogenides, for instance bismuth halides18, was further confirmed by calculations on Bi2TeI40 and by direct measurements on β-Bi4I441. Furthermore, signatures of a possible TCI state were recently calculated for Bi2TeI42,

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making it phenomenologically very similar to the dual topological insulator BiTe38. On top of that a recent theoretical exploration of lattice thermal conductivity in Bi2TeI at room temperature predicts decent thermoelectric performance in this stacked weak 3D TI with an emphasis on the crucial role of topologically trivial spacer layers.43 However, experimental verification of these perspectives for Bi2TeI has so far been impeded by the unavailability of suitably large single crystals or phase-pure powders. Our present study fills up this gap and picks up the baton directly from the earlier pivotal works on Bi2TeI34,44,45; and since we very much take it from where they left it, these papers are addressed in detail in the next section. Another task tackled here is an experimental exploration of a possibility to introduce more [Bi2] fragments into the BiTeI host structure that led to the discovery of Bi3TeI. Its structure demonstrates incorporation of [Bi2] into all van der Waals gaps of the BiTeI host structure. In the first section synthesis of BixTeI (x = 2, 3) powders is optimized and a short account on possible bismuth-richer telluride iodides is given. The second section reports modelling and execution of crystal-growth experiments for BixTeI (x = 2, 3); whereas the third one encompasses crystalstructure elucidation from powder and single crystal X-ray diffraction data, and considers evolution of the chemical bonding in the BiTeI–Bi2TeI–Bi3TeI series. The fourth section summarizes electronic-structure calculations of bulk and surface of Bi3TeI.

RESULTS AND DISCUSSION 1. Powder Synthesis and Thermal Stability of BixTeI Earlier on, annealing of powders for up to several weeks, gas-phase reactions and cooling of melts studied in the temperature range from 300 to 650 °C did not yield phase-pure Bi2TeI or attempted bismuth-richer BixTeI (x = 3, 5, 7) compounds.34 Bi2TeI crystals could not be reproducibly obtained from the stoichiometric mixtures of various starting materials. Moreover, [34] gave evidence for “Bi4TeI1.25” (composition elucidated by EDX) that, as the authors assumed, could correspond to incorporation of the [Bi2] layers into all van der Waals gaps in the parent BiTeI structure; but no further structural evidence could be gained. It should also be mentioned that the nominal composition corresponding to a stack with one [Bi2] layer per each van der Waals gap is Bi3TeI. Ensuing studies44,45 of solid-state equilibria in the Bi–Te–I system and thermodynamic properties of the respective ternaries by electromotive forces (EMF) method offered a plausible explanation to the experimental problems above. Since Bi2TeI and “Bi4TeI1.25” were found to melt incongruently at 450 °C and 415 °C, respectively, attempts to synthesize these phases above the peritectic melting temperatures are not optimal. Further attempts to synthesize BixTeI (x = 2–7)46,47 powders by melting of the starting materials at the first step, followed by mechanochemical activation of ingots, pressing into pellets and annealing at 250–300 °C for up to 2 weeks yielded inhomogeneous powdered samples that either contained impurities or exhibited strong disorder in BixTeI that manifested itself in considerable broadening of the reflections. Similar results were reproduced in this work from the experiments on slow cooling of the starting materials from


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550 °C at the rate of 2 °/hour (Fig. S1). One of the possible reasons could be a compositional shift due to the loss of iodine at elevated temperatures at the first step, since both elemental iodine and BiI3 used for the reactions have high vapor pressure. Elemental bismuth was observed as a by-product in PXRD after the first step, although it was incorporated into the ternaries during the further synthesis steps (mechanochemical activation, long-term annealing) that followed the initial melting.47 1.1. Powder Synthesis Optimization Based on the results of the previous works, we intentionally abstained from using melts at any step of the developed synthetic procedure. Instead all samples were annealed in the subsolidus temperature range for all studied compositions. In order to diminish the gas-phase pressure and to ensure the stoichiometric composition, BiI3 was used as a starting material instead of elemental iodine. Moreover, the reactants were heated up slowly (1 °/min) to circumvent quick evaporation of BiI3 and resultant compositional shifts. Although no clear tendencies could be derived from the choice of starting materials, phase-pure powdered samples could be synthesized with BiI3 only. Mechanochemical activation of the reactants either by thorough grinding in a mortar or by ball milling prior to any temperature treatment has proven to be very efficient. Presynthesized Bi2TeI was observed along with slight Bi impurities after ball milling, before any annealing (see Fig. S2 for respective PXRD patterns). The listed synthetic conditions led to formation of Bi2TeI powders which, however, showed a slight temperature dependence. Whereas PXRD of the samples annealed at 425 °C entirely accorded with the theoretical diffraction pattern of Bi2TeI from the reported structure solution34, samples annealed at 400 °C only exhibited the general motif of the theoretical PXRD pattern plus some unidentified reflections, slight shifts and broadening of some reflections. The PXRD pattern of the former sample is used in a later section for the Rietveld refinement. Importantly, the strongly textured samples synthesized by this optimized procedure are significanlty more ordered and well-crystalline than those obtained by cooling melts (Fig. 1). Furthermore, following the guidance of the previous works34,44,45 we tested the Bi3TeI composition using the newly established tribochemical activation and annealing in the subsolidus region. The exact composition had already been targetted34, but the annealed samples did not show signatures of this phase (likely due to their non-equilibrium nature). Our attempts resulted in powdered samples of this new ternary phase (see EDX, PXRD and SCXRD below). A theoretical PXRD pattern used for identification of Bi3TeI was first constructed based on a hypothetical unit cell. It contained bismuth layers occupying every van der Waals gap in the BiTeI host structure and its unit cell parameters were those determined for “Bi4TeI1.25”34. This starting rough model was refined (see Rietveld refinement and a single-crystal X-ray diffraction experiment in the next section) and the resultant crystallographic parameters where used henceforward. As does Bi2TeI, the new compound already preforms after ball miling (Fig. S2). The synthesis of Bi3TeI appeared to be more precarious, since various by-products, for instance, small amounts of Bi, BiOI, Bi2TeI and unidentified sets of reflections that could be attributed to “Bi3TeI” with a slight shift in parameters, were found after several synthetic attempts

at seemingly identical conditions. An almost phase-pure sample of this bismuth telluride iodide was obtained after 30 days of annealing at 400 °C and was used for the Rietveld refinement and the thermochemical study discussed in detail below. 1.2. Thermal Stability The obtained phase-pure BixTeI (x = 2, 3) samples were used for differential scanning calorimetry (DSC) analysis along with a BiTeI sample synthesized according to [19]. The literature data48–50 on congruent melting of BiTeI were undoubtedly confirmed, while both Bi2TeI and Bi3TeI were found to melt incongruently at ϑons = 448 °C and ϑons = 411 °C, respectively (Fig. 2). After the cooling run, the phase compositions of the samples were analyzed by PXRD yielding a mixture of BiTeI, Bi2TeI, Bi3TeI and Bi for the initial Bi2TeI sample; and a mixture of Bi2TeI, Bi3TeI and Bi for the initial Bi3TeI sample. No hints towards existence of more bismuthrich distinct phases, for instance Bi4TeI, could be obtained based on these PXRD data. All data combined allowed us to sketch a polythermal section of the Bi–BiTeI pseudo-binary phase diagram with the melting points and univariant equilibria (Fig. 3). The DSC cooling curves are given in the Supporting Information together with the respective PXRD patterns after the DSC experiments (Fig. S3 and Fig. S4).

