Downloaded by guest on September 30, 2021 www.pnas.org/cgi/doi/10.1073/pnas.1802836115 Streltsov V. Sergey compound AuTe novel AuTe calaverite structure of crystal incommensurate of puzzle Old h rgno h nomnuaiiyi tl bcr.Ls u not But but Last (1). obscure. incommensurate still is least, is incommensurability structure the of crystal origin Miller the very small real- the was with it that until those odd, ized are looked everything crystal calaverite a in and of indexes, facets natural peculiar Ha stable contradicting the the crystals, understand calaverite not of mineralogists could faceting to concern They much crystallographers: of was crystal and time incommensurate one an at form This natural structure. in having materials few all scrapped carefully very extracted, con- roads. it be these that can waste discovering which “empty” after gold but, an real roads, tains as the paving calaverite for discarded it used first and min- mines where Australia, gold in in rush ers gold the influenced even It aspects. structure crystal incommensurate synthesized. been not AuTe, compound has stable now unknown AuTe until yet as which of an of stability prediction a confirms compounds to leads system stable Au–Te for search the evolutionary in initio ab An of 5p ductivity. Te structure crystal the incommensurate AuTe in explains largely naturally being scenario holes and energy with charge-transfer Pt). negative self-doping, of and picture unusual Pd the these become in explain by phenomena theoretically which we doped exam- Au, calculations initio or on rare ab pressure based Using a systems elevated structure. is few (at crystal it of superconducting incommensurate one scale, with is industrial mineral it Moreover, natural an a on of gold ple com- extract calaverite, few can material—mineral relatively one unique forms a which is 2018 AuTe element, 14, them August inert Weeks Among D. very John pounds. Member a Board Editorial is by accepted Gold and Texas, Austin, Austin, 2018) at 15, Texas February of review University for The (received Chelikowsky, R. James by Edited and Federation; Federation; Russian Russian Skolkovo, Region, 143026 Moscow Dolgoprudny, Russia; Yekaterinburg, 141701 Technology, 620002 and University, Federal Ural Mathematics, Applied a eetgl elrdsalwdu opeitteeitneo a predicted of material. the this existence of report properties the We and predict structure AuTe. crystal to compound: us unknown allowed hitherto dif- tellurides of at study gold structural state ferent extensive superconducting an a Moreover, or pressures. conditions higher normal a crys- at drives incommensurate structure which an tal regime, in energy resulting charge-transfer disproportionation negative charge a in is it critical AuTe with (2–5), doping Pd or Pt upon or temperature GPa 2.3 of pressure telluride— gold is scale industrial an on gold form AuTe the extract which in from found can nature be in one can existing it compound only rarely The very compounds. but of alloys in occurs also It I eateto hoyo o-iesoa pnSses nttt fMtlPyis 290Yktrnug Russia; Yekaterinburg, 620990 Physics, Metal of Institute Systems, Spin Low-Dimensional of Theory of Department cleeet n ti yial ie sapr aieelement. native chem- pure reactive a as least mined the typically of is one it is and gold elements that ical known well very is t nte,vr pcfi etr of feature specific very Another, ntepeetppr eso htalteepoete of properties these all that show we paper, present the In 2 2 AuTe 2 2 n tas ugssapsil ehns fsupercon- of mechanism possible a suggests also it and , which from nature in compound only the being Besides . aaeie hsmtra seteeyitrsigi many in interesting extremely is material This calaverite. , a entrlyepand foetksit con that account into takes one if explained, naturally be can 2 ∼4 a on ob uecnutra eaieylow relatively a at superconductor a be to found was K. a,b,1 aei .Roizen V. Valerii , | calaverite AuTe e I hsklshsIsiu,Universit Institut, Physikalisches II. | superconductivity 2 sta ti n fvery of one is it that is c 2 lxyV Ushakov V. Alexey , 2 yslw Usually law. uy’s ¨ n rdce tblt of stability predicted and n AuTe and ad.This bands. 