DOI: 10.1038/s41467-018-06518-1. Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2

Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2

10.1038/s41467-018-06518-1

Crossref journal-article

Springer Science and Business Media LLC

Nature Communications (297)

Abstract

AbstractSpin–orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin–orbit coupling and spin–momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the b-axis WTe2/Py bilayers of nano-devices but not observed in the a-axis of WTe2/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin–momentum locking effect of the Fermi arcs of the Weyl semimetal WTe2.

Bibliography

Li, P., Wu, W., Wen, Y., Zhang, C., Zhang, J., Zhang, S., Yu, Z., Yang, S. A., Manchon, A., & Zhang, X. (2018). Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2. Nature Communications, 9(1).

Authors 10

Peng Li (first)
Weikang Wu (additional)
Yan Wen (additional)
Chenhui Zhang (additional)
Junwei Zhang (additional)
Senfu Zhang (additional)
Zhiming Yu (additional)
Shengyuan A. Yang (additional)
A. Manchon (additional)
Xi-xiang Zhang (additional)

References 69 Referenced 138

Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555–558 (2012). (10.1126/science.1218197) / Science by L Liu (2012)
Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189–193 (2011). (10.1038/nature10309) / Nature by IM Miron (2011)
Manchon, A. et al. Current-induced spin–orbit torques in ferromagnetic and antiferromagnetic systems. Preprint at https://arxiv.org/abs/1801.09636 (2018).
Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010). (10.1103/RevModPhys.82.3045) / Rev. Mod. Phys. by MZ Hasan (2010)
Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011). (10.1103/RevModPhys.83.1057) / Rev. Mod. Phys. by XL Qi (2011)
Han, J. et al. Room-temperature spin-orbit torque switching induced by a topological insulator. Phys. Rev. Lett. 119, 077702 (2017). (10.1103/PhysRevLett.119.077702) / Phys. Rev. Lett. by J Han (2017)
Wang, Y. et al. Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques. Nat. Commun. 8, 1364 (2017). (10.1038/s41467-017-01583-4) / Nat. Commun. by Y Wang (2017)
Yasuda, K. et al. Current-nonlinear Hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator. Phys. Rev. Lett. 119, 137204 (2017). (10.1103/PhysRevLett.119.137204) / Phys. Rev. Lett. by K Yasuda (2017)
Fan, Y. et al. Magnetization switching through giant spin–orbit torque in a magnetically doped topological insulator heterostructure. Nat. Mater. 13, 699–704 (2014). (10.1038/nmat3973) / Nat. Mater. by Y Fan (2014)
Ndiaye, P. B. et al. Dirac spin-orbit torques and charge pumping at the surface of topological insulators. Phys. Rev. B 96, 014408 (2017). (10.1103/PhysRevB.96.014408) / Phys. Rev. B by PB Ndiaye (2017)
Ghosh, S. & Manchon, A. Spin-orbit torque in a three-dimensional topological insulator–ferromagnet heterostructure: crossover between bulk and surface transport. Phys. Rev. B 97, 134402 (2018). (10.1103/PhysRevB.97.134402) / Phys. Rev. B by S Ghosh (2018)
Xu, S.-Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294–298 (2015). (10.1126/science.1256742) / Science by SY Xu (2015)
Sun, Y., Wu, S.-C. & Yan, B. Topological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbP. Phys. Rev. B 92, 115428 (2015). (10.1103/PhysRevB.92.115428) / Phys. Rev. B by Y Sun (2015)
Ando, Y. et al. Electrical detection of the spin polarization due to charge flow in the surface state of the topological insulator Bi1.5Sb0.5Te1.7Se1.3. Nano Lett. 14, 6226–6230 (2014). (10.1021/nl502546c) / Nano Lett. by Y Ando (2014)
Li, C. et al. Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3. Nat. Nanotechnol. 9, 218–224 (2014). (10.1038/nnano.2014.16) / Nat. Nanotechnol. by C Li (2014)
Tang, J. et al. Electrical detection of spin-polarized surface states conduction in (Bi0.53Sb0.47)2Te3 topological insulator. Nano Lett. 14, 5423–5429 (2014). (10.1021/nl5026198) / Nano Lett. by J Tang (2014)
Dankert, A., Geurs, J., Kamalakar, M. V., Charpentier, S. & Dash, S. P. Room temperature electrical detection of spin polarized currents in topological insulators. Nano Lett. 15, 7976–7981 (2015). (10.1021/acs.nanolett.5b03080) / Nano Lett. by A Dankert (2015)
Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92–95 (2003). (10.1126/science.1089408) / Science by Z Fang (2003)
Liu, Z. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864–867 (2014). (10.1126/science.1245085) / Science by Z Liu (2014)
Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015). / Phys. Rev. X by X Huang (2015)
Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2. Nat. Mater. 14, 280–284 (2015). (10.1038/nmat4143) / Nat. Mater. by T Liang (2015)
Lv, B. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724–727 (2015). (10.1038/nphys3426) / Nat. Phys. by B Lv (2015)
Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015). (10.1038/nature15768) / Nature by AA Soluyanov (2015)
Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413–416 (2015). (10.1126/science.aac6089) / Science by J Xiong (2015)
Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155–1160 (2016). (10.1038/nmat4685) / Nat. Mater. by L Huang (2016)
Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550–554 (2016). (10.1038/nphys3648) / Nat. Phys. by Q Li (2016)
Jiang, J. et al. Signature of type-II Weyl semimetal phase in MoTe2. Nat. Commun. 8, 13973 (2017). (10.1038/ncomms13973) / Nat. Commun. by J Jiang (2017)
Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8, 2150 (2017). (10.1038/s41467-017-02237-1) / Nat. Commun. by P Li (2017)
Wang, Y. et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2. Nat. Commun. 7, 13142 (2016). (10.1038/ncomms13142) / Nat. Commun. by Y Wang (2016)
Lv, Y.-Y. et al. Experimental observation of anisotropic Adler-Bell-Jackiw anomaly in type-II Weyl semimetal WTe1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118, 096603 (2017). (10.1103/PhysRevLett.118.096603) / Phys. Rev. Lett. by YY Lv (2017)
Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014). (10.1038/ncomms6161) / Nat. Commun. by AC Potter (2014)
Moll, P. J. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2. Nature 535, 266–270 (2016). (10.1038/nature18276) / Nature by PJ Moll (2016)
Wang, C. et al. Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal WTe2. Phys. Rev. B 94, 241119 (2016). (10.1103/PhysRevB.94.241119) / Phys. Rev. B by C Wang (2016)