Figure 1. Comparison of the experimental PXRD patterns with the starting Bi2TeI composition prepared via melting (slow cooling of the reactants from 550 °C at 2 °/h for 11 days) and by our optimized procedure with the theoretical Bi2TeI pattern34. Note the strong preferred orientation of Bi2TeI (SSR).

The phase relations and the transition temperatures found in this work are in excellent agreement with those obtained earlier by the EMF method44,45. Moreover, the peritectic melting temperature of Bi3TeI (ϑons = 411 °C, ϑpeak = 414 °C) coincides with that of “Bi4TeI1.25” (only ϑpeak = 415 °C is given)44,45. Unfortunately, a more detailed comparison is impossible since no powder diffraction data were published for “Bi4TeI1.25”. The discrepancies in the thermodynamic parameters and compositions could be due to a broad homogeneity range of the same phase or due to the fact that two different phases are dealt with. Our experimental contribution to this issue is given in the next subsection.



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Figure 2. Heating DSC curves for phase-pure BixTeI samples showing their melting.

Figure 3. Schematic representation of the pseudo-binary Bi– BiTeI section from the DSC data. Existence of Bi4TeI is not confirmed (see text). Characteristic onset-temperatures are given.

Ideas about the optimal single-crystal growth conditions for Bi2TeI and Bi3TeI can be derived from the mutually consistent EMF44,45 and present DSC data. Generally much lower temperatures should be used than those reported in literature (above 550 °C)34,51 and cooling of melts should be avoided due to peritectic behavior. Instead slow cooling of presynthesized phase-pure powders (mineralization) in the range between 450 °C and 410 °C seems to be the most appropriate way to obtain Bi2TeI, and below 410 °C — to obtain Bi3TeI. Advanced thermochemical modelling taking into account the gas-phase was employed to find the optimal crystal-growth conditions. The results of mineralization experiments and vapor-phase reactions are reported in the following section. The above mentioned temperature dependence of phasepurity for Bi2TeI can also be explained based on the explored phase diagramm. The thermodynamically stable Bi3TeI may be a competing phase at 400 °C; hence the temperature for Bi2TeI synthesis was adjusted to 425 °C and thus phase-pure powder samples were reproducibly obtained. In contrast, “Bi3TeI” powder annealed at 400 °C always lost bismuth either as elemental Bi or even as BiOI, thus resulting in an inhomogeneous phase mixture. Nevertheless, Bi3TeI crystals that grew in the long-annealed batches alongside the powder always showed perfectly stoichiometric composition (see

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below). The EDX spectra of these crystals conclusively demonstrate absence of oxygen (Fig. S5). 1.3. Compositions BixTeI with x > 3: a Note on “Bi4TeI1.25” An attempt to find the compositional limit of bismuth incorporation into the BiTeI host structure was already undertaken.47 Those samples were synthesized from the elements, were molten and then annealed at the subsolidus temperatures. They were inhomogeneous and showed strong structural disorder manifesting itself in the broadening of reflections. Nevertheless, it was suggested that the limit lies somewhere between x = 4 and x = 5, since elemental bismuth was observed as a by-product. On the other hand, elemental bismuth was seen as an admixture on various stages of synthesis and it was assumed that it incorporates into the ternaries at the later stages. Since such process is kinetically driven, the limit could not be determined inconclusively. We attempted to synthesize “Bi4TeI1.25” starting from a stoichiometric mixture of Bi, Te and BiI3, and employing ball milling and annealing at 350 °C for 7 days. The PXRD of the homogeneous product strongly resembles the pattern of the phase-pure Bi3TeI with 00l-reflections shifted to lower 2θ values (Fig. 4). The unit cell paramters determined via Le Bail analysis are a = 439.7(1) pm and c = 3245.8(2) pm, whereas the subcell reported for “Bi4TeI1.25”34 is a = 438.7(3) pm, c = 652(1) pm. Hence the c axis for our sample is only 14.2 pm shorter than the fivefold c axis (3260(5) pm) of “Bi4TeI1.25”. Furthermore, a DSC experiment of the ball-milled presynthesized product shows only peritectic melting at ϑons = 395 °C, ϑpeak = 398 °C, and no traces of any reactions of formation between the reactants at lower temperatures (Fig. S6). The phase composition of the sample after the DSC study reveals a mixture of Bi3TeI, Bi2TeI and Bi (Fig. S7). The described sample contained no crystals, so further crystal-growth attempts were undertaken. An experiment that yielded the targetted crystals was concieved as follows: two scoops with TeI4 and elemental bismuth (taken in tenfold molar excess with respect to TeI4) were spatially separated in a vacuum-sealed ampoule and kept at 425 °C for 60 hours, then slowly cooled down at about 2 °/min down to room temperature. Abundant crystalline lamellae (> 500 µm in length) with the averaged composition Bi64Te15I21 (EDX) grew exclusively on the bismuth melt. This determined composition matches “Bi4TeI1.25” fairly well (EDX, in at. %): Bi, 63.1; Te, 16.8; I, 21.034. Structural analysis of the extracted crystals was not possible due to strong structural disorder (diffuse scattering along the stacking direction). The PXRD of the collected crystals once again resembled the Bi3TeI pattern, although with very broad reflections and admixtures of bismuth (Fig. S8). These data allow us to assume that: 1) Bi3TeI may have a homogeneity range stretching towards tellurium-deficient compositions or iodine-richer ones; 2) there are likely no distinct bismuth-richer phases with a different structural motif. Based on that, we suggest to interprete Bi64Te15I21 and “Bi4TeI1.25”34 as a Te-poorer Bi3Te1–yI (y ~ 0.2) phase rather than a bismuth-richer phase with a caveat that a more detailed study is required to clarify this point.


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Chemistry of Materials they describe entirely all relevant gas-phase species. Both the total pressure and the composition of the gas phase determine the crystallization behavior of the respective compounds in the course of vapor-phase crystallization. Calculations of gasphase composition for different compositions reveal that the total pressure is dominated by the partial pressures of BiI3(g) for the areas I to VII, where additionally subsidiary species BiI(g), Te2(g) and I2 are formed. The areas VIII and IX are characterized by dominant gas species BiI(g), BiI3(g), Te2(g), and I(g).

Figure 4. Experimental PXRD for a “Bi4TeI1.25” sample compared with the theoretical pattern for Bi3TeI derived from the crystal-structure solution (see following sections).

An attempt to prepare a “Bi4TeI” sample following the developed synthesis procedure yielded a two-phase mixture of Bi3TeI and elemental bismuth (Fig. 5). Thus, our findings do not support further incorporation of bismuth into the BiTeI host structure and formation of adjacent pairs of [Bi2] layers next to each other. Figure 6. Calculation of the ternary phase diagram of the Bi–Te–I system at ϑ = 400°C.

The areas I, II, and III are subject to the existence of BiI3(s,l) and its equilibrium pressure of sublimation p(BiI3(g)) (Fig. 7).

Figure 5. Experimental PXRD for a “Bi4TeI” sample compared with the theoretical pattern for Bi3TeI derived from the crystal-structure solution.