3 and d c aeil icvr aoaoy klooIsiueo cec n Technology, and Science of Institute Skolkovo Laboratory, Discovery Materials a tz K zu at ¨ opttoa aeil icvr aoaoy ocwIsiueo Physics of Institute Moscow Laboratory, Discovery Materials Computational re .Oganov R. Artem , 1073/pnas.1802836115/-/DCSupplemental hsatcecnan uprigifrainoln at online information supporting contains article This 1 the under Published hsatcei NSDrc umsin ...i us dtrivtdb h Editorial the by invited editor guest a is J.R.C. Submission. Direct PNAS Board. a is article This interest.y of conflict no declare wrote authors D.I.K. The and S.V.S. and per- data; A.V.U. analyzed paper. and y D.I.K. V.V.R., the and S.V.S., A.R.O., research; S.V.S., designed calculations; D.I.K. formed and S.V.S. contributions: Author risof erties AuTe Structure Crystal Calaverite’s of Puzzle Old otepsiiiyo hredsrprinto noAu into disproportionation charge of Au possibility the to more with systems in but oxides, Au(AuF in actually bonds—in ionic was not [It however gold.” made, “magnetic indeed dream—a Au old stabilize an really of to realization manage could one Au If as exists It Au bilize: that knows chemist every state, Fe gold” valencies of Au assignment proposed formal in (10) the Boer on de based and structure explanation Schutte another corre- 9). band at (8, surface vectors accurate Fermi charge wave the sponding of a but nesting in found instability, not results have calculations which (CDW) be structure, can wave it electronic that density specific argue a mechanism may to One The due unclear. makes (7). periodic is which incommensurability a incommensurate direction, of is structure [010] there crystal However, the overall between. along in modulation atoms displacive Te with Au group of space has structure age owo orsodnesol eadesd mi:[email protected] Email: addressed. be should correspondence whom To hc hoeial svr tbe n epeitiscrystal its predict we and AuTe, stable, compound structure. very unknown is previously theoretically a which crystal discovered unique also we a AuTe Au, doped such superconductiv- reduces of on explains ity creating also substantially mechanism much for same This The so structure. costs sites. not energy Te occurs Coulomb on structure predominantly crystal but mod- of incommensurate ulations with associated that demonstrate redistribution system. we incommen- charge charge-transfer methods, negative of computational AuTe a modern puzzle Using as of considered long-standing is structure the material crystal that shown surate is It Significance h hnmnno kpe aec 1)o Au of (12) valence skipped of phenomenon The 3+ l,D597Clge Germany Cologne, D-50937 oln, ¨ y n tsest aual xli h rudsaeprop- ground-state the explain naturally to seems it and , 2 2+ a itre layered distorted a has (Te 2+ AuTe (S 2 ) 2− 2 ) NSlicense.y PNAS 2 2− si ok o xml in example for works it as , i nlg ihaohrmnrlte“fool’s mineral—the another with analogy [in .Hwvr hra Fe whereas However, ]. c,d 2 xlrn ifrn uT compositions, Au–Te different Exploring . 1+ n ailI Khomskii I. 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PHYSICS The fact that the CDW due to such charge disproportionation We claim that the same phenomenon also occurs in systems 2+ is incommensurate in AuTe2, in contrast to Cs2Au2Cl6, may be containing Au , such as, e.g., Cs2Au2Cl6 (13), and also in related to the triangular lattice, which Au ions form in AuTe2. calaverite AuTe2, where one can write this reaction as This lattice is not bipartite, and the resulting frustration can 2+ 9 1+ 10 3+ 8 lead to incommensurate modulation. While overall modulation 2Au (d ) → Au (d ) + Au (d ), [1] of the lattice is complex, the local distortions seem to confirm this skipped valence interpretation: Some Au ions, say at the but in fact it should be visualized as maximum of CDW, are in a linear, or dumbbell coordination 2+ 1+ 1+ 1+ 2 2Au ≡ 2Au L → Au + Au L . [2] (two short and four long Au–Te bonds), typical for d 10 ions, 1+ here Au , whereas at the “other end,” say in the minimum of Two holes (L2) in the Te p band form something like a bound the CDW, Au ions are square coordinated—coordination typical 8 3+ 3+ 6 2 2 2 2 2 0 state, with the symmetry of a low-spin d state of Au with for Au (t2g (3z − r ) (x − y ) ) (5). Local surroundings for which it hybridizes. Below we confirm this picture by the ab initio other Au interpolate between these two limits. band structure calculations. This interpretation, however, was put in doubt. First, pho-

toemission (14) and then X-ray absorption (15) measurements Mechanism of Incommensurability in AuTe2: Negative showed that apparently electronic configuration of all Au ions CT Gap Energy is the same, close to Au1+. [A recent spectroscopic study, how- It is impossible to carry out ab initio calculations for the real ever, did show the existence of slightly inequivalent Au ions (4).] incommensurate structure with the existing codes based on den- Also ab initio calculations performed for the artificial supercell sity function theory (DFT). One needs to approximate this structure with four Au ions mimicking the small-period CDW do structure by some supercell with a commensurate CDW. We bor- not show any difference in occupation of the d shell for different rowed an idea on how to construct it from nature, taking the Au ions (8). (Note that the structure used in ref. 8 is somehow initial crystal structure from the