Wu, Y. et al. Observation of Fermi arcs in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 94, 121113 (2016). (10.1103/PhysRevB.94.121113) / Phys. Rev. B by Y Wu (2016)
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011). (10.1103/PhysRevB.83.205101) / Phys. Rev. B by X Wan (2011)
Balents, L. Weyl electrons kiss. Physics 4, 36 (2011). (10.1103/Physics.4.36) / Physics by L Balents (2011)
Sun, X.-Q., Zhang, S.-C. & Wang, Z. Helical spin order from topological Dirac and Weyl semimetals. Phys. Rev. Lett. 115, 076802 (2015). (10.1103/PhysRevLett.115.076802) / Phys. Rev. Lett. by XQ Sun (2015)
Sun, Y., Zhang, Y., Felser, C. & Yan, B. Strong intrinsic spin Hall effect in the TaAs family of Weyl semimetals. Phys. Rev. Lett. 117, 146403 (2016). (10.1103/PhysRevLett.117.146403) / Phys. Rev. Lett. by Y Sun (2016)
Kes, P., Aarts, J., Vinokur, V. & Van der Beek, C. Dissipation in highly anisotropic superconductors. Phys. Rev. Lett. 64, 1063 (1990). (10.1103/PhysRevLett.64.1063) / Phys. Rev. Lett. by P Kes (1990)
Wang, X. et al. Magnetoresistance of two-dimensional and three-dimensional electron gas in LaAlO3/SrTiO3 heterostructures: influence of magnetic ordering, interface scattering, and dimensionality. Phys. Rev. B 84, 075312 (2011). (10.1103/PhysRevB.84.075312) / Phys. Rev. B by X Wang (2011)
Liu, L. et al. Spin-polarized tunneling study of spin-momentum locking in topological insulators. Phys. Rev. B 91, 235437 (2015). (10.1103/PhysRevB.91.235437) / Phys. Rev. B by L Liu (2015)
Peng, X., Yang, Y., Singh, R. R., Savrasov, S. Y. & Yu, D. Spin generation via bulk spin current in three-dimensional topological insulators. Nat. Commun. 7, 10878 (2016). (10.1038/ncomms10878) / Nat. Commun. by X Peng (2016)
Avci, C. O. et al. Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers. Phys. Rev. B 90, 224427 (2014). (10.1103/PhysRevB.90.224427) / Phys. Rev. B by CO Avci (2014)
Wen, Y. et al. Temperature dependence of spin-orbit torques in Cu-Au alloys. Phys. Rev. B 95, 104403 (2017). (10.1103/PhysRevB.95.104403) / Phys. Rev. B by Y Wen (2017)
Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Quantitative characterization of the spin-orbit torque using harmonic Hall voltage measurements. Phys. Rev. B 89, 144425 (2014). (10.1103/PhysRevB.89.144425) / Phys. Rev. B by M Hayashi (2014)
Wang, Y. et al. Planar Hall effect in type-II Weyl semimetal WTe2. Preprint at https://arxiv.org/abs/1801.05929 (2018).
Burkov, A. Giant planar Hall effect in topological metals. Phys. Rev. B 96, 041110 (2017). (10.1103/PhysRevB.96.041110) / Phys. Rev. B by A Burkov (2017)
Nandy, S., Sharma, G., Taraphder, A. & Tewari, S. Chiral anomaly as the origin of the planar Hall effect in Weyl semimetals. Phys. Rev. Lett. 119, 176804 (2017). (10.1103/PhysRevLett.119.176804) / Phys. Rev. Lett. by S Nandy (2017)
Mellnik, A. et al. Spin-transfer torque generated by a topological insulator. Nature 511, 449–451 (2014). (10.1038/nature13534) / Nature by A Mellnik (2014)
Shao, Q. et al. Strong Rashba-Edelstein effect-induced spin–orbit torques in monolayer transition metal dichalcogenide/ferromagnet bilayers. Nano Lett. 16, 7514–7520 (2016). (10.1021/acs.nanolett.6b03300) / Nano Lett. by Q Shao (2016)
MacNeill, D. et al. Thickness dependence of spin-orbit torques generated by WTe2. Phys. Rev. B 96, 054450 (2017). (10.1103/PhysRevB.96.054450) / Phys. Rev. B by D MacNeill (2017)
Wang, L. et al. Tuning magnetotransport in a compensated semimetal at the atomic scale. Nat. Commun. 6, 8892 (2015). (10.1038/ncomms9892) / Nat. Commun. by L Wang (2015)
Bianchi, M. et al. Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3. Nat. Commun. 1, 128 (2010). (10.1038/ncomms1131) / Nat. Commun. by M Bianchi (2010)
King, P. et al. Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi 2 Se 3. Phys. Rev. Lett. 107, 096802 (2011). (10.1103/PhysRevLett.107.096802) / Phys. Rev. Lett. by P King (2011)
Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014). (10.1038/nature13763) / Nature by MN Ali (2014)
Haney, P. M., Lee, H.-W., Lee, K.-J., Manchon, A. & Stiles, M. D. Current induced torques and interfacial spin-orbit coupling: semiclassical modeling. Phys. Rev. B 87, 174411 (2013). (10.1103/PhysRevB.87.174411) / Phys. Rev. B by PM Haney (2013)
Gorbar, E., Miransky, V., Shovkovy, I. & Sukhachov, P. Origin of dissipative Fermi arc transport in Weyl semimetals. Phys. Rev. B 93, 235127 (2016). (10.1103/PhysRevB.93.235127) / Phys. Rev. B by E Gorbar (2016)
Resta, G., Pi, S.-T., Wan, X. & Savrasov, S. Y. High surface conductivity of Fermi-arc electrons in Weyl semimetals. Phys. Rev. B 97, 085142 (2018). (10.1103/PhysRevB.97.085142) / Phys. Rev. B by G Resta (2018)
Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847–12865 (1997). (10.1103/PhysRevB.56.12847) / Phys. Rev. B by N Marzari (1997)
Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994). (10.1103/PhysRevB.50.17953) / Phys. Rev. B by PE Blöchl (1994)
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758–1775 (1999). (10.1103/PhysRevB.59.1758) / Phys. Rev. B by G Kresse (1999)
Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996). (10.1103/PhysRevLett.77.3865) / Phys. Rev. Lett. by JP Perdew (1996)
Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188–5192 (1976). (10.1103/PhysRevB.13.5188) / Phys. Rev. B by HJ Monkhorst (1976)
Mar, A., Jobic, S. & Ibers, J. A. Metal-metal vs tellurium-tellurium bonding in WTe2 and its ternary variants TaIrTe4 and NbIrTe4. J. Am. Chem. Soc. 114, 8963–8971 (1992). (10.1021/ja00049a029) / J. Am. Chem. Soc. by A Mar (1992)
Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001). (10.1103/PhysRevB.65.035109) / Phys. Rev. B by I Souza (2001)
Mostofi, A. A. et al. wannier90: A tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685–699 (2008). (10.1016/j.cpc.2007.11.016) / Comput. Phys. Commun. by AA Mostofi (2008)
Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405–416 (2018). (10.1016/j.cpc.2017.09.033) / Comput. Phys. Commun. by Q Wu (2018)
Sancho, M. L., Sancho, J. L. & Rubio, J. Quick iterative scheme for the calculation of transfer matrices: application to Mo (100). J. Phys. F 14, 1205–1215 (1984). (10.1088/0305-4608/14/5/016) / J. Phys. F by ML Sancho (1984)
Sancho, M. L., Sancho, J. L., Sancho, J. L. & Rubio, J. Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F 15, 851–858 (1985). (10.1088/0305-4608/15/4/009) / J. Phys. F by ML Sancho (1985)