2. Crystal Growth of BixTeI (x = 2, 3) Since crystallization from melts is not optimal or controllable for BixTeI, the potential of chemical-vaportransport (CVT) for crystal growth is exploited further. 2.1. Calculation of an Isothermal Phase Diagram and Vapor Pressure Behavior of the Bi–Te–I System Bi3TeI exists on a pseudo-binary line between BiTeI and elemental bismuth, besides the already known phase Bi2TeI (Fig. 3, [44, 45]). These ternary phases coexist in several ternary areas with the binary compounds Bi2Te3, BiI3, BiI, and elemental tellurium, respectively. These different areas (labeled by Roman numerals, Fig. 6) are characterized by typical vapor-pressure behavior. Only a selected number of known binary Bi–Te and Bi–I phases were considered here for the sake of computational convenience and due to the fact that

Figure 7. Calculation of total pressure behavior within the ternary areas of the Bi–Te–I system55, lg(p/bar) vs. temperature. The total pressure is dominated by the partial pressures of BiI3(g) for the areas I to VII; subsidiary the species BiI(g), Te2(g) and I2 occurs. The areas VIII and IX show dominant vapor pressure of BiI(g) besides BiI3(g), Te2(g), and I(g).

Substance mixtures within the areas I to III already cause condensation of BiI3. Depending on temperature, BiI3 is obtained as solid crystals or as a liquid (ϑm = 409 °C52). Area IV is well suited for crystallization of BiTeI. The vapor-phase deposition of BiTeI can be described as a decomposition sublimation (ϑ2 = 530 °C to ϑ1 = 490 °C53). If the substance amount of BiTeI within the area IV is much lower than needed for saturation of the respective equilibrium pressure (below curve IV, Fig. 7), the vapor transport of Bi2Te3 (ϑ2 = 500 °C to



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ϑ1 = 450 °C) can be performed without condensation of BiTeI54. According to our calculations, area V is preferred for deposition of Bi2TeI besides BiTeI. The areas VI and VII are dominated by evaporation and deposition of BiI(s), if a temperature gradient is applied for vapor transport. Finally, the existence of the newly identified compound Bi3TeI is bordered by ternary areas VIII and IX (Fig. 6). 2.2. Crystal Growth of Bi2TeI In contrast to previously reported attempts to grow Bi2TeI crystals at elevated temperatures (e.g. 650/550 °C by CVT34, 700 °C by Bridgman technique46,47 or by cooling of a bismuthrich melt from 850 °C to 550 °C51) we focused on the temperature range at around 400 °C. Presynthesized phasepure powder was used as a charge. Short-distance transport56,57 or mineralization of the initial solid via the gas-phase appeared to be possible, but only when the charge was exposed to a small temperature gradient (for instance, 410 °C → 390 °C). Platelet-like crystals of about 1 mm in diameter grew on the “colder” side of the widely distributed charge (flattened over appr. 2 cm on the ampoule’s bottom) over 2 weeks. Increasing time to 4 weeks resulted in the crystals of up to 2 mm in diameter (Fig. 8). EDX confirmed the uniform composition of the crystals (Fig. 8).

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According to the modelling of heterogeneous phase equilibria, in the course of thermal decomposition of Bi3TeI the vapor phase is dominated by BiI(g). The remained solid Bi2Te3 decomposes in further degradation with significantly lower partial pressures of BiTe(g) and Te2(g) (Fig. 9). Additional homogeneous gas-phase equilibria form more bismuth-, tellurium-, and iodine-containing species. Decomposition: 3Bi3TeI(s) ⇌ Bi2Te3(s) + 4Bi(s,l) + 3BiI(g) 2/5 Bi2Te3(s) ⇌ 4/5 BiTe(g) + 1/5 Te2(g) Homogeneous gas phase equilibria: 3 BiI(g) ⇌ BiI3(g) + Bi2(g) Bi2(g) ⇌ 2 Bi(g) BiI3(g) ⇌ BiI(g) + I2(g) I2(g) ⇌ 2 I(g) Te2(g) ⇌ 2 Te(g)

Figure 9. Composition of the gas-phase of Bi3TeI within the ternary area IX of the Bi–Te–I phase diagram calculated using the program TRAGMIN55 applying the thermodynamic standard data (Table E1, Experimental Section). Figure 8. Bi2TeI crystals from a single-growth experiment (upper row). Typical single crystals of Bi2TeI used for an SCXRD experiment (lower row). EDX data (averaged over 10 crystals (ca. 10 points per crystal) from 3 batches, in at.%): Bi, 50.3(3); Te, 25.4(2); I, 24.3(2).

The described synthetic conditions also correspond to those predicted to promote CVT (autotransport) of Bi2TeI in the area V (Fig. 6). The mass transport was however negligible, and only a couple of transported crystals were found in the middle of one of the ampoules. 2.3. Crystal Growth of Bi3TeI Crystal-growth processes of phases in the Bi–Te–I system can easily be described by various vapor-phase-reactions mechanisms (related examples of BiTeI and Bi2Te3 are discussed in the Supplement).56,57 With the vapor transport of BiTeI in mind (cf. Supplement and [53, 58]) the crystallization of Bi3TeI has been studied via the gas phase within the stability range of the compound (below 410 °C).

Due to the high activity of bismuth, the total vapor pressure, and thus all the species partial pressures remain lower in comparison to the one of BiTeI and Bi2TeI (see Fig. 7). Below the peritectic decomposition, partial pressures of only 10‒5 bar for BiI(g) down to 10‒8 bar for the other species result. Actually, these partial pressures are too low to be efficient for regular vapor transports: it is well known that changes in partial pressures ∆p(i) source→sink of transport relevant species has to be at least 10‒4 bar.56,57 Nevertheless, short-distance transport56,57 or mineralization of the initial solid via the gasphase appears to be possible. Thereby, the transport mechanism can be described based on the calculated transport efficiencies55 (Fig. 10). Transport efficiency: ∆

∗

∗

∗ →

Here, negative value of transport efficiency w(i) indicates the function of the transport agent: this gas species is depleted


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at the source and released at the sink. Otherwise, transport relevant species feature positive values w(i), as they evaporate at source and condense at the sink under formation of the crystalline solid. This way, the crystallization of Bi3TeI via the gas-phase can be described by the evaporation reaction with BiI3(g) as a transport agent under formation of transport relevant species BiI(g) and Te2(g) (Fig. 10). Additional homogeneous vapor equilibria have a share in the calculated values of transport efficiencies, but do not take part in mass transfer of the solid. Vapor transport: Bi3TeI(s) + BiI3(g) ⇌ 4 BiI(g) + ½ Te2(g) Homogeneous gas-phase equilibria: BiI3(g) ⇌ BiI(g) + 2 I2(g) I2(g) ⇌ 2 I(g) Te2(g) ⇌ 2 Te(g)

3. Crystal Structures and Structural Comparison of BixTeI (x = 2, 3) 3.1. Bi3TeI: The crystal structure of Bi3TeI was elucidated in an SCXRD experiment (Fig. 12). The new compound crystallizes in the polar (non-centrosymmetric) space group (R3m, no. 160) with lattice parameters a = 440.12(2) pm and c = 3223.1(2) pm (Table 1). The refined structure accords well with the initial structure model that was proposed for a regularly alternating stacking of buckled [Bi2] layers and 2 ∞[BiTe3/3I3/3] triple layers. The polarity of the structures arises from stacking of the triple layers [Te–Bi–I] in a uniform way, like in BiTeI. In contrast, the stacking of the triple layers in Bi2TeI induces an inversion center and destroys the overall polarity. However, the real structure of Bi3TeI is very prone to intergrowth of the polar domains, cf. below. Inversion twining was taken into account in the course of structure refinements and a balanced domain ratio of 1:1 were obtained. This points towards a polysynthetic twinning which is introduced during the crystal growth process.