mineral sylvanite—AuAgTe . unnatural in a sense that four short Au–Te bonds do not lie in 4 Au and Ag ions in sylvanite are ordered in stripes, with Ag one plane.) being in a linearly coordinated site, typical for ions with d 10 We argue that nevertheless the physics of AuTe2 is related to 1+ 2+ configuration, that is, it is Ag (Au-D in Fig. 1B); and Au the eventual instability of Au against charge disproportiona- ions occupy a square-coordinated position, corresponding to, tion, which determines the main properties of AuTe2, including nominally, Au3+ (Au-P in Fig. 1B) with its strong Jahn–Teller not only incommensurate CDW, but also the tendency to super- distortion (6). This structure was relaxed in the generalized gra- conductivity. As demonstrated below, the resolution of the con- dient approximation (GGA), taking into account the spin–orbit troversy mentioned above lies in the fact that actually AuTe2 is a coupling (SOC), and then Ag was substituted by an Au ion negative charge-transfer (CT) energy system (16, 17), with all of the holes predominantly in the 5p bands of Te. and relaxed again, keeping the unit cell volume the same as AuTe Te The notion of CT insulators was introduced in the semi- in real 2 (this structure is labeled as AuAu’ 4 in what nal paper by Zaanen, Sawatzky, and Allen (18). These are follows). Te materials with strongly correlated electrons. However, the low- First, we found that the AuAu’ 4 structure is stable and there est charge excitations in them correspond not to transfer of are still two differently coordinated Au ions. Second, this struc- electrons between localized d states, d n d n → d n+1d n−1, as in ture is lower in energy than the average C 2/m structure (6) Mott–Hubbard insulators, but to electron transfer between ions at experimental volume [by 22 meV/formula units (f.u.)]. Thus, of transition metals (TMs) and ligands, that is, to the pro- one may see that we gain a lot of energy by making distortions cesses d n p6 → d n+1p5 = d n+1L, where L stands for the ligand corresponding to the CDW (in this case a commensurate one). hole. In CT insulators this CT excitation energy is positive, A close inspection of the Au 5d occupation numbers in the n+1 5 n 6 AuAu’Te4 structure, however, shows that from the point of view ∆CT = E(d p ) − E(d p ) > 0, but in principle it can be very small or even negative (naively speaking, when anion p levels of d occupation both Au ions are 1+: Corresponding occupan- lie above d levels of TM ions). In this case we refer to nega- cies of the d shell [as obtained within the projector augmented tive CT energy. Usually this situation is met when the oxidation wave (PAW) method] are 9.90 and 9.92, so that the difference state of a metal is unusually high—e.g., 4+ for Fe or 3+ for is negligible: δnAu−d = 0.02 electrons [the Bader analysis (24) gives an even smaller difference, <0.01 electrons] (note that in Cu. If such states are created by doping, as in high-Tc cuprates, real sylvanite, AuAgTe4, δn ∼ 0.5 electrons; that is, in sylvanite the doped holes go predominantly to oxygen p states (although 1+ 3+ 3+ these are of course strongly hybridized with d states of Cu). we can indeed refer to Ag and Au , Au again with a lot But this situation can be realized also in undoped stoichiomet- ric compounds such as CaFeO3. In this case there can occur spontaneous transfer of electrons from ligands to the TM ion, that is, Fe4+ →Fe3+L. This situation can be called a self-doping (19). This picture, which in physics we describe by the (nega- tive) CT energy, is reminiscent of the notion of dative bonding in chemistry [A “dictionary” helping to establish the correspon- dence between physical and chemical language is contained in the famous book by Goodenough (20) and a very clear paper by Hoffmann et al. (21).] Interestingly enough, in many systems of this class there occurs spontaneous charge disproportionation, like 2Fe4+ → Fe3++Fe5+, but occurring predominantly on ligands; that is, this “reaction” should be visualized as 2Fe3+L →Fe3++Fe3+L2. Fig. 1. (A) GGA + SOC total and partial density of states for the AuAu’Te4 ~ RNiO structure (for experimental volume). (B) Charge density ρ(r) correspond- This process is now well established also in nickelates 3 ing to the topmost, partially filled band [isosurface corresponding to (R = Pr, Nd), where it leads to a real phase transition, originally 0.003 e/A˚ 3 ≈10% of maximal value of ρ(~r) is presented. Shown are results interpreted as charge ordering on Ni (2Ni3+ → Ni2+ + Ni4+) of the GGA + SOC calculations for AuTe2 in the fully optimized “AuAgTe4” (22), but which is actually much better described by the reaction structure. Au-P and Au-D stand for Au ions having plaquette and dumbbell 2+ 2+ 1+ 2 2Ni L → Ni + Ni L (23). surroundings.