Dates

Type	When
Created	6 years, 11 months ago (Sept. 24, 2018, 7:50 a.m.)
Deposited	2 years, 8 months ago (Dec. 20, 2022, 1:33 p.m.)
Indexed	6 days, 3 hours ago (Aug. 23, 2025, 9:43 p.m.)
Issued	6 years, 11 months ago (Sept. 28, 2018)
Published	6 years, 11 months ago (Sept. 28, 2018)
Published Online	6 years, 11 months ago (Sept. 28, 2018)

Funders 1

King Abdullah University of Science and Technology 10.13039/501100004052
Region: Asia
pri (Universities (academic only))
Labels2
1. جامعة الملك عبدالله للعلوم والتقنية
2. KAUST
Awards2
1. CRF-2015-2626-RG4
2. CRF-2015-SENSORS-2709

BibTeX

@article{Li_2018, title={Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2}, volume={9}, ISSN={2041-1723}, url={http://dx.doi.org/10.1038/s41467-018-06518-1}, DOI={10.1038/s41467-018-06518-1}, number={1}, journal={Nature Communications}, publisher={Springer Science and Business Media LLC}, author={Li, Peng and Wu, Weikang and Wen, Yan and Zhang, Chenhui and Zhang, Junwei and Zhang, Senfu and Yu, Zhiming and Yang, Shengyuan A. and Manchon, A. and Zhang, Xi-xiang}, year={2018}, month=sep }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        24
      ]
    ],
    "date-time": "2025-08-24T01:43:48Z",
    "timestamp": 1755999828161,
    "version": "3.37.3"
  },
  "reference-count": 69,
  "publisher": "Springer Science and Business Media LLC",
  "issue": "1",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2018,
            9,
            28
          ]
        ],
        "date-time": "2018-09-28T00:00:00Z",
        "timestamp": 1538092800000
      },
      "content-version": "tdm",
      "delay-in-days": 0,
      "URL": "https://creativecommons.org/licenses/by/4.0"
    },
    {
      "start": {
        "date-parts": [
          [
            2018,
            9,
            28
          ]
        ],
        "date-time": "2018-09-28T00:00:00Z",
        "timestamp": 1538092800000
      },
      "content-version": "vor",
      "delay-in-days": 0,
      "URL": "https://creativecommons.org/licenses/by/4.0"
    }
  ],
  "funder": [
    {
      "DOI": "10.13039/501100004052",
      "name": "King Abdullah University of Science and Technology",
      "doi-asserted-by": "publisher",
      "award": [
        "CRF-2015-SENSORS-2709",
        "CRF-2015-2626-RG4"
      ],
      "id": [
        {
          "id": "10.13039/501100004052",
          "id-type": "DOI",
          "asserted-by": "publisher"
        }
      ]
    }
  ],
  "content-domain": {
    "domain": [
      "link.springer.com"
    ],
    "crossmark-restriction": false
  },
  "abstract": "<jats:title>Abstract</jats:title><jats:p>Spin\u2013orbit torque has recently been intensively investigated for the purposes of manipulating the magnetization in magnetic nano-devices and understanding fundamental physics. Therefore, the search for novel materials or material combinations that exhibit a strong enough spin-torque effect has become one of the top priorities in this field of spintronics. Weyl semimetal, a new topological material that features open Fermi arc with strong spin\u2013orbit coupling and spin\u2013momentum locking effect, is naturally expected to exhibit an enhanced spin-torque effect in magnetic nano-devices. Here we observe a significantly enhanced spin conductivity, which is associated with the field-like torque at low temperatures. The enhancement is obtained in the <jats:italic>b</jats:italic>-axis WTe<jats:sub>2</jats:sub>/Py bilayers of nano-devices but not observed in the <jats:italic>a</jats:italic>-axis of WTe<jats:sub>2</jats:sub>/Py nano-devices, which can be ascribed to the enhanced spin accumulation by the spin\u2013momentum locking effect of the Fermi arcs of the Weyl semimetal WTe<jats:sub>2</jats:sub>.</jats:p>",
  "DOI": "10.1038/s41467-018-06518-1",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2018,
        9,
        24
      ]
    ],
    "date-time": "2018-09-24T11:50:10Z",
    "timestamp": 1537789810000
  },
  "update-policy": "https://doi.org/10.1007/springer_crossmark_policy",
  "source": "Crossref",
  "is-referenced-by-count": 138,
  "title": "Spin-momentum locking and spin-orbit torques in magnetic nano-heterojunctions composed of Weyl semimetal WTe2",
  "prefix": "10.1038",
  "volume": "9",
  "author": [
    {
      "ORCID": "https://orcid.org/0000-0001-8633-9045",
      "authenticated-orcid": false,
      "given": "Peng",
      "family": "Li",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "Weikang",
      "family": "Wu",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Yan",
      "family": "Wen",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0002-0124-6315",
      "authenticated-orcid": false,
      "given": "Chenhui",
      "family": "Zhang",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "given": "Junwei",
      "family": "Zhang",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0002-8752-4194",
      "authenticated-orcid": false,
      "given": "Senfu",
      "family": "Zhang",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0002-7186-2543",
      "authenticated-orcid": false,
      "given": "Zhiming",
      "family": "Yu",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0001-6003-1501",
