Downloaded by guest on September 27, 2021 fe usata ato tm aebe elcdi the in replaced been have atoms V of even part V intact, substantial remain electrons a change Dirac after extreme The composition. tolerate chemical can of which paper, electrons this VAl topological semimetal In Dirac robust type-II devices. the their electronic that to report restricts future we which vulnerable in change, application usually 2019) environment potential 11, are October and review doping semimetals for (received chemical 2020 in 8, May electrons approved and Topological CA, Irvine, California, of University Fisk, Zachary by Edited and China; China; 100871, Beijing Matter, Taiwan; 701, Taiwan; Tainan University, 701, Tainan Kung Cheng National Physics, of neteeceia opsto hne efidta the that find We change. composition V chemical extreme an (DSM) future This in application band. potential topological TSMs’ devices. the electronic the change from limits may small defect away vulnerability to tiny the electrons sensitive This environment. contrast, very depopulate external is In and composition TSMs perturbations. of in local pro- potential small topologically chemical against The state robustly topological are fermions. their is because they Dirac mobile highly therefore, are and and, electrons tected Weyl physics, particle as in dubbed equation Dirac representations the of obeys excitation low-energy electrons’ These T electron Dirac rational topological a chemical-bond-protected materials. robust, suggests elec- search semimetals and to topological bond, approach in chemical properties count, the tronic elec- on electron understanding holes Dirac Our among center. the the gravity interrelations bonding words, by their is other depopulated orbital long In VAl fully as substitution. in transition are trons Ti this orbitals from in bonding donated broken completely the is as bond V–Al The x 117546; Singapore Singapore, of University National Centre, Research 70803; LA Rouge, Baton University, a Xie Weiwei Liu Yiyuan semimetal robust Dirac in transition Lifshitz induced Bond-breaking www.pnas.org/cgi/doi/10.1073/pnas.1917697117 atoms (V) a induces vanadium from substitution of transition (Ti) part Titanium Lifshitz replaced. substantial been a have after (35%) even DSM, of DS 71) eettertclwr eosrtdta there that demonstrated per states work of electrons theoretical density Recent 14 the (7–11). in of occurs (DOS) number” pseudogap crystal a ”magic when this a metal that transition by clarified stabilized band have is their orbitals structure on molecular studies and Previous structure (4–6). the structure within partial occurs bonding covalent metallic strong which in 4, intermetallics Fig. (see atoms the V/Ti of arrangement the from built the shields which tran- bond, robustly. Lifshitz V–Al electrons This covalent Dirac the broken. by completely controlled is is bond sition V–Al the as long nentoa etrfrQatmMtras colo hsc,Pkn nvriy ejn 081 China; 100871, Beijing University, Peking Physics, of School Materials, Quantum for Center International 1−x = 1−x ee erpr outtplgcleetosi ia semi- Dirac in electrons topological robust report we Here, n itilmnd rsalz nasm tutr hc is which structure same a in crystallize trialuminide Ti and V 5 hr isiztasto to transition Lifshitz a where 0.35, adcosn onsi hi lcrncsrcue (1–3). structures electronic their in points near band-crossing electrons relativistic host (TSMs) semimetals opological Ti Ti x Al x Al k 3 unu aeil n eie iiin ejn cdm fQatmIfrainSine,Biig109,China 100193, Beijing Sciences, Information Quantum of Academy Beijing Division, Devices and Materials Quantum 3 a oi ouin.Ti ia eiea tt nsat ends state semimetal Dirac This solutions. 