3 BiI(g) + Te2(g) ⇌ BiI3(g) + 2 BiTe(g)

Figure 10. Transport efficiency of the gas species for the vapor transport of Bi3TeI calculated using the program TRAGMIN55 applying the thermodynamic standard data (Table E1).

Based on these contemplations, the growth of Bi3TeI crystals succeeded via a mineralization reaction of the presynthesized solid at 400 °C for 30 days, already within an uncontrollable small temperature gradient in the furnace due to internal convection. An employed gradient of 400 °C → 390 °C favors for increased mass transport and growth of larger crystals. Crystals with the sizes of 50–300 µm always grew on the surface of the powdered solid (Fig. 11).

Figure 11. Typical single crystals of Bi3TeI used for an SCXRD experiment (see below). EDX data (averaged over 10 crystals (ca. 10 points per crystal) from 3 batches, in at.%): Bi, 60.7(3); Te, 19.5(3); I, 19.8(2).

Figure 12. A view of the Bi3TeI crystal structure. Ellipsoids represent 99 % probability.

All atoms in Bi3TeI occupy Wyckoff positions 3a (0, 0, z); therefore the absolute z-value of one atom in the asymmetric unit can be chosen as origin arbitrarily. Keeping that in mind, we assigned z(I1) = 0 and non-standardized coordinates to the remaining atoms in the asymmetric unit (Table 2, left) in order to elucidate the polar motif, but also to highlight the presence of a pseudo-inversion center in the crystal structure leading to a reversed polarity of the 2∞[BiTe3/3I3/3] triple layers. This may very well lead to the formation of polysynthetic domain growth as both orientations merely differ in energy; the metrics are identical anyhow. The actual position of the noncrystallographic element remains unknown until the arrangement of the domains manifold is determined. But it nevertheless helps to comprehend the intergrowth/twinning issue, since the arrangement of the “inverted” domains with respect to this virtual pseudo-inversion center can clarify the conspicious displacement parameters of Te1 and Bi3 (vide infra). The atomic parameters calculated by the twin operator leads to an almost perfect interchange of the coordinates for the Bi1 and Bi2 atoms, as well as for the Bi3 and Te1 atoms, respectively (Table 2), with only small deviations in z. The



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atomic arrangements in the ideal structure and in its inverted domains are illustrated in Fig. 13. In a real crystal either a large amount of domain boundaries or small-sized domains within the coherence length of the X-rays (below 10 nm) lead to correlation of the atomic positions for the Bi3 and Te1 atoms. Seemingly lower electron density results on Bi3 and extra electron density on Te1. This further entails unusual displacement parameters for both atoms (Ueq(Bi3) = 304(7) pm2 and Ueq(Te1) = 104(6) pm2 compared to Ueq(Bi1) = 222(6) pm2 and Ueq(Bi2) = 226(6) pm2). Table 1. Crystallographic data for Bi3TeI from an SCXRD experiment. Crystal system, space group

trigonal, R3m (no. 160)

Formula units

Z=3

Lattice parameters

a = 440.12(2) pm c = 3223.1(2) pm V = 540.68(6) × 106 pm3 ρcalc. = 8.12 g cm–3

Range for data collection; Index ranges; collected reflections

3.79° ≤ 2θ ≤ 66.50° (λ = 71.073 pm); –6 ≤ h ≤ 6, –6 ≤ k ≤ 6, –48 ≤ l ≤ 49; 4176 measured; 613 unique

R indices of merging

Rint = 0.032, Rσ = 0.016

Structure Refinement

Full-matrix least-squares based on F2, anisotropic displacement parameters, extinction coefficient 6.2(5) × 10–4, inversion twin with a balanced domain ratio 1:1

Data / restraints / parameters

613 / 1 / 17

Final R indices and Goodness-of-fit on F2

R1[577 Fo > 4σ(Fo)] = 0.019 wR2(all Fo2) = 0.048 GooF = 1.100

min./max. residual electron density

–1.92 / 2.80 e × 10–6 pm–3

The ED patterns and HRTEM images of Bi3TeI showing the stacking direction are summarized in Fig. 14, Fig. 15 and Fig. S9. The indexing based on the unit cell found by X-ray diffraction accords well with the proposed symmetry and lattice parameters. The observed reflection conditions concert with the trigonal space group R3m; no additional, superstructure reflections were detected. Early generation image correctors in TEM are known59 to introduce distortions in the diffraction patterns, as can be observed in Fig. 14 (small deviations from 90°). Note, however, how no such distortion can be observed in the Fourier transforms in Fig. 15, indicating that there are no underlying structural reasons for the distortions. Besides the discussed discrepancies, the Fourier transform agrees with the experimental ED pattern (cf. Fig. 15, right and 14, left).

Figure 13. Comparison of the atomic positions of inversion twins for Bi3TeI. Atom labels upon inversion are highlighted in bold. Ellipsoids represent 99 % probability.

Figure 14. Main zone electron diffraction patterns for Bi3TeI including the c* direction. Note strong mosaicity in [100]* DP.

The HRTEM images evidence ordered alternation of [Bi2] layers and [BiTeI] triple layers. Simulated and measured contrast (Fig. 15) match well. In Fig. 15, right bright spots correspond to the atoms, while the dark areas show cavities. The choice of the unit cell corresponds with Fig. 12 and 13. Iodine atoms are represented by gray spots in between two rows of bright-white atomic rows corresponding to the bismuth atoms from both [Bi2] and [BiTeI] layers.

Figure 15. Left: Theoretical (f = 90 nm, t = 4 nm, in the 0]* zone HRTEM image dashed insert) and experimental [0 of Bi3TeI. The Fourier transform of the experimental image is shown in the inset. A unit cell is outlined by a solid white line. Right: Theoretical (f = 51 nm, t = 4 nm, in the dashed insert) and experimental [210]* zone HRTEM image of Bi3TeI. The Fourier transform of the experimental image is shown in the inset (compare to the corresponding [210]* ED in Fig. 14). A unit cell is outlined by a solid white line.