      "authenticated-orcid": false,
      "given": "Shengyuan A.",
      "family": "Yang",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0002-4768-293X",
      "authenticated-orcid": false,
      "given": "A.",
      "family": "Manchon",
      "sequence": "additional",
      "affiliation": []
    },
    {
      "ORCID": "https://orcid.org/0000-0002-3478-6414",
      "authenticated-orcid": false,
      "given": "Xi-xiang",
      "family": "Zhang",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "297",
  "published-online": {
    "date-parts": [
      [
        2018,
        9,
        28
      ]
    ]
  },
  "reference": [
    {
      "key": "6518_CR1",
      "doi-asserted-by": "publisher",
      "first-page": "555",
      "DOI": "10.1126/science.1218197",
      "volume": "336",
      "author": "L Liu",
      "year": "2012",
      "unstructured": "Liu, L. et al. Spin-torque switching with the giant spin Hall effect of tantalum. Science 336, 555\u2013558 (2012).",
      "journal-title": "Science"
    },
    {
      "key": "6518_CR2",
      "doi-asserted-by": "publisher",
      "first-page": "189",
      "DOI": "10.1038/nature10309",
      "volume": "476",
      "author": "IM Miron",
      "year": "2011",
      "unstructured": "Miron, I. M. et al. Perpendicular switching of a single ferromagnetic layer induced by in-plane current injection. Nature 476, 189\u2013193 (2011).",
      "journal-title": "Nature"
    },
    {
      "key": "6518_CR3",
      "unstructured": "Manchon, A. et al. Current-induced spin\u2013orbit torques in ferromagnetic and antiferromagnetic systems. Preprint at https://arxiv.org/abs/1801.09636 (2018)."
    },
    {
      "key": "6518_CR4",
      "doi-asserted-by": "publisher",
      "first-page": "3045",
      "DOI": "10.1103/RevModPhys.82.3045",
      "volume": "82",
      "author": "MZ Hasan",
      "year": "2010",
      "unstructured": "Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045\u20133067 (2010).",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "6518_CR5",
      "doi-asserted-by": "publisher",
      "first-page": "1057",
      "DOI": "10.1103/RevModPhys.83.1057",
      "volume": "83",
      "author": "XL Qi",
      "year": "2011",
      "unstructured": "Qi, X.-L. & Zhang, S.-C. Topological insulators and superconductors. Rev. Mod. Phys. 83, 1057 (2011).",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "6518_CR6",
      "doi-asserted-by": "publisher",
      "first-page": "077702",
      "DOI": "10.1103/PhysRevLett.119.077702",
      "volume": "119",
      "author": "J Han",
      "year": "2017",
      "unstructured": "Han, J. et al. Room-temperature spin-orbit torque switching induced by a topological insulator. Phys. Rev. Lett. 119, 077702 (2017).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR7",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/s41467-017-01583-4",
      "volume": "8",
      "author": "Y Wang",
      "year": "2017",
      "unstructured": "Wang, Y. et al. Room temperature magnetization switching in topological insulator-ferromagnet heterostructures by spin-orbit torques. Nat. Commun. 8, 1364 (2017).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR8",
      "doi-asserted-by": "publisher",
      "first-page": "137204",
      "DOI": "10.1103/PhysRevLett.119.137204",
      "volume": "119",
      "author": "K Yasuda",
      "year": "2017",
      "unstructured": "Yasuda, K. et al. Current-nonlinear Hall effect and spin-orbit torque magnetization switching in a magnetic topological insulator. Phys. Rev. Lett. 119, 137204 (2017).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR9",
      "doi-asserted-by": "publisher",
      "first-page": "699",
      "DOI": "10.1038/nmat3973",
      "volume": "13",
      "author": "Y Fan",
      "year": "2014",
      "unstructured": "Fan, Y. et al. Magnetization switching through giant spin\u2013orbit torque in a magnetically doped topological insulator heterostructure. Nat. Mater. 13, 699\u2013704 (2014).",
      "journal-title": "Nat. Mater."
    },
    {
      "key": "6518_CR10",
      "doi-asserted-by": "publisher",
      "first-page": "014408",
      "DOI": "10.1103/PhysRevB.96.014408",
      "volume": "96",
      "author": "PB Ndiaye",
      "year": "2017",
      "unstructured": "Ndiaye, P. B. et al. Dirac spin-orbit torques and charge pumping at the surface of topological insulators. Phys. Rev. B 96, 014408 (2017).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR11",
      "doi-asserted-by": "publisher",
      "first-page": "134402",
      "DOI": "10.1103/PhysRevB.97.134402",
      "volume": "97",
      "author": "S Ghosh",
      "year": "2018",
      "unstructured": "Ghosh, S. & Manchon, A. Spin-orbit torque in a three-dimensional topological insulator\u2013ferromagnet heterostructure: crossover between bulk and surface transport. Phys. Rev. B 97, 134402 (2018).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR12",
      "doi-asserted-by": "publisher",
      "first-page": "294",
      "DOI": "10.1126/science.1256742",
      "volume": "347",
      "author": "SY Xu",
      "year": "2015",