3 b | uFiLiu Yu-Fei , oi ouin etr tnadtasotbehaviors transport standard feature solutions solid n hagJia Shuang and , r rtce yteVA od hs molecular whose bond, V–Al the by protected are isiztransition Lifshitz VAl h hsc iiin ainlCne o hoeia cecs snh 01,Taiwan; 30013, Hsinchu Sciences, Theoretical for Center National Division, Physics 3 hs lcrncsrcuecntolerate can structure electronic whose , a n .Te eogt ru fpolar of group a to belong They Inset). i Gui Xin , j tp S to DSM -type A etrfrEclec nTplgclQatmCmuain nvriyo hns cdm fSine,Biig100190, Beijing Sciences, of Academy Chinese of University Computation, Quantum Topological in Excellence for Center CAS | c lcrncount electron eateto hsc,Ntoa nvriyo igpr,Snaoe117542; Singapore Singapore, of University National Physics, of Department a,i,j,k,1 Al b hn Xiang Cheng , 12 tp rva ea occurs. metal trivial p-type uothdacontaining cuboctehedra VAl p tp rva ea,as metal, trivial -type | hmclbond chemical 3 ot exceptional, hosts 3 a u-i Zhou Hui-Bin , g etrfrQatmFoteso eerh&Tcnlg,Ntoa hn ugUniversity, Kung Cheng National Technology, & Research of Frontiers Quantum for Center doi:10.1073/pnas.1917697117/-/DCSupplemental at online information supporting contains article This 1 is ulse ue1,2020. 18, June published First BY-NC-ND) (CC 4.0 NoDerivatives License distributed under is article access open This Submission.y Direct PNAS a is article This interest.y competing no and declare Y.L. authors and The data; analyzed S.J. and paper. y and the H-B.Z., W.X., wrote C.X., T.-R.C., S.J. X.G., H.L., Y.-F.L., Y.L., Y.L., research; research; performed designed C.-H.H. S.J. and Y.L. contributions: Author xs aro itdoe ia oe ntepedgpi the in (E pseudogap level the Fermi in the cones VAl above Dirac slightly tilted-over space of energy-momentum pair a exist tutr itrin h odfrainatmt olwrthe lower to attempts at the formation DOS for bond The responsible bonds—in distortion. bond—are Hamilton maximizing structure V–Al the orbital interplanar that the crystal reveal particular, the we on (COHP), emphasis electronic-structure population the performing with By occurs. calculation transition Lifshitz a as such properties topological in PHE the that reveals a investigation from observe ther changes We signal 13. Concomitantly, Hall to distortion. the 14 lattice from bond-breaking-induced changes V–Al count electron of the solutions solid which isostructural the of properties interrelations the properties considered topological in has and bond, study chemical count, relevant electron among no far, So (16, planar in 18). topological space the (PHE) and momentum effect surface in Hall Fermi the tunneling recently, Very Klein 17). direction-dependent and as anomaly such rise properties, chiral give physical can exotic which many 15), to (14, fermions Dirac symmetry-breaking a owo orsodnemyb drse.Eal [email protected] Email: addressed. be may correspondence whom To e hagHnHsu Chuang-Han , o einn e unu aeil i otoln their controlling via materials quantum bond. is chemical new bond V–Al designing approach the rational for a as highlights long finding Dirac as Our from broken. occurs transition completely metal Lifshitz trivial A to replaced. semimetal been have atoms V odat sasil o rtcigtetplgclelectrons V topological the VAl the protecting semimetal for Dirac shield in V–Al a the as that show acts manipulate we to bond paper, way this effective In electrons. an topological as the considered quantum less is new bond chem- a designing ical controlling and far, for So functionality. structure desired crucial with materials crystal is between properties electronic relation the Understanding Significance nttt fPyis cdmaSnc,Tie 12,Taiwan; 11529, Taipei Sinica, Academia Physics, of Institute nti ae,w ou ntecytlsrcueadelectronic and structure crystal the on focus we paper, this In VAl 3 1,1) h itdoe ia oe ottp-ILorentz- type-II host cones Dirac tilted-over The 13). (12, 3 1−x . VAl E Ti f 3 x n rtcstetp-IDrcfrin when fermions Dirac type-II the protects and Al eanitc fe usata isbttto,until substitution, Ti substantial after intact remain PNAS 3 oi ouin,ee fe usata atof part substantial a after even solutions, solid i olbrtv noainCne fQuantum of Center Innovation Collaborative | c,d b VAl eateto hmsr,LusaaState Louisiana Chemistry, of Department uy7 2020 7, July 3 h ia lcrn eanitc in intact remain electrons Dirac The . snLin Hsin , 3 d . eeilsrtdi xeiet(13, experiment in illustrated were y etefrAvne DMtrasand Materials 2D Advanced for Centre n raieCmosAttribution-NonCommercial- Commons Creative yeto type | . y e o.117 vol. https://www.pnas.org/lookup/suppl/ a-ogChang Tay-Rong , p yeat type | o 27 no. V x 1−x | 0 = f Department Ti 15517–15523 Fur- .35 x Al f,g,h f 3 x of ) in , , is