2 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1802836115 Streltsov et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 teto tal. et Streltsov C The is overestimated. slightly one The is next volume 2). equilibrium (Fig. the volume while one, the on depend AuAu’Te structures crystal these of AuAu’ Te of that than higher atom per by characterized structure ions the a Au and all equivalent, and high-pressure structurally become disappears the which superstructure atom) it: incommensurate per the meV with 100 of be of compete interval to hundreds may the appear among (in There structures energy USPEX. two the total only with lowest obtained the structures has other still CDW For the AuAu’ (28–30). the metals that heavy found on based materials, those different including many of properties structural for applied of successfully investigation struc- previously was possible USPEX calculation. all the the in for in evolu- search that the to of used from tures (27) equi- we USPEX different the difficulty algorithm be first addition, tionary the can In overcome DFT structures, energy. To the other experiment. total in no lower are volume a there librium give that would guarantee no which is There energy tive. the minimize CDW. we the ligands, of to formation the density of charge costs the of part same energy a the the on holes with (two other energy each Coulomb Au of the lot with a cost CDW real having a were energy ions were CT the there if reminis- Indeed, and CDW. structure, positive the of crystal formation the calaverite of cent distorted strongly a favors Au are ions Au skipped all by that largely Au driven of disproportionation valence charge of valence (d picture 1+ ions to Au corresponds all Te case elec- for this the local state in The ions in situation. Au energy of are CT structure holes negative tronic a of note may number one and largest the that firms uhasae Nt htti ria isi h ln fteTe Au-D the instead at of corresponds density band plane the charge this to the thus, the and, in of symmetric lies spherically part is orbital central for this the typical while that coordination plaquette, (Note square state. has active a ion JT such this hypothetical why a of explains that urally as same the is Au 1B) wave (L Fig. ground-state the in the (Au-P of to symmetry holes The ligand function. the of largest contribution the icant Te while the band, from comes least-filled part the Au is to the there corresponding from that density see contribution may minor One a distribution. filled only partially hole topmost, a the illustrating to bands corresponding density charge the sites? Au on CDW the in distortions (JT) (∼0.3 Jahn–Teller as of systems JT magnitude classical of such order the of is is bonds Au–Te and long linear-coordinated and short linearly between one The dif- Au. difference have (3+) very We square-coordinated another ions: give and Au contrast (1+) which two coordinated strong for optimization, in coordination lattice be local the ferent to from seems results however, with This, holes). ligand of 2/m ntescn tpw aeul hce o oa energies total how checked carefully we step second the In qualita- only be can structures two only of analysis However, Au and Te between electrons of redistribution a Moreover, con- also 1A, Fig. in shown states, of density the of Analysis oase hsqeto epo nFg 1B Fig. in plot we question this answer To 3+ Cmmm )(6.Wa rvssc togltiedsotos fnot if distortions, lattice strong such drives What (26). A) 3z o ihtohlso the on holes two with ion ˚ and AuTe 2 4 − tutr orsodn oteCWi tl h lowest the still is CDW the to corresponding structure Cmmm P pc ru,tettleeg fwihi y9 meV 90 by is which of energy total the group, space 5d r 2 2+ 2 3m ¯ 10 ihaleprmnal nw tutrsincluded structures known experimentally all with orbital.) ihteeprmna aa(4 5,wihshow which 15), (14, data experimental the with 1 and ih55 mle oue n h average the and volume, smaller 5.5% with tutrsaemc ihri energy. in higher much are structures Te 10 5d 1+ ∼0.35 5p .Teerslsalwu orcniethe reconcile to us allow results These ). 4 8 rmtesetocpcpito view. of point spectroscopic the from tutr ihdsotosresembling distortions with structure lcrnccngrtos hswould this configurations, electronic rias hs n a oeasignif- a note may one Thus, orbitals. U LaMnO hc is which , nsur-oriae u This Au. square-coordinated in A ˚ x 2 2 oesaeaon “Au around state hole ) 3 − (0.27 4 y . 