      "unstructured": "Xu, S.-Y. et al. Observation of Fermi arc surface states in a topological metal. Science 347, 294\u2013298 (2015).",
      "journal-title": "Science"
    },
    {
      "key": "6518_CR13",
      "doi-asserted-by": "publisher",
      "first-page": "115428",
      "DOI": "10.1103/PhysRevB.92.115428",
      "volume": "92",
      "author": "Y Sun",
      "year": "2015",
      "unstructured": "Sun, Y., Wu, S.-C. & Yan, B. Topological surface states and Fermi arcs of the noncentrosymmetric Weyl semimetals TaAs, TaP, NbAs, and NbP. Phys. Rev. B 92, 115428 (2015).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR14",
      "doi-asserted-by": "publisher",
      "first-page": "6226",
      "DOI": "10.1021/nl502546c",
      "volume": "14",
      "author": "Y Ando",
      "year": "2014",
      "unstructured": "Ando, Y. et al. Electrical detection of the spin polarization due to charge flow in the surface state of the topological insulator Bi1.5Sb0.5Te1.7Se1.3. Nano Lett. 14, 6226\u20136230 (2014).",
      "journal-title": "Nano Lett."
    },
    {
      "key": "6518_CR15",
      "doi-asserted-by": "publisher",
      "first-page": "218",
      "DOI": "10.1038/nnano.2014.16",
      "volume": "9",
      "author": "C Li",
      "year": "2014",
      "unstructured": "Li, C. et al. Electrical detection of charge-current-induced spin polarization due to spin-momentum locking in Bi2Se3. Nat. Nanotechnol. 9, 218\u2013224 (2014).",
      "journal-title": "Nat. Nanotechnol."
    },
    {
      "key": "6518_CR16",
      "doi-asserted-by": "publisher",
      "first-page": "5423",
      "DOI": "10.1021/nl5026198",
      "volume": "14",
      "author": "J Tang",
      "year": "2014",
      "unstructured": "Tang, J. et al. Electrical detection of spin-polarized surface states conduction in (Bi0.53Sb0.47)2Te3 topological insulator. Nano Lett. 14, 5423\u20135429 (2014).",
      "journal-title": "Nano Lett."
    },
    {
      "key": "6518_CR17",
      "doi-asserted-by": "publisher",
      "first-page": "7976",
      "DOI": "10.1021/acs.nanolett.5b03080",
      "volume": "15",
      "author": "A Dankert",
      "year": "2015",
      "unstructured": "Dankert, A., Geurs, J., Kamalakar, M. V., Charpentier, S. & Dash, S. P. Room temperature electrical detection of spin polarized currents in topological insulators. Nano Lett. 15, 7976\u20137981 (2015).",
      "journal-title": "Nano Lett."
    },
    {
      "key": "6518_CR18",
      "doi-asserted-by": "publisher",
      "first-page": "92",
      "DOI": "10.1126/science.1089408",
      "volume": "302",
      "author": "Z Fang",
      "year": "2003",
      "unstructured": "Fang, Z. et al. The anomalous Hall effect and magnetic monopoles in momentum space. Science 302, 92\u201395 (2003).",
      "journal-title": "Science"
    },
    {
      "key": "6518_CR19",
      "doi-asserted-by": "publisher",
      "first-page": "864",
      "DOI": "10.1126/science.1245085",
      "volume": "343",
      "author": "Z Liu",
      "year": "2014",
      "unstructured": "Liu, Z. et al. Discovery of a three-dimensional topological Dirac semimetal, Na3Bi. Science 343, 864\u2013867 (2014).",
      "journal-title": "Science"
    },
    {
      "key": "6518_CR20",
      "first-page": "031023",
      "volume": "5",
      "author": "X Huang",
      "year": "2015",
      "unstructured": "Huang, X. et al. Observation of the chiral-anomaly-induced negative magnetoresistance in 3D Weyl semimetal TaAs. Phys. Rev. X 5, 031023 (2015).",
      "journal-title": "Phys. Rev. X"
    },
    {
      "key": "6518_CR21",
      "doi-asserted-by": "publisher",
      "first-page": "280",
      "DOI": "10.1038/nmat4143",
      "volume": "14",
      "author": "T Liang",
      "year": "2015",
      "unstructured": "Liang, T. et al. Ultrahigh mobility and giant magnetoresistance in the Dirac semimetal Cd3As2. Nat. Mater. 14, 280\u2013284 (2015).",
      "journal-title": "Nat. Mater."
    },
    {
      "key": "6518_CR22",
      "doi-asserted-by": "publisher",
      "first-page": "724",
      "DOI": "10.1038/nphys3426",
      "volume": "11",
      "author": "B Lv",
      "year": "2015",
      "unstructured": "Lv, B. et al. Observation of Weyl nodes in TaAs. Nat. Phys. 11, 724\u2013727 (2015).",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "6518_CR23",
      "doi-asserted-by": "publisher",
      "first-page": "495",
      "DOI": "10.1038/nature15768",
      "volume": "527",
      "author": "AA Soluyanov",
      "year": "2015",
      "unstructured": "Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495\u2013498 (2015).",
      "journal-title": "Nature"
    },
    {
      "key": "6518_CR24",
      "doi-asserted-by": "publisher",
      "first-page": "413",
      "DOI": "10.1126/science.aac6089",
      "volume": "350",
      "author": "J Xiong",
      "year": "2015",
      "unstructured": "Xiong, J. et al. Evidence for the chiral anomaly in the Dirac semimetal Na3Bi. Science 350, 413\u2013416 (2015).",
      "journal-title": "Science"
    },
    {
      "key": "6518_CR25",
      "doi-asserted-by": "publisher",
      "first-page": "1155",
      "DOI": "10.1038/nmat4685",
      "volume": "15",
      "author": "L Huang",
      "year": "2016",