PHYSICS PHE less than 0.35. The V–Al antibonding orbital builds up the Dirac (ρxx ) in DSMs can be described as the following formula electron band, which is fully depopulated as long as the Lifshitz (24, 25): transition occurs. The relationship among the structure, electron PHE ρyx = −∆ρchiralsinθcosθ, [1] count, and electronic properties in various TSMs (19–21) has PHE been considered, but the influence of the presence or absence ρxx = ρ⊥ − ∆ρchiralcos2θ, [2] of a chemical bond on topological electrons is less pondered (22). Our finding highlights a chemical-bonding gravity center where ρ⊥ and ρk are the resistivity for current perpendicu- (23) of topological electrons, in particular, TSMs. Understand- lar and parallel to the magnetic-field direction, respectively; ing this chemical-protection mechanism in various TSMs will ∆ρchiral = ρ⊥ − ρk gives the anisotropy in resistivity induced by help to develop more robust electronic devices, which may have chiral anomaly. A previous study showed large PHE in VAl3 (18), potential application in the future. and, here, we focus on its change when Ti atoms are substituted. PHE PHE As shown in Fig. 2, the ρyx and ρxx show explicit periodic Results dependence on θ, which can be well-fitted by using Eqs. 1 and We firstly demonstrate the electronic properties of V1−xTixAl3. 2 when x is less than 0.35. Remarkably, the angular dependent PHE PHE Fig. 1 shows the Hall resistivity (ρyx ) with respect to the external ρyx and ρxx suddenly drop to almost zero at x = 0.35, which magnetic field (H ) at different for representative is coincident with the n–p transition. We extract ∆ρchiral and ρ⊥ samples. VAl3 is a n-type semimetal whose ρyx is large and neg- for each x, as shown in Fig. 3. atively responsive to field (18). ρyx is not linearly dependent on The carrier concentration (n and p for electron and hole, H below 50 K, indicating that two types of carriers coexist. If we respectively) and mobility (µ) for V1−xTixAl3 are obtained by adopt a rigid-band approximation, a small Ti substitution (3.5%) fitting the field-dependent resistivity and ρyx at different temper- is expected to compensate the destitute conduction electrons in atures. As shown in Fig. 3, the carrier concentration in the V-rich VAl3 and leads to a n–p transition. Surprisingly, the profile of semimetal region is nearly invariant as x increases from 0 to 0.3, ρyx remains almost intact after 35% of V atoms are replaced. We while the mobility is relatively large during the process. As com- find a robust semimetal state in VAl3 which can tolerant large parison, because the carrier density and electron scattering are chemical composition change. governed by increasing charge defects (26) in topological trivial This semimetal state ends at x = 0.35. When x = 0.4, ρyx is alloys in the Ti-rich region, the hole mobility drops significantly very small because the lowly mobile electrons and holes are when x changes from 1 to 0.55. Concomitant with the n–p transi- compensated. Yet, we can discern that the ρyx is positively tion, the ∆ρchiral and ρ⊥ dramatically drop to almost zero when dependent on H at 300 K, but negatively dependent on H at x is more than 0.35. Previous studies suggested that the PHE and 2 K, indicating a n–p transition onsite. When x is more than 0.4, angular-dependent resistivity are determined by the Berry curva- the alloy becomes a p-type metal, showing a small and linear, ture in nonmagnetic TSMs (25, 27). Our observation reveals that -independent ρyx . the n–p transition at x = 0.35 is a topological transition from a We then investigated the PHE in V1−xTixAl3, which is known DSM to a trivial metal. as an evidence of existing Dirac fermions (18, 24). The pla- The unusual evolution of electronic properties in the isostruc- PHE nar Hall resistivity (ρyx ) and anisotropic magneto-resistivity tural solutions motivated us to examine their crystal-structure