0e) Redistributing eV). ∼10 2 5d ria;ta s tnat- it is, that orbital; P )(5 and (25) A) ˚ ttst h charge the to states 3m ¯ h itiuinof distribution the 1 hs,where phase, 1+ ∼0.25 d AuTe n Au and 5p ierepel site K 2 bands CuF 2 in A ˚ 3+ we 3+ ” 4 vrsiae qiiru oue h rtclpesr o the experimental for The pressure uniform (AuAu’ Te critical to the transition CDW volume, commensurate equilibrium overestimates the with structure to (P of pressure derivative ical first the Taking Superconductivity and Phase High-Pressure formation the corresponding for of and crucial structure are energy incommensurate holes the CT of ligand negative of contribution the large that once proves This disappear. again frequencies phonon imaginary these above, would structure homogeneous superstructure. incommensurate the an to of lead instability indeed real the Thus, the at frequency to minimal correspond vectors the wave with incommensurate imaginary phase became frequencies high-pressure homogeneous spec- phonon the the of calculated (31) we trum structure incommensurate AuAu’Te get our struc- sylvanite, commensurate a closest computational the of by to ture it model due to had above, we explained limitations As incommensurate. is to the due result CDW a the as energy. of in and costs above, energy explained leads AuAu’Te the which as of sites, interaction, increase Au Coulomb the drastic on a mostly to been have would tionation energy ∆ CT negative Au a the to corresponds which 1A), AuAu’Te by modeled dif- energy total is The AuAu’Te energy: ference in the lowest high-pressure the destabilize equivalent shift the to structurally the makes enough that it is found and eV and We energy 1 holes. CT only Te the of of increasing contribution thus the energy, reducing in up of shifted Au ficially structure the where real calculations, AuAu’Te model performed the the of imitating formation tortions, the for energy structure crystal the of optimization volume, each performed. was For results). SOC + (GGA 2. Fig. CT eysgicnl,we eshift we when significantly, Very real in why is question important An tti tg n a eosrt rca oeo h CT the of role crucial a demonstrate can one stage this At P 3m ¯ ree a aei oiie hntecag dispropor- charge the Then positive. it make can even or oa nryv.vlm o ifrn osbecytlstructures crystal possible different for volume vs. energy Total 5d 1 4 E s26Ga ti tiigta hl u optimized our while that striking is It GPa. 2.6 is tutr ihieuvln u eoe uhhigher much becomes Aus inequivalent with structure riasu ed oadces faslt au of value absolute of decrease a to leads up orbitals P AuTe 3m ¯ 1 c − eurdfrtetasto rmAuAu’Te from transition the for required ) P 2 E c P eide on htwe esatfrom start we when that found indeed We . 2 = AuAu 3m ¯ 4 P h Au the , 3m ¯ .5 1 0 Te P (5). GPa 1 i.S1B). Fig. Appendix, (SI structure) 4 srpoue ihgo accuracy: good with reproduced is ≈ E q e/..I h real the In meV/f.u. −2 4 5d ( ≈ P ocekfrtepsiiiyto possibility the for check To . V 3m ¯ 0.41a AuTe ttsleblwTe below lie states n a n htacrit- a that find can one ), d 1 AuTe eesu,a explained as up, levels NSLts Articles Latest PNAS hs ihalA ions Au all with phase 0 + P 2 . AuTe 4 3m ¯ 2 .5c 5d tutr ihdis- with structure h superstructure the oephonon some 1, ad eearti- were bands (where 2 o hswe this For . ∆ CT 4 4 structure, slightly ) Shifting . 5p a AuTe | and (Fig. f6 of 3 2 4 c ,

PHYSICS The high-pressure phase of AuTe2 is also very interesting due to another aspect—the superconductivity, which appears in it below Tc = 2.3 K (2). One may stabilize this phase not only by pressure, but also by Pt doping (3), which also results in the sta- bilization of the same P3¯m1 structure. The superconductivity was proposed to be induced by breaking of Te–Te dimers, which exist in the C 2/m phase, but disappear in the high-pressure superconducting P3¯m1 phase (3). In particular, it was specu- lated that the formation of Te–Te dimers modifies the electronic structure of AuTe2 through formation of bonding (σ) and anti- Fig. 4. (A and B) Diagrams illustrating (A) conventional Bardin–Cooper– bonding (σ∗) Te 5p bands (3). We have seen that the bands at Schrieffer “t-channel” pairing and (B) “s-channel” pairing proposed for the Fermi level indeed have a very large contribution of the Te AuTe2. 5p states, but they are strongly hybridized with Au 5d and have the symmetry of Au 5d orbitals (Fig. 1), while the σ-bonded Te 2+ 5p states are far away from the Fermi level (∼5.2 eV below and that the chemical tendency of Au to charge disproportionately 1+ 3+ ∼3.2 eV above EF ). Thus, it seems that the Te–Te dimerization into, nominally, Au and Au , which is the main ingredient is not directly related to the suppression of the superconductiv- of our theory and which, as we argued above, plays a crucial ity. In fact, this is just one of the consequences of the formation role in explaining the main properties of AuTe2, may be also of the CDW. In Fig. 3 the directions of Te atom displace- instrumental in providing the mechanism, or at least helping the ments due to the CDW are indicated. One may see that the realization, of superconductivity in AuTe2 when doped or under