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Bond-Breaking Induced Lifshitz Transition in Robust Dirac Semimetal

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Bond-Breaking Induced Lifshitz Transition in Robust Dirac Semimetal Bond-breaking induced Lifshitz transition in robust Dirac semimetal VAl3 Yiyuan Liua, Yu-Fei Liua, Xin Guib, Cheng Xianga, Hui-Bin Zhoua, Chuang-Han Hsuc,d , Hsin Line , Tay-Rong Changf,g,h, Weiwei Xieb, and Shuang Jiaa,i,j,k,1 aInternational Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China; bDepartment of Chemistry, Louisiana State University, Baton Rouge, LA 70803; cDepartment of Physics, National University of Singapore, Singapore 117542; dCentre for Advanced 2D Materials and Graphene Research Centre, National University of Singapore, Singapore 117546; eInstitute of Physics, Academia Sinica, Taipei 11529, Taiwan; fDepartment of Physics, National Cheng Kung University, Tainan 701, Taiwan; gCenter for Quantum Frontiers of Research & Technology, National Cheng Kung University, Tainan 701, Taiwan; hPhysics Division, National Center for Theoretical Sciences, Hsinchu 30013, Taiwan; iCollaborative Innovation Center of Quantum Matter, Beijing 100871, China; jCAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, China; and kQuantum Materials and Devices Division, Beijing Academy of Quantum Information Sciences, Beijing 100193, China Edited by Zachary Fisk, University of California, Irvine, CA, and approved May 8, 2020 (received for review October 11, 2019) Topological electrons in semimetals are usually vulnerable to exist a pair of tilted-over Dirac cones in the pseudogap in the chemical doping and environment change, which restricts their energy-momentum space slightly above the Fermi level (Ef ) of potential application in future electronic devices. In this paper, VAl3 (12, 13). The tilted-over Dirac cones host type-II Lorentz- we report that the type-II Dirac semimetal VAl3 hosts exceptional, symmetry-breaking Dirac fermions (14, 15), which can give rise robust topological electrons which can tolerate extreme change to many exotic physical properties, such as direction-dependent of chemical composition. The Dirac electrons remain intact, even chiral anomaly and Klein tunneling in momentum space (16, after a substantial part of V atoms have been replaced in the 17). Very recently, the Fermi surface and the topological planar V1−xTixAl3 solid solutions. This Dirac semimetal state ends at Hall effect (PHE) in VAl3 were illustrated in experiment (13, x = 0:35, where a Lifshitz transition to p-type trivial metal occurs. 18). So far, no relevant study has considered the interrelations The V–Al bond is completely broken in this transition as long among electron count, chemical bond, and topological properties as the bonding orbitals are fully depopulated by the holes in VAl3. donated from Ti substitution. In other words, the Dirac elec- In this paper, we focus on the crystal structure and electronic trons in VAl3 are protected by the V–Al bond, whose molecular properties of the isostructural solid solutions of V1−xTixAl3, in PHYSICS orbital is their bonding gravity center. Our understanding on the which the electron count changes from 14 to 13. We observe a interrelations among electron count, chemical bond, and elec- V–Al bond-breaking-induced lattice distortion. Concomitantly, tronic properties in topological semimetals suggests a rational the Hall signal changes from n type to p type at x = 0:35. Fur- approach to search robust, chemical-bond-protected topological ther investigation reveals that the topological properties such as materials. PHE in VAl3 remain intact after substantial Ti substitution, until a Lifshitz transition occurs. By performing electronic-structure Dirac electron j Lifshitz transition j electron count j chemical bond calculation with the emphasis on the crystal orbital Hamilton population (COHP), we reveal that the maximizing bonds—in opological semimetals (TSMs) host relativistic electrons near particular, the interplanar V–Al bond—are responsible for the Tband-crossing points in their electronic structures (1–3). structure distortion. The bond formation attempts to lower the These electrons’ low-energy excitation obeys the representations DOS at Ef and protects the type-II Dirac fermions when x is of Dirac equation in particle physics, and, therefore, they are dubbed as Weyl and Dirac fermions. The topologically pro- Significance tected electrons are highly mobile because their topological state is robustly against small local perturbations. In contrast, the chemical potential in TSMs is very sensitive to small change Understanding the relation between crystal structure and of composition and external environment. This tiny defect may electronic properties is crucial for designing new quantum depopulate electrons away from the topological band. This materials with desired functionality. So far, controlling a chem- vulnerability limits the TSMs’ potential application in future ical bond is less considered as an effective way to manipulate electronic devices. the topological electrons. In this paper, we show that the V–Al Here, we report robust topological electrons in Dirac semi- bond acts as a shield for protecting the topological electrons in Dirac semimetal VAl3. The Dirac electrons remain intact in metal (DSM) VAl3, whose electronic structure can tolerate an extreme chemical composition change. We find that the the V1−xTixAl3 solid solutions, even after a substantial part of V atoms have been replaced. A Lifshitz transition from Dirac V1−xTixAl3 solid solutions feature standard transport behaviors of DSM, even after a substantial part of vanadium (V) atoms semimetal to trivial metal occurs as long as the V–Al bond is (35%) have been replaced. Titanium (Ti) substitution induces a completely broken. Our finding highlights a rational approach Lifshitz transition from n-type DSM to p-type trivial metal, as for designing new quantum materials via controlling their long as the V–Al bond is completely broken. This Lifshitz tran- chemical bond. sition is controlled by the covalent V–Al bond, which shields the Author contributions: Y.L. and S.J. designed research; Y.L., Y.-F.L., X.G., C.X., H-B.Z., and Dirac electrons robustly. C.-H.H. performed research; Y.L., H.L., T.-R.C., W.X., and S.J. analyzed data; and Y.L. and V and Ti trialuminide crystallize in a same structure which is S.J. wrote the paper.y built from the arrangement of the Al12 cuboctehedra containing The authors declare no competing interest.y V=Ti atoms (see Fig. 4, Inset). They belong to a group of polar This article is a PNAS Direct Submission.y intermetallics in which strong metallic bonding occurs within the This open access article is distributed under Creative Commons Attribution-NonCommercial- covalent partial structure (4–6). Previous studies on their band NoDerivatives License 4.0 (CC BY-NC-ND).y structure and molecular orbitals have clarified that this crystal 1 To whom correspondence may be addressed. Email: [email protected] structure is stabilized by a ”magic number” of 14 electrons per This article contains supporting information online at https://www.pnas.org/lookup/suppl/ transition metal when a pseudogap occurs in the density of states doi:10.1073/pnas.1917697117/-/DCSupplemental.y (DOS) (7–11). Recent theoretical work demonstrated that there First published June 18, 2020. www.pnas.org/cgi/doi/10.1073/pnas.1917697117 PNAS j July 7, 2020 j vol. 117 j no. 27 j 15517–15523 Downloaded by guest on September 27, 2021 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 temperatures 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.
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