AD

B E

CF

Fig. 1. Field-dependent Hall resistivity (ρyx ) at different temperatures for representative samples in V1−xTixAl3.(A–C) x = 0 (A), 0.2 (B), and 0.35 (C) at 2 K, 50 K, 100 K, 200 K, and 300 K. The data at 2 K (green) and 50 K (purple) are nearly identical. (D–F) x = 0.4 (D), 0.8 (E), and 1 (F) at 2 K and 300 K.

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T–T needs closed-shell 4 count a by S1). electron Fig. connected Appendix, the is (SI atom supporting Therefore, T–Al T the each through bonds which suggested sigma in (33–35) picture colleagues bonding and a transition Yannello various (28–32). in chemistry (TAl pseudogap trialuminide the and metal structures crystal The properties Discussion electronic of evolution break- the bond structure. in chemical crystal role a and crucial that region. a prove this plays will in we ing part, intact following remain expectation, the properties In our for transport to distorted electrical Contrary seriously the atoms. is Ti structure and crystal the V the than from of coming less effect size pressure is different chemical a change to ascribed nonlinear be curious cannot This S4). Fig. when accelerately to respect with parameters lattice the for for plate flat chunk a from of 4, evolves Fig. crystals shape facets. rod-like rectangle (110) the commonly glossy comparison, is unit shape As tetragonal slender, crystal cells. by such composed compounds and the in facets, observed (001) glossy shows hmclbn,w oprdteeetoi tutrsbetween structures electronic the compared we bond, chemical further needs properties theory. electronic in elaboration and distortion, structural dis- easily of can crystals we TiAl single rod-like characterization, the any tinguish doing Before change. ersnaiesmlsi V in samples representative (ρ i.2. Fig. i tal. et Liu xx PHE ose ih nterlto ewe lcrncutand count electron between relation the on light shed To ihrsett h angle the to respect with (B ) ) 13e 3 tfis ih Fg 4, (Fig. sight first at lnrHl eitvt (ρ resistivity Hall Planar − V 1−x x e oml.W xetatasto rmsmmtlto semimetal from transition a expect We formula. per 0 = Ti n hnt ogrdfor rod long a to then and .35, x x Al when x 3 u h eainhpaogeeto count, electron among relationship the but , sls hn03 Fg and 4 (Fig. 0.35 than less is a 1−x , x 3 c Ti aeatatdmc teto in attention much attracted have ) yx PHE smr hn03,btte change they but 0.35, than more is x n h ai of ratio the and Al .Tesur lt of plate square The Insets). n nstoi magneto-resistivity anisotropic and (A) ) 3 θ . namgei edo t2Kfor K 2 at T 5 of field magnetic a in x 1 = Insets 18 VAl TiAl oathree-dimensional a to , − 3 hwta h crystal the that show 14e = 4 c rmteplate-like the from 3 steprototype the as , /a x x VAl < 0 = hiklinearly shrink 0. − IAppendix, SI 3 whereas 35, Moreover, . oachieve to u it but 2%, aefour have TiAl 3 rV pi into The split V) 5. or Fig. in of presented perspective also molecular the on based picture electron, one saturated partially for reducing to state state By bonding saturated structure. fully from this degrades This in time. 3× bonding + same (5 the the electrons at valence filled 14 fully that valence just indicates the space and momentum state in chemical-bonding band the make atoms V from TiAl hc h odi ul broken. fully is until bond bond the substitution which V–Al(II) Ti The the bond. weakens Al(I)– V–Al(I) successively weak stable rather the and with bond the compared adjustable Al(II) that orientation more has bonding derive it and we because role length 5, crucial a Fig. plays in bond T–Al(II) calculation for COHP wider the much Combining angle bond Al(II)–T–Al(II) for the bond makes T–Al(I) the than T–Al(II) more and much T–Al(I) when the of elongate both bonds angle Although bond series. Al(II)–T–Al(II) whole the the for and length bond T–Al(I) planar covalent S3. Fig. a Appendix, in SI orbitals exists molecular there related The above, the b Given 7). in bond V–Al Fig. between (see occurs (BZ) inversion band the and as long as reduces between splitting orbital the with i.3. Fig. oi ice,smsldsas n pnsursrpeettedt t2K, 2 at data the K. represent (C 2 respectively. at squares K, 300 open and and K, 150 stars, semisolid circles, solid 2g i.6sostecag fteitrlnrTA(I n inner- and T–Al(II) interplanar the of change the shows 6 Fig. rias n htgpi iiie tthe at minimized is gap that and orbitals, b 3 1g and (A (d TiAl and E x VAl 2 f −y n oiiy( mobility and (A) density Carrier B) VAl 3 oaigbetween locating 3 2 ocaiyteobtlcnrbtos schematic a contributions, orbital the clarify To . a silsrtdi i.5 h oepi felectrons of pair lone the 5, Fig. in illustrated As . from ) 1g 3 (d hc eeae suoa between pseudogap a generates which z PNAS 2 ), x Γ b nrae,teTA(I odchanges bond T–Al(II) the increases, on to point e 1g | g (d ) (d uy7 2020 7, July ∆ρ d xz x 2 , riaso rniinmtl (Ti transition on orbitals chiral −y e d g VAl Z yz 2 and ), and and ) on nteBilunzone Brillouin the in point e 3 x g | ρ and (d < ⊥ o.117 vol. b xz 2g namgei edo T 5 of field magnetic a in b 0. for 3 2g , TiAl neetnl,the Interestingly, . n hschange this and 35, o V for B) d Z TiAl (d yz x on nteBZ. the in point xy ,and ), VAl | 0 = 3 significantly ) o 27 no. 3 r hw in shown are 1−x beyond .35, and 3 optimize ) Ti b x a x 2g 1g VAl < Al | e (d g 3 (d VAl 0.35 15519 The . and xy 3 z 2 is ), 3 )