formation of AuTe4 plaquettes and AuTe2 dumbbells naturally pressure. results in dimerization of the Te atoms, which, however, is not One can phenomenologically describe this situation by an a driving force but rather a consequence of the CDW formation effective Hamiltonian like the Anderson lattice model (where 5p in AuTe2. electrons of Te play the role of conduction electrons, while 5d One can argue that the physics disclosed in our calculations, electrons of Au are localized), but with an effective attraction— specifically the origin of the incommensurability—the tendency with negative U on localized levels. After excluding d electrons, to the skipped valence and charge disproportionation of “Au2+,” we get in effect also an attraction of conduction electrons, which, occurring in the situation with negative CT energy with the on one hand, can provide the mechanism of CDW formation self-doping—is also instrumental in providing a mechanism of (not even requiring nesting of the Fermi surface, although nest- superconductivity in AuTe2 under pressure or with doping. This ing would help). And, on the other hand, in this model we have tendency, both on the d levels (reaction Eq. 1) and more realis- a natural mechanism of formation of Cooper pairs leading to tically on ligand states (reaction Eq. 2), means that there exists a superconductivity. In diagrammatic language, this mechanism tendency for holes to form pairs; that is, there exists an effective of pairing is described in Fig. 4B [two electrons (or holes) of attraction of these holes. a conduction band “drop” into the Au 5d levels, where they The idea that the tendency to charge disproportionation experience attraction and form pairs, before decaying again into (which actually means the local “chemical” tendency to form conduction electrons.] This situation is reminiscent of a model pairs of electrons or holes) can be instrumental in providing the with bipolarons (36) and is different from the usual electron– mechanism of Cooper pairing was first suggested by Rice and phonon exchange in Fig. 4A (although the standard electron– Sneddon (32) in connection with the superconductivity of doped phonon coupling could also contribute). Thus, AuTe2 may be BaBiO3. This material is also known to experience charge dis- the long-sought second example of the same physics as pro- proportionation of the type 2Bi4+ → Bi3+ + Bi5+ (and again posed for BaBiO3 (32), with the same mechanism of both charge with a lot of action on ligands, e.g., ref. 17). For high-Tc cuprates disproportionation and superconductivity. a similar idea was proposed in ref. 33. It is also closely related to some theoretical studies of superconductivity in systems with As Yet Unknown Compound AuTe coexisting ordinary electrons and bipolarons (e.g., refs. 34 and Since USPEX has shown its efficiency in determining the AuTe2 35). We suppose, by analogy with the abovementioned papers, crystal structure, we extended these calculations to a whole Au1−x Tex series with arbitrary x. Fig. 5 shows thermodynamic convex hulls and a phase diagram of the Au–Te system in the GGA and GGA + SOC approximations. A compound is ther- modynamically stable if its thermodynamic potential (e.g., the Gibbs free energy) is lower than that of any other phase or phase assemblage of the same composition. On a graph show- ing the enthalpy of formation of all compounds of a given system (e.g., Au–Te system) from the elements, all points correspond- ing to stable compounds can be connected to form a convex hull. Height above the convex hull is a measure of thermody- namic instability of a compound. One may note that in addition to experimentally observed structures such as AuTe2 and AuTe3 (37) there appears another one: AuTe. AuTe has never been synthesized so far, but there exists min- eral muthmannite, AuAgTe2, found in Western Romania (38), where Au and Ag ions are in a 1:1 ratio. Muthmannite has a Fig. 3. Formation of the Te–Te dimers due to charge disproportionation distorted NiAs-type structure with space group P2/m. Our cal- on Au sites. The “strength” of distortions in AuTe6 octahedra is not the same for all Au–Te bonds. There are “strongly” distorted with respect to culations have shown that the C2/c structure predicted for AuTe ¯ by USPEX is significantly more stable (by 0.164 eV per atom undistorted P3m1 (δAu–Te ∼ 0.45 − 0.55 A)˚ and “weakly” distorted Au–Te bonds (δAu–Te ∼ 0.15 A).˚ Plotting (for simplicity) only strongly distorted Au– with SOC) than the muthmannite structure. The predicted C2/c Te bonds (red lines; arrows show direction of distortions), one immediately structure of AuTe, shown in Fig. 6, can be considered a distorted obtains Te–Te dimers (shown by blue arrows). NaCl-type structure (NiAs and NaCl structures are relatives).