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The electron microscopy experiments did not reveal any domain boundaries, even on a larger scale (Fig. S9). The likely cause is that our experimental parameters do not allow observation of the “inverted” domains as corroborated by additional simulations (Fig. S10, Fig. S11). Moreover, the ordering of alternating structural fragments appears perfect on the nanometer scale and is not disrupted by stacking faults, incorporation of different layer sequences, antiphase boundaries, etc. An ensuing in-depth TEM study of BixTeI (x = 2, 3) is called for. The crystal structure model for Bi3TeI was also confirmed by the Rietveld refinement (Fig. 16, Tables 2–3). The phase purity of the sample was about 95 wt.-%. The obtained structure model indicates the same electron density problem for the Bi3 and Te1 positions as discused for the SCXRD data above. As twinning should not affect the refinement against powder data, correlations – due to small domain sizes (on the size-scale of 10 nm) or domain boundaries – should be taken into account. To stabilize the structure refinement, the isotropic displacement parameter of Te1 was fixed to 127 pm2. Table 2. Synopsis of the atomic and displacement parameters for Bi3TeI determined by SCXRD and Rietveld refinement. Ueq is defined as one third of the trace of the orthogonalized Uij tensor. Note: z(I1) and Uiso(Te1) were not refined in the Rietveld refinement. Further details are listed in Tables S1–S3 of the Supporting Information. Bi3TeI, SCXRD Atom Bi1 Bi2 Bi3 Te1 I1 Bi1 Bi2 Bi3 Te1 I1

z

Ueq / pm2

1/3 2/3 0.0734(1) –1/3 –2/3 –0.0762(1) –2/3 –1/3 –0.1285(1) 2/3 1/3 0.1272(1) 0 0 0.0000(3) Bi3TeI, Rietveld refinement

222(6) 226(6) 304(7) 104(6) 235(4)

x

1/3 –1/3 –2/3 2/3 0

y

2/3 –2/3 –1/3 1/3 0

0.0711(3) –0.0777(3) –0.1289(3) 0.1273(2) 0.0000

236(10) 243(20) 272(10) 127 122(10)

Figure 16. Powder X-ray diffraction pattern (black) and Rietveld refinement (red) of Bi3TeI. BiOI may originate from oxidation of BiI3 impurities during the sample preparation for PXRD measurements.

3.2. Bi2TeI: The Rietveld refinement (Fig. 17, Tables S4, S5 of the Supporting Information) of a powdered Bi2TeI sample was based on the previously reported34 monoclinic crystal structure. However, the crystallographic transformation of the unit cell by the matrix {–1/2 1/2 0, 0 –1 0, 1 0 3} yields nearly trigonal rhombohedral metric (a = 437.98(5) pm ≈ b = 438.00(1) pm, c = 5267.9(9) pm, α = 90°, β = 89.995(2)°, and γ = 120.00(1)°). Since the atomic coordinates differ less than by 0.1 pm from the special Wyckoff position 6c (0, 0, z) after the transformation, the correct space group type of Bi2TeI might be R3m (no. 166). The obtained Bi2TeI crystals showed even more tremendous twinning problems than Bi3TeI. These real-structure defects hindered SCXRD investigations of the possibly higher symmetry of the crystal structure. Optimization of the growth conditions will be conducted further with the aim to obtain single crystals of higher quality.

Table 3. Crystallographic data for Bi3TeI from a Rietveld refinement. Crystal system, space group

trigonal, R3m (no. 160)

Formula units

Z=3

Lattice parameters

a = 441.193(1) pm c = 3219.06(2) pm V = 542.646(4) × 106 pm3 ρcalc. = 8.09 g cm–3

Range for data collection

5° ≤ 2θ ≤ 90°; ∆(2θ) = 0.013° (λ = 154.06 pm) 6538 data points

Data / Parameters

166 reflections (all phases) 39 parameters

R indices

Rp = 0.061; wRp = 0.081 RBragg = 0.022; χ2 = 1.138

Figure 17. Powder X-ray diffraction pattern (black) and Rietveld refinement (red) of Bi2TeI.

3.3. Chemical Bonding in the BixTeI series (x = 1, 2, 3) The concept of bond valence was applied in order to gain better understanding of bonding characteristics in the



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compounds at hand. This theoretical approach is based on the notion of “bond number” by Pauling60 and was later evolved by Brown and O’Keeffe into a method for prediction of bond lengths in ionic crystals61,62. An empirical expression describing the relationship between bond valence and bond length defines the bond valence vij between the atoms i and j 63 as:

!" #$!"

%

,

here Rij denotes the empirical bond valence parameters (Bi-Te = 287 pm; Bi-I = 284 pm63,64) which are close to a sum of the covalent radii of the elements, dij refers to the experimental distance between the atoms and b is a constant equal to 37 pm63,64. It is postulated that the sum of all bond valences vij between the given atom i and its j neighbours with opposite charges restores the total valence (or formal charge) of the atom i, independent from its coordination polyhedron. Thanks to this correlation, the sums of the bond valences can be used to verify the experimental assignment of atomic positions in case of doubt. Bismuth in [BiTeI] triple layers generally inherents its asymmetric octahedral coordination with three shorter and three longer bonds from its elemental structure, but ambiguity remains with respect to which interatomic distances corresponds to Bi–I and Bi–Te. Since the scattering cross sections of tellurium and iodine are almost identical they cannot be distinguished from a regular X-ray diffraction experiment. The aforementioned propensity to formation of inverted twins in BixTeI aggravates this issue even more. Table 4. Bond-valences sums for BixTeI (x = 1, 2, 3) calculated from experimental bond lengths. Interatomic distances for BiTeI are taken from [19]. Interatomic distances for Bi2TeI determined in [34] and this work are nearly identical. Bond

Bi–Te Bi–I

Experimental bond length dij / pm 303.9* 327.3*

Calculated bond valence νij BiTeI19 0.63 0.31

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undoubtedly confirms the assignment of tellurium and iodine positions for Bi2TeI and Bi3TeI done in [34] and this work. Furthermore the bond valence sums decrease in Bi2TeI and especially in Bi3TeI as the bismuth content increases, thus deviating stronger from the aforementioned values in an ideal ionic case. Simultaneously, the distances between the [Bi2] and [BiTeI] structural fragments almost even out in Bi3TeI, e. g. Bi···I = 353 pm (cf. 363 pm in Bi2TeI), Bi···Te = 357 pm, whereas the Bi–Bi bond lengths within the [Bi2] layers amount to 305 pm. Thus, the bonding situation in Bi3TeI resembles elemental bismuth with the shorter 307 pm and the longer 353 pm interatomic distances. Altogether these findings emphasize stronger intra-layer interactions and higher delocalization introduced by the increasing number of [Bi2] layers. This is further reflected by metallic character of the electronic structure of Bi3TeI and complex hybridization of states discussed in detail in the next section. 4. Electronic structure of Bi3TeI Without spin-orbit coupling (SOC) taken into account, Bi3TeI is a Weyl semimetal as demonstrated by the prominent Weyl points on the Г–K and A–L lines projecting onto the and Γ–Μ directions of a 2D Brillouin zone (BZ) surface Γ–Κ (Fig. 18a). The bulk bands forming the Weyl points are mainly composed of the pz-Bi states contributions from both BiTeI triple layers (denoted further as Biin) and [Bi2] (denoted further as Bilayer) structural fragments. Note a cone-shaped feature predominantly constituted by bismuth pz-orbitals that was also observed in the scalar-relativistic band structure of the 3D weak topological insulator Bi14Rh3I9.65,66

Calculated total bond-valence sum Σνij ΣνBi = 2.8 ΣνTe = 1.9 ΣνI = 0.9

Bi2TeI34 Bi–Te Bi–I

Bi–Te Bi–I

305.4 338.0

0.61 0.23

311.9 343.6

Bi3TeI 0.51 0.20

ΣνBi = 2.5 ΣνTe = 1.8 ΣνI = 0.7 ΣνBi = 2.1 ΣνTe = 1.5 ΣνI = 0.6

* the values are taken from Table 319. Note discrepancy between the interatomic distances given in the Table 3 “Selected interatomic distances” and those derived from Table 2 “Atomic parameters” in [19]. As can be seen from Table 4, the bond-valence sums calculated for the constituents of the 2∞[BiTe3/3I3/3] triple layer in BiTeI show very good agreement with the expected values of 3, 2 and 1 for bismuth, tellurium and iodine, respectively. Hence the bond-length–bond-strength concept offers a simple but effective tool to tell tellurium and iodine apart and further

Figure 18. Bulk band structure of Bi3TeI (black lines) without (a) and with spin-orbit coupling (b). The 3D Brillouin zone is shown in Fig. S12. The green ovals (I, II, III) encircle hybridization gaps. The color-coding for atomic contributions is the same in both panels. The size of the colored circles correlates with atomic contributions with px and py symmetry.