PHYSICS Remember that the Lifshitz transition point (x = 0.35) divides the whole series into metal and semimetal regions in which the crystal structure and the electronic transport properties change in different ways (Figs. 3 and 4). We focus on the semimetal region in which the topological electrons remain intact, in defi- ance of the large change of the unit cell. We check the band structure of VAl3 in which two conduction bands (CB1 and CB2) and two valence bands (VB1 and VB2) are near the Ef (Fig. 7). The conduction band CB1 crosses with the valence band VB1 along the Γ − Z direction, forming the Dirac nodes near the Z point, which host the highly mobile Dirac electrons. Another hole pocket of VB2 emerges along the Σ1 − Z direc- tion below 15 meV of the Ef . Although these bands are formed by the hybridization of different orbitals, we can sleuth out their mainly component atomic orbitals by the symmetry in k space. The cloverleaf-shaped electron pocket of CB1 along the diagonal direction mainly stems from the b2g (dxy ) orbital, while the hole pocket of VB2 along the straight direction mainly stems from the degenerated eg (dxz , dyz ) orbitals. On the other hand, the large dispersion along the kz direction in the VB1 top inherits the pz orbital of Al and a1g (dz 2 ) orbital of V. This rough estimation is consistent with our molecular energy-level diagram on the Γ and Z points (Fig. 5). The n–p transition occurs as long as the electrons fully depopulate the b2g orbital. This bond breaking corresponds to the Lifshitz transition, in which the Ef leaves the CB1 bottom and starts to touch the VB2 top. The V–Al bond is fully broken, and the system degenerates to a trivial p-type metal as long as the VB2 starts to be populated when x is more than 0.35. Hoffmann (23) suggested that maximizing bond, acting as a reservoir to store electrons, always makes every effort to lower Fig. 4. Lattice parameters (a and c) for V1−xTixAl3. The error bar of x is esti- the DOS at the Ef . When x is less than 0.35 in V1−xTixAl3, ± % < × −3 ˚ mated as 2 , while the error bar of a and c ( 3 10 A) is smaller than the bond formation demands extra electrons, which compen- the square data point. The straight dashed lines are guides to the eye. Inset sates the V substitution, and, therefore, the Ef is pinned on in the top left corner shows the unit cell of TAl3. Insets from left to right show photos of the single crystals for x = 0, 0.35, 0.4, and 1, respectively. the VB2 top. Vice versa, the Ti substitution in VAl3 breaks the V–Al bond at first, and such a bond-breaking process acts as a buffer to retard the Lifshitz transition. In the scenario The change of the crystal shape in V1−xTixAl3 reflects the of the molecular orbitals, the covalent bond of V–Al(II) acts bond breaking as well. Remember that all of the crystals form in as the bonding gravity center (23) of the topological elec- molten Al, so the V–Al(II) dangling bonds should attract more trons in VAl3. The type-II Dirac electrons are protected by the atoms along the c axis for x < 0.35. Because the facets of crys- V–Al bond. tals always intent to have fewer dangling chemical bonds, the strong V–Al(II) bond gives rise to the rod-like shape of VAl3 Conclusion single crystals. We observe robust Dirac electrons which are protected by The bond-breaking scheme above naturally explains the the V–Al chemical bond in the V1−xTixAl3 solid solutions. unusual change of the electronic properties in V1−x Tix Al3. When Ti atoms substitute V atoms, the V–Al bond acts as a