4 of 6 | www.pnas.org/cgi/doi/10.1073/pnas.1802836115 Streltsov et al. Downloaded by guest on September 30, 2021 Downloaded by guest on September 30, 2021 oia vrg aec fgl in The gold calculations. following: of the initio valence is average ab calculations nominal of our from basis emerging the picture on The explain now we properties calaverite, and is puzzles, unresolved synthesize to try and predictions mate- AuTe. our similar study check a to although interesting AuTe however, studied. muthmannite synthesized, mineral the and rial, and been known a that second are not indicates The likely compound has which stabilized.] third is K, entropy “popular” it 0 entirely less = but probably such T with is (39), compound at it stable atoms calculations a in Te found not stoichiometry and have We Au solution. stable solid of three distribution system cal Au–Te the also in exists AuTe, exist com- properties. compounds: there of nontrivial stoichiometric with that example gold, found element, interesting inert We an very a presents of pounds system Au–Te The Conclusions superconducting. be also could it that high-pressure large the of resemble too should are phase AuTe The repulsion effect in plaquettes): Coulomb Thus, on-site AuTe. and the in calaverite dumbbells to for due in corre- costs did ions: solution energy it Au the as inequivalent find disproportionation, not (two charge did are to USPEX there why sponding that explain shows may level, This Fermi to the contributions density, at equal nearly bands charge the the to of sponding Analysis calculations. SOC yet not is AuTe why explain may known. and field and inert) stability AuTe of more narrow fields relatively it stability the making shrinking effect of stability expense (in the Au expands SOC of poten- the chemical field of vs. inclusion energy that free demonstrates Gibbs tial in of changes plot large The are of fields. there stability stability structures, crystal show that and calculations 5 phases SOC Fig. same + from the GGA see and can GGA One both system. while Au–Te the in phases Au ferent the of two position with the plaquettes distorted strongly the in (2.68 short are ions Au The potential 5. Fig. ihvr e xetos.Ad otipraty ohAu al. et both Streltsov importantly, most And, exceptions). few very Au with (only unstable chemically like pyrites uhbte tde,btsilpeetn eea,utlnow until several, presenting still but studied, better Much + GGA the in metal nonmagnetic a be to found was AuTe lowers additionally SOC the that mentioning worthwhile is It hroyai ovxhlsadGbsfe nryGv.chemical vs. G energy free Gibbs and hulls convex Thermodynamic µ AuTe o h uT ytmwt ifrn econcentrations. Te different with system Au–Te the for )adtoln (2.90 long two and A) Au ˚ FeS 3 2 Te 2 ihalA qiaet n n ol expect could one and equivalent, Au all with , and 7 ihasml ui tutr n statisti- and structure cubic simple a with MnS 5d adadtu fet tblt fdif- of stability affects thus and band AuAgTe 2 ρ( 4) u hssaei,fis fall, of first is, state this But (40). 1+ ~ r AuTe ) n Au and )A–ebonds. Au–Te A) ˚ rmAu from AuTe 2 AuTe skon twudb very be would It known. is , 2 hsi h ytmwhose system the is This . 2 3+ 2 s2,smlrt many to similar 2+, is and , 5d r nw oexist, to known are n Te and AuTe AuTe ρ( AuTe ~ r 3 5p corre- ), 2 [There . tthe at , states. 3 The . 