      "unstructured": "Huang, L. et al. Spectroscopic evidence for a type II Weyl semimetallic state in MoTe2. Nat. Mater. 15, 1155\u20131160 (2016).",
      "journal-title": "Nat. Mater."
    },
    {
      "key": "6518_CR26",
      "doi-asserted-by": "publisher",
      "first-page": "550",
      "DOI": "10.1038/nphys3648",
      "volume": "12",
      "author": "Q Li",
      "year": "2016",
      "unstructured": "Li, Q. et al. Chiral magnetic effect in ZrTe5. Nat. Phys. 12, 550\u2013554 (2016).",
      "journal-title": "Nat. Phys."
    },
    {
      "key": "6518_CR27",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms13973",
      "volume": "8",
      "author": "J Jiang",
      "year": "2017",
      "unstructured": "Jiang, J. et al. Signature of type-II Weyl semimetal phase in MoTe2. Nat. Commun. 8, 13973 (2017).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR28",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/s41467-017-02237-1",
      "volume": "8",
      "author": "P Li",
      "year": "2017",
      "unstructured": "Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8, 2150 (2017).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR29",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms13142",
      "volume": "7",
      "author": "Y Wang",
      "year": "2016",
      "unstructured": "Wang, Y. et al. Gate-tunable negative longitudinal magnetoresistance in the predicted type-II Weyl semimetal WTe2. Nat. Commun. 7, 13142 (2016).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR30",
      "doi-asserted-by": "publisher",
      "first-page": "096603",
      "DOI": "10.1103/PhysRevLett.118.096603",
      "volume": "118",
      "author": "YY Lv",
      "year": "2017",
      "unstructured": "Lv, Y.-Y. et al. Experimental observation of anisotropic Adler-Bell-Jackiw anomaly in type-II Weyl semimetal WTe1.98 crystals at the quasiclassical regime. Phys. Rev. Lett. 118, 096603 (2017).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR31",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms6161",
      "volume": "5",
      "author": "AC Potter",
      "year": "2014",
      "unstructured": "Potter, A. C., Kimchi, I. & Vishwanath, A. Quantum oscillations from surface Fermi arcs in Weyl and Dirac semimetals. Nat. Commun. 5, 5161 (2014).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR32",
      "doi-asserted-by": "publisher",
      "first-page": "266",
      "DOI": "10.1038/nature18276",
      "volume": "535",
      "author": "PJ Moll",
      "year": "2016",
      "unstructured": "Moll, P. J. et al. Transport evidence for Fermi-arc-mediated chirality transfer in the Dirac semimetal Cd3As2. Nature 535, 266\u2013270 (2016).",
      "journal-title": "Nature"
    },
    {
      "key": "6518_CR33",
      "doi-asserted-by": "publisher",
      "first-page": "241119",
      "DOI": "10.1103/PhysRevB.94.241119",
      "volume": "94",
      "author": "C Wang",
      "year": "2016",
      "unstructured": "Wang, C. et al. Observation of Fermi arc and its connection with bulk states in the candidate type-II Weyl semimetal WTe2. Phys. Rev. B 94, 241119 (2016).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR34",
      "doi-asserted-by": "publisher",
      "first-page": "121113",
      "DOI": "10.1103/PhysRevB.94.121113",
      "volume": "94",
      "author": "Y Wu",
      "year": "2016",
      "unstructured": "Wu, Y. et al. Observation of Fermi arcs in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 94, 121113 (2016).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR35",
      "doi-asserted-by": "publisher",
      "first-page": "205101",
      "DOI": "10.1103/PhysRevB.83.205101",
      "volume": "83",
      "author": "X Wan",
      "year": "2011",
      "unstructured": "Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Y. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR36",
      "doi-asserted-by": "publisher",
      "first-page": "36",
      "DOI": "10.1103/Physics.4.36",
      "volume": "4",
      "author": "L Balents",
      "year": "2011",
      "unstructured": "Balents, L. Weyl electrons kiss. Physics 4, 36 (2011).",
      "journal-title": "Physics"
    },
    {
      "key": "6518_CR37",
      "doi-asserted-by": "publisher",
      "first-page": "076802",
      "DOI": "10.1103/PhysRevLett.115.076802",
      "volume": "115",
      "author": "XQ Sun",
      "year": "2015",
      "unstructured": "Sun, X.-Q., Zhang, S.-C. & Wang, Z. Helical spin order from topological Dirac and Weyl semimetals. Phys. Rev. Lett. 115, 076802 (2015).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR38",
      "doi-asserted-by": "publisher",
      "first-page": "146403",
      "DOI": "10.1103/PhysRevLett.117.146403",
      "volume": "117",
      "author": "Y Sun",
      "year": "2016",
      "unstructured": "Sun, Y., Zhang, Y., Felser, C. & Yan, B. Strong intrinsic spin Hall effect in the TaAs family of Weyl semimetals. Phys. Rev. Lett. 117, 146403 (2016).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR39",
      "doi-asserted-by": "publisher",
      "first-page": "1063",
      "DOI": "10.1103/PhysRevLett.64.1063",
      "volume": "64",
      "author": "P Kes",
      "year": "1990",