Fig. 5. (A) COHP for TiAl3 and VAl3.(B and C) Molecular energy-level diagrams at Γ and Z points for TiAl3 and VAl3, respectively.

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Structure and Composition 0.5 to vrapro f5dy,floe ydcnigi etiue h typical The centrifuge. a in decanting by followed V K days, of 1,023 5 size to of 1,323 period homogeneity. from the cooling a ensure the over to involved h process 10 for crystal-growth K atmosphere. the 1,323 argon Then, to partial up pieces under heated ampoule were V silica mixtures fused The of a in materials sealed raw was which The in V:Ti:Al together of (36). mixed ratio were molar (99 .9%) flux a ingot Al the and (99.99%), as powders Ti Al (99.99%), with method solution Synthesis. will Methods and Materials materials quantum in electron-counting quan- study and rules. models functional future materials chemical-bonding the various Our topological involve designing around in materials. for part bond tum that consideration dispersive chemical suggest more a of bears we as manipulation In Finally, acts popu- the cones. center. which partially Dirac molecular-orbital-energy may cone, formation the tilted-over Dirac bond the the the late host structure, which unique band likely such TSMs is protection type-II chemical-bond of in kind this that infer the broken, in p completely electrons is Dirac bond the for shield eye. the for guides are lines dashed straight i tal. et Liu V for (B) 6. Fig. tp rva ea hog isiztasto.W further We transition. Lifshitz a through metal trivial -type × n lI)TA(I odangle bond Al(II)–T–Al(II) and (A) length bond T–Al(II) and T–Al(I) 0.5 1−x 1−x igecytl fV of crystals Single × Ti Ti x x α mm 5 Al Al aito.Tedfrcindt o V for data diffraction The radiation. 3 3 . eiscytl aisfo 2 from varies crystals series A, 3 o rod-like. for =x Inset : 1 hw h -etrdAl V-centered the shows − 1−x x Ti : 9adte lcdi nauiacrucible, alumina an in placed then and 49 x Al 3 eegonvaahigh-temperature- a via grown were n VAl tp S eeeae to degenerates DSM -type odrXrydfrcin(XRD) diffraction X-ray Powder 3 × sln steV–Al the as long As . 2 × mm 0.1 12 1−x uothda The cuboctahedra. Ti x 3 Al o plate-like for 3 eis(x series = ygoercrltos eas ple igecytlXDfrtesamples the obtained for were S1–S3 XRD angle single-crystal and applied Al(II) length also 0.5), bond of 0, We The (0, relations. 0)]. [Al(I) 0, geometric (0, positions by V/Ti high-symmetry and in .25), 0 located 0.5, (0, are refined of atoms were determination 1) the The of converged. 0.9, for quickly 0.8, positions parameter were the atomic 0.7, method calculation and .6, 0 the parameters 0.5, as crystal 0.4, the 0.35, and VAl 0.3, Rietica, Rietveld .2, 0 by 0.1, 0.05, 0, lnrHl eitvt as remove resistivity To the contacts. Hall determined Hall we and background, planar zero-field current and the contribution of Hall regular plane the the in kept was direction ed(µ field l aaaecnandi h aucittx and text manuscript the in contained are data All of energy Availability Data cutoff a self- with calculations in computations included were the effects consistently. coupling in spin-orbital The used eV. 500 was mesh 15 k-point gener- A the (47). within schemes package approximation wave (46) gradient VASP alized the projector-augmented in implemented the method. as tetrahedron 45), using (44, Recipro- the method structures using reasonable. electronic by all computed out calculated were carried were We were spheres obtained integrations empty so space these cal values of the radii radii and and ASA positions automatically, The the filling. space as achieve well to as order in introduced were spheres Intersti- (43). tial (ASA) approximation sphere local atomic the and approximation in density method