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Included SOC leads to dramatic changes in the bulk band structure of Bi3TeI. First of all, the semimetallic electronic spectrum transforms into a metallic one (Fig. 18b). Second, a complex inversion takes place predominately between the Te px- and py-states, and the pz-states of both Biin and Bilayer; thus generating several hybridization gaps among the inverted bands (areas I, II, and III in Fig. 18b). In contrast to the cousin compound Bi2TeI where the bulk-band inversion occurs between the states of two distinct structural blocks40,42, the inversion in Bi3TeI involves atomic orbitals, which indicates strong interaction between all constituents. This observation is in line with the conclusions of the previous section. In the context of elaborate hybridization, emergence of surface states with topological nature can be expected in Bi3TeI. Due to increased intra-layer interactions, Bi3TeI does not possess an obvious cleaving plane, e. g. both iodine- and tellurium-terminated surfaces are seemingly equiprobable. In the following, the surface state on the Te-terminated surface is discussed in detail as the most representative case, whereas the I-terminated surface is presented in the Supporting Information (Fig. S13). To simulate the semi-infinite (001) Te-terminated surface of Bi3TeI by DFT calculations, we considered a 28-atom-thick slab (e. g. 6 consecutive [BiTeI] and 5 [Bi2] layers) with the iodine side passivated by a hydrogen monolayer. As can be seen from Fig. 19, the surface spectrum with included SOC accomodates a spin-polarized surface state in the local bulk band gap. One branch of this state propagates in the Γ–Κ direction: it originates from the upper edge of the local bulk band gap and penetrates into the bulk-bands continuum aiming to the center of the 2D BZ. The other branch shows similar direction. This spin-polarized surface behavior along the Γ–Μ state is essentially the upper part of a Dirac cone with the Dirac point submerged into the bulk continuum of the valence band. The charge density of this surface state is localized mainly within the surface Te-layer and the underlying Bi-layer (Fig. 19c), thus it has a very small penetration depth.

Figure 19. Band structure of the Te-terminated surface in Bi3TeI with localization (a) and with spin-resolution (b). The sizes of blue, lilac and orange dots in the panel (a) are proportional to the respective contributions of the states localized on the Te- and I-sides of the slab, and on H, respectively. The inset in panel (b) zooms in the surface state encircled by a light-brown square. The charge density distribution (c) integrated over the ab plane is represented for direction depicted the point of the surface state in the )–* within the light-brown square the insert in the panel (b).

In order to trace stepwise the Dirac cone development, we regarded the surface band structure with various SOC

constants within a tight-binding model (TB). Band-bending effect was omitted for simplification. At λ/ λ0 = 0 (e. g. without SOC) a single parabolic surface state resides at the Γ point (Fig. 20). When SOC is “switched on”, a topological phase transition takes place, similar to the Kane–Mele model67. As a result, a hybridized band gap appears and a topological surface state with the Dirac point in the local bulk band gap emerges even at small spin-orbit contribution to the Hamiltonian. Increasing SOC entails strong modifications of the Bi3TeI electronic structure. At λ/ λ0 = 0.4 the Dirac point sinks down into the bulk band continuum and an additional local valence bulk band gap appears at the Γ point (Fig. 20). Further, at λ/ λ0 = 0.6 the Dirac point moves into the additional local valence bulk band gap and stays close to its lower edge. Increase of λ/ λ0 from 0.6 to 1 causes a shift of the Dirac point into the bulkband continuum which is accompained by changes in the dispersion of both the edge of the bulk continuum and the surface state. Note that the surface band structures approximated by TB (Fig. 20, λ = λ0) and DFT (Fig. 19) show a good match; hence, the band-bending effect does not significantly affect the surface state dispersion in Bi3TeI.

Figure 20. Band structure of the Te-terminated surface in Bi3TeI calculated for the SOC constant λ ranging between 0 and its natural value λ0 within the tight-bonding model.

An unconventional surface state observed on various surface terminations in Bi3TeI is a result of the complex hybridization of atomic states which is caused by their strong intermixing. It cannot be classified as a topologically protected state in the classic sense67 since the inversion does not occur at a TRIM point, but is thus even more interesting to be studied further. Note unconventional topological surface states reported in the natural superlattice Bi4Se39. They generally differ from the state described in the present work, but, just like this state, exhibit markedly different dispersions on different surface terminations.



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CONCLUSIONS The discovery of Bi3TeI enriches a series of topological superlattice materials based on incorporation of the buckled [Bi2] layers into the van der Waals gaps of the layered BiTeI host structure. It also allows us to review interrelations between the topological properties and the structural modifications in the series of bismuth telludide-iodides of bismuth and point out remaining open questions. Altogether BiTeI, Bi2TeI and Bi3TeI constitute a structural family which can be described by the joint formula [Bi2]m[BiTeI]n. It remains open to future studies whether higher bismuth content can be achieved with this structural motif remaining intact. Our preliminary experimental data do not support such possibility. It would be also valuable to learn more about the structural tolerance to deficit / excess / mixed occupancy of tellurium and iodine as well as about the types of possible point defects and their influence on the transport properties, as was done for the Bi2X3 topological insulators. Increase of [Bi2] layers per [BiTeI] triple layers promotes metallic properties and strong intermixing of atomic states, which make their presence evident in the enhanced intra-layer bonding and band structures of the compounds at hand. Unlike in layered structures with van der Waals gaps, quasi-onedimensional β-Bi4I4,41 or salt-like Bi14Rh3I965,66, [Bi2] layer in Bi3TeI interacts strongly with its chemical environment and cannot be considered as a separate fragment, both structurally and electronically. Topological surface states in Bi2TeI42 and Bi3TeI are intricate and do not follow directly the mechanisms devised for classic topological insulators since they originate from complex hybridization of states. Whereas the band inversion in Bi2TeI can be understood as a result of interactions between [Bi2] layers and [BiTeI] triple layers40,42, intense hybridization of all states in Bi3TeI under spin-orbit coupling cannot be easily scrutinized, making this example quite intriguing for future considerations. It should be noted that a topological transition in Bi3TeI under SOC does not create a topological surface state according to the Fu–Kane Z2 classification67 since the inverted gap does not occur in one of the TRIM points. This state bears signatures of a topological one but its nature requires further theoretical advances for final clarification (this is emphasized by the usage of quotation marks for the respective properties in Fig. 21). In terms of topological properties the Bi2TeI–Bi3TeI duo resembles the BiTe–Bi4Se3 pair: incorporation of one corrugated bismuth layer per two building blocks of the host structure triggers a TCI and a weak 3D TI, whereas the doubled amount of [Bi2] stabilizes a topologically non-trivial metallic state (Fig. 21). The existence of two generally matching series of topological heterostructures [Bi2]n[Bi2Te3]m and [Bi2]n[BiTeI]m gives rise to a more general research task, e. g. to unravel how coupling effects between 2D TI building units and other structural fragments influence topological properties of the entire stack and to learn to manipulate them via chemical modifications. Known topological materials with lowdimensional structural fragments exhibit an entire spectrum of realized possibilities. 2D TI fragments can constitute a 3D weak TI40,42,65,66, or even enhance to a 3D strong TI41,68 from essentially a stack of 2D TI66,69. On the other hand, topological