      "unstructured": "Kes, P., Aarts, J., Vinokur, V. & Van der Beek, C. Dissipation in highly anisotropic superconductors. Phys. Rev. Lett. 64, 1063 (1990).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR40",
      "doi-asserted-by": "publisher",
      "first-page": "075312",
      "DOI": "10.1103/PhysRevB.84.075312",
      "volume": "84",
      "author": "X Wang",
      "year": "2011",
      "unstructured": "Wang, X. et al. Magnetoresistance of two-dimensional and three-dimensional electron gas in LaAlO3/SrTiO3 heterostructures: influence of magnetic ordering, interface scattering, and dimensionality. Phys. Rev. B 84, 075312 (2011).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR41",
      "doi-asserted-by": "publisher",
      "first-page": "235437",
      "DOI": "10.1103/PhysRevB.91.235437",
      "volume": "91",
      "author": "L Liu",
      "year": "2015",
      "unstructured": "Liu, L. et al. Spin-polarized tunneling study of spin-momentum locking in topological insulators. Phys. Rev. B 91, 235437 (2015).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR42",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms10878",
      "volume": "7",
      "author": "X Peng",
      "year": "2016",
      "unstructured": "Peng, X., Yang, Y., Singh, R. R., Savrasov, S. Y. & Yu, D. Spin generation via bulk spin current in three-dimensional topological insulators. Nat. Commun. 7, 10878 (2016).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR43",
      "doi-asserted-by": "publisher",
      "first-page": "224427",
      "DOI": "10.1103/PhysRevB.90.224427",
      "volume": "90",
      "author": "CO Avci",
      "year": "2014",
      "unstructured": "Avci, C. O. et al. Interplay of spin-orbit torque and thermoelectric effects in ferromagnet/normal-metal bilayers. Phys. Rev. B 90, 224427 (2014).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR44",
      "doi-asserted-by": "publisher",
      "first-page": "104403",
      "DOI": "10.1103/PhysRevB.95.104403",
      "volume": "95",
      "author": "Y Wen",
      "year": "2017",
      "unstructured": "Wen, Y. et al. Temperature dependence of spin-orbit torques in Cu-Au alloys. Phys. Rev. B 95, 104403 (2017).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR45",
      "doi-asserted-by": "publisher",
      "first-page": "144425",
      "DOI": "10.1103/PhysRevB.89.144425",
      "volume": "89",
      "author": "M Hayashi",
      "year": "2014",
      "unstructured": "Hayashi, M., Kim, J., Yamanouchi, M. & Ohno, H. Quantitative characterization of the spin-orbit torque using harmonic Hall voltage measurements. Phys. Rev. B 89, 144425 (2014).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR46",
      "unstructured": "Wang, Y. et al. Planar Hall effect in type-II Weyl semimetal WTe2. Preprint at https://arxiv.org/abs/1801.05929 (2018)."
    },
    {
      "key": "6518_CR47",
      "doi-asserted-by": "publisher",
      "first-page": "041110",
      "DOI": "10.1103/PhysRevB.96.041110",
      "volume": "96",
      "author": "A Burkov",
      "year": "2017",
      "unstructured": "Burkov, A. Giant planar Hall effect in topological metals. Phys. Rev. B 96, 041110 (2017).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR48",
      "doi-asserted-by": "publisher",
      "first-page": "176804",
      "DOI": "10.1103/PhysRevLett.119.176804",
      "volume": "119",
      "author": "S Nandy",
      "year": "2017",
      "unstructured": "Nandy, S., Sharma, G., Taraphder, A. & Tewari, S. Chiral anomaly as the origin of the planar Hall effect in Weyl semimetals. Phys. Rev. Lett. 119, 176804 (2017).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR49",
      "doi-asserted-by": "publisher",
      "first-page": "449",
      "DOI": "10.1038/nature13534",
      "volume": "511",
      "author": "A Mellnik",
      "year": "2014",
      "unstructured": "Mellnik, A. et al. Spin-transfer torque generated by a topological insulator. Nature 511, 449\u2013451 (2014).",
      "journal-title": "Nature"
    },
    {
      "key": "6518_CR50",
      "doi-asserted-by": "publisher",
      "first-page": "7514",
      "DOI": "10.1021/acs.nanolett.6b03300",
      "volume": "16",
      "author": "Q Shao",
      "year": "2016",
      "unstructured": "Shao, Q. et al. Strong Rashba-Edelstein effect-induced spin\u2013orbit torques in monolayer transition metal dichalcogenide/ferromagnet bilayers. Nano Lett. 16, 7514\u20137520 (2016).",
      "journal-title": "Nano Lett."
    },
    {
      "key": "6518_CR51",
      "doi-asserted-by": "publisher",
      "first-page": "054450",
      "DOI": "10.1103/PhysRevB.96.054450",
      "volume": "96",
      "author": "D MacNeill",
      "year": "2017",
      "unstructured": "MacNeill, D. et al. Thickness dependence of spin-orbit torques generated by WTe2. Phys. Rev. B 96, 054450 (2017).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR52",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms9892",
      "volume": "6",
      "author": "L Wang",
      "year": "2015",
      "unstructured": "Wang, L. et al. Tuning magnetotransport in a compensated semimetal at the atomic scale. Nat. Commun. 6, 8892 (2015).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR53",