linear-muffin--orbital tight-binding, 3s: self-consistent, were Al Hii for and 0.7052; −11.000eV 4s: 4s: were Ti 4.550, for parameters The −8.97eV (42). methods extended-H semiempirical binding with (41) CAESAR using by calculated Calculation. Electronic in vibrating are S7. results and SQUID relevant (MPMS the and Device magnetometer), sample Interference Quantum VAl sus- Superconducting of ) S5 molar a magnetization Fig. temperature-dependent Field-dependent Appendix, The and which reference. (SI ceptibility system, the K measurement as 100 thermoelectric Hall constantan to home-built anomalous used a 300 the in from and measured effect coefficient was Hall Seebeck regular The the effect. from contribution no of was method data-analysis and setting experiment The the sweeping by measured voltage- ρ was to resistivity due from contribution Hall field resistivity the longitudinal misalignment, the with probe avoid S2 ) to Fig. order Appendix, (SI In resistivity metallic are room-temperature series whole measure- a the resistance that Temperature-dependent showed contacts temperature. ment paste room silver the at Sys- with Measurement technique cured four-probe Property standard Physical the Design using Quantum tem, a in performed were Measurements. Magnetic and Electrical paper. the (±1%). this of instrument homogeneity the the verified of have V measurements tolerance XRD estimated and EDS the our to Since 1 close V of and is elements Ti starting which of energy-dispersion the ratio tainty, as by the same series, determined is whole crystals the were the For in series 80. X-Max the an for in (EDS) Ti com- spectroscopy The and diffractometer. V PSL-Laue Science of Photonic isostruc- positions determined a low were are in crystals at diffraction single they Laue the annealing that by of time orientations verified The long solutions. measurements a solid XRD tural after our transition and and structural temperature, sluggish any V of very show crystals single not a our do via that found temperature We (37–39). low reaction incomplete at superstructure complicated a yx 1−x (H x = 3 ζ = Ti = ) n TiAl and −6.50 oeltrtr eotdta h oyrsaln TiAl polycrystalline the that reported literature Some . [ = x Coefficient ,1 n h eut r in are results the and 1, 0.8, 0.6, .4, 0 0.2, 0, 0 1.300, Al H 4p: ; ρ(+H 3 = , o9Ta aiu eprtrsadte ymtie as symmetrized then and temperatures various at T 9 to −9 oi ouin 4) eue h starting the used we (40), solutions solid eV ± ζ 3 Hii ) = ζ ata O n OPcluain eepromdb the by performed were calculations COHP and DOS Partial . ) n h apewsrttds httemagnetic-field the that so rotated was sample the and T), 5 eeue ssatn ons l enmnsuigL Bail Le using refinements All points. starting as used were a − = 4.750, = 1 and ρ(−H 0.675, = −8.81eV 0.4206; c h lcrncsrcue fTiAl of structures electronic The .TePEwsmaue nafie magnetic fixed a in measured was PHE The )]/2. PNAS a opeeydsrb h tutr eas all because structure the describe completely can Coefficient ρ Hii yx PHE 4 ; = ζ (H | 2 p: −5.44eV ζ ρ = ) uy7 2020 7, July = 300K [ = ζ 1.400, 1 1.167, = ρ = yx PHE 1.300, prxmtl qaig100 equaling approximately h eitne alefc,adPHE and effect, Hall resistance, The 0.4755; n 3d and , (+ Coefficient Hii H ) Hii | + = ζ o.117 vol. ρ = −12.30eV × 2 yx PHE − : −5.52eV = 15 Hii ρ x 1 (−H yx PHE 1.700, x : = × x 3 is S6 Figs. Appendix, SI = Tables Appendix, SI stenominal the as within 89 o were V for 0.7839; nue htthere that ensured eemaue in measured were 5MonkhorstPack 15 )] 3 | −10.810eV IAppendix. SI /2 4p: ; ζ n VAl and o 27 no. n 3d and , 3 = Coefficient − rnfrsto transforms 1.075, ±2% ρ uckel-tight- ¨ yx PHE ζ 1−x = | (H 3 µΩ : ; uncer- 1.167, Ti 15521 Hii Hii were = ζ x x 2 1 cm. Al 0). in = = = = 3