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properties may get disrupted when 2D TI fragments get coupled pairwise70. The analogy between the Bi–Te and the Bi–Te–I systems extends beyond the physical properties of selected compounds towards their synthesis and thermodynamic properties. The quasi-binary Bi–BiTeI section of the ternary phase diagram bears similarities to the Bi–Bi2Te3 polythermal section71: bismuth-richer phases melt with decomposition and thus complicate crystal growth of targeted phases. Apparently, even prolonged annealing of the samples crystallized from a melt in the subsolidus temperature range cannot heal the structural disorder. The reason of this retardation lies most likely in energetic similarities of various stacking sequences. Therefore we intentionally abstained from using melts at any step of the developed synthetic procedure and effectively replaced them with ball milling as a homogenisation step.

Figure 21. Schematic representation of the topological bismuth chalcogenides and bismuth telluride-iodides and their correlating electronic properties. Grey blocks with a green outline depict [Bi2Te3] quintuple layers, grey blocks with an orange outline depict [BiTeI] triple layers, blue blocks depict [Bi2] layers. Properties that require further confirmation are given in quotation marks. Unit cells are outlined in black lines. The dotted line denotes the monoclinic cell for Bi2TeI34.

Periodic crystal structure with long-range ordering is essential for correct evaluation of topological properties. One of the possible ways to diminish heavy structural disorder is controlled MBE growth used for BiTe38. In contrast to this highly ordered thin film, bulk samples of BiTe are difficult to access. In the present work we have pushed structural ordering in the BixTeI (x = 2, 3) materials to a new level by means of tailored solid-state synthesis and gas-phase transport supported by extensive thermodynamic modelling and thermochemical studies. As a result, large crystals and phase-pure powders of Bi2TeI suitable for ensuing physical-property characterisation were reproducibly synthesized for the first time. Nevertheless, innate stacking disorder in this material could not be ameliorated completely. Just like the bismuth-rich phases in the Bi–Te system, massive powdered samples of Bi3TeI are still hard to access but controllable crystal-growth can be performed in the subsolidus region of the phase diagram. The obtained crystal sizes remain quite small due to limited mass transfer because of fundamental, thermodynamic reasons.

EXPERIMENTAL SECTION Powder synthesis. Powder samples (Microcrystalline samples) were obtained by annealing of a stoichiometric mixture of Bi, Te, and BiI3 (bismuth, MERCK, treated at


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220 °C in H2-flow; tellurium, MERCK, > 99.9%; bismuth(III)iodide, synthesized from the elements and sublimated twice). The starting materials were pulverized by ball milling (“Pulverisette 23”, Fritsch) for 25 minutes under argon atmosphere in a glovebox. The homogeneous powder was sealed in an evacuated silica ampoule. The samples of BixTeI (x = 2, 3) were annealed at 425 °C and 390 °C, respectively (temperatures chosen with regard to previously determined stability ranges) for at least three days. The “Bi4TeI” sample was annealed at 350 °C for 1 week in order to ensure a solidstate reaction without melting. All samples were quenched into water if not stated otherwise. BiOI impurities observed for some bismuth-rich samples may originate from oxidation of BiI3 impurities during the sample preparation or from contact of BiI3 with residual moist. Crystal growth. Phase-pure powders synthesized via the above described procedure were used as batches for crystalgrowth experiments. Small single crystals (up to 200 µm) for single-crystal X-ray diffraction studies were obtained via mineralization for 2–4 weeks at 425 and 390 °C for Bi2TeI and Bi3TeI, respectively. Larger single crystals were grown via chemical vapor transport reactions (CTR). For this purpose phase-pure powder was sealed in an evacuated silica ampoule and exposed to a temperature gradient between 410 and 390 °C at the distance of approx. 15 cm for one week, thus ensuring a small transport rate and, therefore, good crystal quality. The “hot” ends of all ampoules were quenched in cold water in order to avoid contamination of the crystals with the remaining gas-phase species. Energy dispersive X-ray spectra (EDX) were collected using an Oxford Silicon Drift X-MaxN detector at an acceleration voltage of 20 kV and a 100 s accumulation time. The EDX analysis was performed using the P/B-ZAF standardless method (where Z = atomic no. correction factor, A = absorption correction factor, F = fluorescence factor, P/B = peak to background model). X-ray diffraction experiments. Single-crystal X-ray diffraction was measured on a four-circle Kappa APEX II CCD diffractometer (Bruker) with a graphite(002)monochromator and a CCD-detector at T = 296(2) K. Mo-Kα radiation (λ = 71.073 pm) was used. A numerical absorption correction based on an optimized crystal description72 was applied and the initial structure solution was performed in JANA2006.73 The structure was refined in SHELXL against Fo2.74,75 Further details on the crystal structure investigation of Bi3TeI can be obtained from the Fachinformationszentrum Karlsruhe, 76344 Eggenstein-Leopoldshafen, Germany (fax: (+49)7247-808-666; e-mail: [email protected]), on quoting the depository number CSD-432224. Powder X-ray diffraction data were measured using a X’Pert Pro diffractometer (PANalytical) with Bragg–Brentano geometry, a curved Ge(111) monochromator, and Cu-Kα1 radiation (λ = 154.06 pm). Variable divergence slits were used to keep the illuminated sample area constant. For Rietveld refinements of the data the fundamental parameter approach was applied in the TOPAS package.76 Preferred orientation of the crystallites was described by spherical harmonics functions. hkl-dependent peak shape broadening was considered as mixture of Gaussian and Lorentzian components.77

Graphics of the structures were developed with Diamond78 software. Thermodynamic modelling of heterogeneous phase equilibria has been performed using Calphad-methods based on the Eriksson—Gibss energy minimizer implemented in the program Tragmin55. In order to evaluate the phase relations of ternary compounds BiTeI, Bi2TeI, and Bi3TeI, the phase equilibria in the Bi–Te–I ternary system have been calculated isothermally in the temperature range 150–550 °C with ∆T = 10 °C for different compositions. The data sets of all gaseous species and binary compounds containing the components bismuth, tellurium, and iodine were adopted from [52] and [56], respectively. Thermodynamic standard data for the ternary phases BiTeI and Bi2TeI were accessible from [58] and [44]. Due to lack of thermodynamic values of Bi3TeI their estimation has been realized based on standard data of the other systems phases BiTeI and Bi2TeI (Table E1). Table E1. Thermodynamic standard data of condensed compounds in the Bi–Te–I system. Phase

∆H0298 / kJ·mol

S0298 /

Cp(T) /

Cp(T) /

Cp(T) /

J·mol−1 ·K−1

J·mol−1 ·K−1

J·mol−1 ·K−1

J·mol−1 ·K−1

a*

b*

c*

Ref.