2+ V h SE iuainicue 0srcue e eeainfra for generation per k- structures used 80 relaxations included Structure simulation of phases. USPEX 2π cutoff of stable The was wave resolution eV. for (27) plane a USPEX search and with algorithm respectively, mesh the prediction atoms, in structure Te (radius evolutionary applied core and The [Kr] and eV. Au scalar-relativistic a.u.) 400 2.1 used for (radius and a.u.) the core SOC [Xe] in the 2.2 an realized account with as potentials into PAW (42) took GW We method PAW (43). code all-electron VASP the Perdew–Burke–Ernzerhof the using within (41) performed functional were calculations DFT The for Methods important physics. interesting more very and, of history example inter- rich an extremely as its us, is of indeed because telluride, both esting, gold material, exciting this super- of doped appearance in the for conductivity instrumental electron be form pairs—may to hole tendency or the fact in is which disproportionation, chemistry. coordination in known bonding AuTe dative in of a particular analogue with in existing and holes gap ligand CT of lot negative with in situation Ni The (or superconducting. Au all with state the RNiO metallic to homogeneous leads a doping of or pressure formation by superstructure Au this valence of (skipped pression Au here, of, with property connected “atomic” intrinsically the is disproportionation bond or of charge occupation constant of apparently d showing characteristics data, structural spectroscopic the both of lattice explains triangular frustrated of a formation nicke- the e.g., with in, lates transition as commensurate structural superstructures, a There corresponding similar: case very this is in outcome occurs the But (17). disproportionation orsodt hr n ogA–ebns respectively. bonds, Au–Te long and short to correspond 6. Fig. lengths bond Au–Te Au the Au of for change coordination—linear the local (and by driven) largely in is as (and not described is Eq. disproportionation corresponding the is, on that systems: much other so again not several however, which, occurs in case disproportionation, this also charge In or met Te) valence, 19). the phenomenon (here (17, a ligand self-doping of occurs to situation there go the holes actually the is with This of hybridization significant all with still fact (but bands in that means This nry hti,patclyAu practically is, that energy, Au and eageta h aemcaimtetnec ocharge to tendency mechanism—the same the that argue We hlso u ept hseuvlne h ednyt this to tendency the equivalence, this Despite Au. of shells 1+ u nta si Eq. in as instead but 1, RNiO L 3 2 eoigeuvln,adin and equivalent, becoming ) 3+ h rsa tutr fAT.Tiksldaddse lines dashed and solid Thick AuTe. of structure crystal The ;ta s tsol ebte aldntcag,btbond but charge, not called better be should it is, that ); in 3 AuTe 1,2,2)o nomnuaea ntecs of case the in as incommensurate or 23) 22, (17, 2 orsodt h iuto ihngtv CT negative with situation the to correspond AuTe × d 0.03 2 2+ hstasto saccompanied is transition This 2. hlstesle,bto ligands; on but themselves, shells or →Au A ˚ AuTe −1 AuTe n lcrncsern f0.1 of smearing electronic and 1+ AuTe 1+ 2 2 L NSLts Articles Latest PNAS hspcuenaturally picture This . n qaefrAu for square and ne rsue Thus, pressure. under n Au and 2 hssaebecomes state this 2 AuTe stesldstate solid the is d 3+ ttso Au). of states →Au 2 2+ n the and .Sup- ). | 1+ 3+ f6 of 5 L = 2 .

PHYSICS variable-composition run. Also all known Au–Ag–Te compounds (with sil- Foundation of Basic Research (16-32-60070), by the Federal Agency of Sci- ver atoms substituted by gold) were included in the calculation (6, 37, 39, entific Organizations (“spin” AAAA-A18-118020290104-2), by the Russian 44, 45). Phonon calculations were performed using Phonopy (31) with a Ministry of Science and High Education (02.A03.21.0006), by Russian Pres- 4 × 4 × 2 supercell. ident Council on Science (MD-916.2017.2), by the DFG (SFB 1238), and by the German Excellence Initiative. A.R.O. thanks the Russian Science Founda- ACKNOWLEDGMENTS. We are grateful to G. Sawatzky, S.-W. Cheong, tion (16-13-10459). V.V.R. was supported by Project 5-100 of Moscow Institute P. Becker, and L. Bohaty for discussions. This work was supported by the of Physics and Technology, and computations were performed on the Rurik UralBranch of Russian Academy of Sciences (18-10-2-37), by the Russian supercomputer.

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