PHYSICS A B

CB2 Dirac cone CB1

VB2 VB1 Energy (eV) Energy

Σ Γ

C CB1 D VB2

VB1 VB1

V-Al( ) bond break E F eh h

Fig. 7. (A) BZ of VAl3.(B) Band structure in the vicinity of the type-II Dirac node in VAl3.(C) Electron (CB1; red) and hole (VB1; blue) pockets of VAl3.(D)

Hole pockets (VB1 and VB2; blue) in V1−xTixAl3 for x > 0.35 as long as the V–Al(II) bond breaks. (E) dxy (red) and dz2 (blue) orbitals compose CB1 and VB1, respectively. (F) Degenerated dyz/dxz and dz2 orbitals compose VB2 and VB1, respectively.

ACKNOWLEDGMENTS. We thank Xi-Tong Xu for his useful advice in gram from the Ministry of Science and Technology (MOST) in Taiwan, experiment and Guang-Qiang Wang for his help in Laue orientation. under MOST Grant MOST109-2636-M-006-002 (for the Columbus Pro- This work was supported by National Natural Science Foundation of gram); National Cheng Kung University, Taiwan; and National Center China Grants U1832214 and 11774007; National Key R&D Program of for Theoretical Sciences, Taiwan. This work was supported partially by China Grant 2018YFA0305601; and Chinese Academy of Sciences Strate- MOST Grant MOST107-2627-E-006-001. This research was supported in gic Priority Research Program Grant XDB28000000. The work at Louisiana part by the Higher Education Sprout Project, Ministry of Education to State University was supported by the Beckman Young Investigator the Headquarters of University Advancement at National Cheng Kung program. T.-R.C. was supported by the Young Scholar Fellowship Pro- University.

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