−1

Bi (s)

0

56.7

10.98

31.45

−78.7

261.1

107.99

55.23

BiI3(s)

−150.6

224.7

40.96

108.63

BI(s)

−54.6

125.5

42.00

BiTeI(s)

–83.7

162.0

49.36

Bi2Te3(s)

0.4451

[52] [52]

2.887

[52] [56]

55.27

0.9623

[58], Cp optimized in this work

Bi2TeI(s)

−110.7

211.3

60.34

86.71

1.4074

[44], Cp this work

Bi3TeI(s)

−119.7

264.0

71.33

118.15

1.8525

this work

* Cp(T) = (a + b · 10−3 · T −1 + c · 106 · T −2)

Assuming thermodynamic stability of all the three ternary compounds according to the formation reactions a) and b), the respective enthalpy value of Bi3TeI has been estimated (∆H0298 = −119.7 kJ·mol−1) from the given values of BiTeI (∆H0298 = −83.7 kJ·mol−1) and Bi2TeI (∆H0f,298 = −110.7 kJ·mol−1). Entropy and heat capacity have been calculated applying the rule of Neuman and Kopp (∆rS, ∆rCp ≈ 0). Using the obtained data, the calculated phase diagram finally fitted completely the experimentally observed phase relations (Fig. 6). a) Bi2TeI(s) + Bi(s) → Bi3TeI(s) ∆rH = −9 ± 4 kJ·mol−1 ∆rS, ∆rCp = ≈ 0 ± 5 J·mol−1·K−1 b)

½ Bi3TeI(s) + ½ BiTeI(s) → Bi2TeI(s)



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∆rH = −9 ± 4 kJ·mol−1 ∆rS, ∆rCp = 0 ± 5 J·mol−1·K−1

Author Contributions

∆H0298(Bi3TeI) = −119.7 ± 4 kJ·mol−1 S

298(Bi3TeI)

Corresponding Author * Email: [email protected].

resulting in:

0

Page 14 of 18

−1

= 264.0 ± 5 J· mol K

−1

Cp(Bi3TeI) = (71.33 + 118.15 · 10−3 · T · 10−3 + 1.8525 · 106 · T−2) ± 5 J· mol−1K−1 Thermal properties of BiTeI, Bi2TeI, Bi3TeI and “Bi4TeI1.25” were analyzed by means of differential scanning calorimetry (DSC) using a Setaram Labsys ATD-DSC device with a k-probe (Ni–Cr/Ni–Al; Tmax = 800 °C) and Al2O3 as a reference compound. Heating and cooling rates of 2 °/min were employed. The substance was sealed in an evacuated silica glass ampoule. Transmission and Scanning Electron Microscopy. SEM images were collected on a Hitachi SU8020 microscope. Acceleration voltages of 10 to 30 kV and current of 10 µA were used to create the SEM images. For TEM, thin lamellas were cut from a single crystal of Bi3TeI perpendicular to the largest facet, i. e. along the stacking direction, with an ultramicrotome (Ultracut, Leica Microsystems) equipped with a diamond knife. Prior to it, the crystal was embedded in the epoxy resin Epon (Fluka) that was then polymerized at 60 °C. The nominal lamella thickness was approx. 50 nm while locally crystalline flakes with lower thickness were observed. High-resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) studies were performed on a FEI Titan F20 microscope with CS-correction operating at 80 kV. For image acquisition, a 2k × 2k SlowScan CCD-Camera (Gatan) was used. Image simulations were done with the JEMS software79. Computational details. Electronic structure calculations were carried out within the density functional theory using the projector augmented-wave method80 as implemented in the VASP code81,82. The exchange-correlation energy was treated using the generalized gradient approximation83. The Hamiltonian contained the scalar relativistic corrections and the spin-orbit coupling was taken into account. The large slab Hamiltonian within tight-binding method derived from the bulk one was afterwards used to calculate surface Green functions84–86. Hence the TB models were constructed using WANNIER90 code87,88. The chosen basis consisted of six spinor p-type orbitals for each atom: + ,↑ ., + 0↑ ., + 1↑ ., + ,↓ ., + 0↓ ., + 1↓ . . The low-lying s-orbitals were not taken into consideration.

ASSOCIATED CONTENT Supporting Information Powder diffraction patterns for analysis of the synthesis, DSC curves and a short description of vapor transport of BiTeI and Bi2Te3, additional electron microscopy data for Bi3TeI, additional crystallographic data Bi3TeI and Bi2TeI (incl. atomic parameters and isotropic displacement parameters, selected interatomic distances and bond angles), and results of band-structure calculations for the iodine-terminated surface of Bi3TeI are available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION

The manuscript was written by A.I., A.Z., P.S., M.K., T.V.M., I.P.R. through contributions of all authors. A.Z. conducted optimized synthesis, crystal-growth and characterization of samples. A.V.M. conducted synthesis via melts and characterized these samples. M.K. and A.Z. determined crystal structures and analyzed twin problems under supervision of T.D. A.Z. conducted and analyzed the DSC experiments. P. S. performed thermochemical modelling and analyzed the data. A.I. and W.V.d.B. conducted and interpreted the TEM experiments. T.V.M. and I.P.R. performed all computational work and analyzed the data under supervision of E.V.C. A.I and M.R. supervised the project. All authors have given approval to the final version of the manuscript.

Funding Sources This work was supported by the German Research Foundation (DFG) in the framework of the Special Priority Program (SPP 1666) “Topological Insulators” and by the ERA-Chemistry Program. We acknowledge support by Academic D.I. Mendeleev Fund Program of Tomsk State University in 2015 (research grant No. 8.1.05.2015), by Saint Petersburg State University (project No. 15.61.202.2015), by the Spanish Ministry of Science and Innovation (grants no. FIS2013-48286-C02-02-P and FIS201348286-C02-01-P) and by the Basque Departamento de Educacion, UPV/EHU (grant IT-756-13).

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENT This research received its initial impetus and supervision from Prof. Boris A. Popovkin (1937–2008), to whom the authors are indebted for inspiration. Dr. B. M. Saparov is thanked for preliminary data on BixTeI that were considered in his diploma thesis at Moscow State University in 2006. We are grateful to Prof. C. T. Koch (Humboldt-University Berlin, Germany) and Prof. U. Kaiser (University of Ulm, Germany) for the provided TEM facilities at the Physics Department of the University of Ulm, and to Mr. E. Schmid (Central facility for electron microscopy, University of Ulm) for ultramicrotomy of our samples.

ABBREVIATIONS TI topological insulator; TCI topological crystalline insulator; SSR solid-state reaction; DSC differential scanning calorimetry; EMF electromotive forces; PXRD powder X-ray diffraction; SCXRD single-crystal X-ray diffraction; DP diffraction pattern; SEM scanning electron microscopy; TEM transmission electron microscopy; ED electron diffraction; HRTEM high-resolution transmission electron microscopy; SOC spin-orbit coupling; BZ Brillouin zone.

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(88) Zhang, W.; Yu, R.; Zhang, H.-J.; Dai, X.; Fang, Z. Firstprinciples studies of the three-dimensional strong topological insulators Bi2Te3, Bi2Se3 and Sb2Te3. New J. Phys. 2010, 12, 065013.



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Modular Design with 2D Topological-Insulator Building Blocks

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