      "doi-asserted-by": "publisher",
      "DOI": "10.1038/ncomms1131",
      "volume": "1",
      "author": "M Bianchi",
      "year": "2010",
      "unstructured": "Bianchi, M. et al. Coexistence of the topological state and a two-dimensional electron gas on the surface of Bi2Se3. Nat. Commun. 1, 128 (2010).",
      "journal-title": "Nat. Commun."
    },
    {
      "key": "6518_CR54",
      "doi-asserted-by": "publisher",
      "first-page": "096802",
      "DOI": "10.1103/PhysRevLett.107.096802",
      "volume": "107",
      "author": "P King",
      "year": "2011",
      "unstructured": "King, P. et al. Large tunable Rashba spin splitting of a two-dimensional electron gas in Bi 2 Se 3. Phys. Rev. Lett. 107, 096802 (2011).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR55",
      "doi-asserted-by": "publisher",
      "first-page": "205",
      "DOI": "10.1038/nature13763",
      "volume": "514",
      "author": "MN Ali",
      "year": "2014",
      "unstructured": "Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205\u2013208 (2014).",
      "journal-title": "Nature"
    },
    {
      "key": "6518_CR56",
      "doi-asserted-by": "publisher",
      "first-page": "174411",
      "DOI": "10.1103/PhysRevB.87.174411",
      "volume": "87",
      "author": "PM Haney",
      "year": "2013",
      "unstructured": "Haney, P. M., Lee, H.-W., Lee, K.-J., Manchon, A. & Stiles, M. D. Current induced torques and interfacial spin-orbit coupling: semiclassical modeling. Phys. Rev. B 87, 174411 (2013).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR57",
      "doi-asserted-by": "publisher",
      "first-page": "235127",
      "DOI": "10.1103/PhysRevB.93.235127",
      "volume": "93",
      "author": "E Gorbar",
      "year": "2016",
      "unstructured": "Gorbar, E., Miransky, V., Shovkovy, I. & Sukhachov, P. Origin of dissipative Fermi arc transport in Weyl semimetals. Phys. Rev. B 93, 235127 (2016).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR58",
      "doi-asserted-by": "publisher",
      "first-page": "085142",
      "DOI": "10.1103/PhysRevB.97.085142",
      "volume": "97",
      "author": "G Resta",
      "year": "2018",
      "unstructured": "Resta, G., Pi, S.-T., Wan, X. & Savrasov, S. Y. High surface conductivity of Fermi-arc electrons in Weyl semimetals. Phys. Rev. B 97, 085142 (2018).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR59",
      "doi-asserted-by": "publisher",
      "first-page": "12847",
      "DOI": "10.1103/PhysRevB.56.12847",
      "volume": "56",
      "author": "N Marzari",
      "year": "1997",
      "unstructured": "Marzari, N. & Vanderbilt, D. Maximally localized generalized Wannier functions for composite energy bands. Phys. Rev. B 56, 12847\u201312865 (1997).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR60",
      "doi-asserted-by": "publisher",
      "first-page": "17953",
      "DOI": "10.1103/PhysRevB.50.17953",
      "volume": "50",
      "author": "PE Bl\u00f6chl",
      "year": "1994",
      "unstructured": "Bl\u00f6chl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953\u201317979 (1994).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR61",
      "doi-asserted-by": "publisher",
      "first-page": "1758",
      "DOI": "10.1103/PhysRevB.59.1758",
      "volume": "59",
      "author": "G Kresse",
      "year": "1999",
      "unstructured": "Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 59, 1758\u20131775 (1999).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR62",
      "doi-asserted-by": "publisher",
      "first-page": "3865",
      "DOI": "10.1103/PhysRevLett.77.3865",
      "volume": "77",
      "author": "JP Perdew",
      "year": "1996",
      "unstructured": "Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865\u20133868 (1996).",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "6518_CR63",
      "doi-asserted-by": "publisher",
      "first-page": "5188",
      "DOI": "10.1103/PhysRevB.13.5188",
      "volume": "13",
      "author": "HJ Monkhorst",
      "year": "1976",
      "unstructured": "Monkhorst, H. J. & Pack, J. D. Special points for Brillouin-zone integrations. Phys. Rev. B 13, 5188\u20135192 (1976).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR64",
      "doi-asserted-by": "publisher",
      "first-page": "8963",
      "DOI": "10.1021/ja00049a029",
      "volume": "114",
      "author": "A Mar",
      "year": "1992",
      "unstructured": "Mar, A., Jobic, S. & Ibers, J. A. Metal-metal vs tellurium-tellurium bonding in WTe2 and its ternary variants TaIrTe4 and NbIrTe4. J. Am. Chem. Soc. 114, 8963\u20138971 (1992).",
      "journal-title": "J. Am. Chem. Soc."
    },
    {
      "key": "6518_CR65",
      "doi-asserted-by": "publisher",
      "first-page": "035109",
      "DOI": "10.1103/PhysRevB.65.035109",
      "volume": "65",
      "author": "I Souza",
      "year": "2001",
      "unstructured": "Souza, I., Marzari, N. & Vanderbilt, D. Maximally localized Wannier functions for entangled energy bands. Phys. Rev. B 65, 035109 (2001).",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "6518_CR66",
      "doi-asserted-by": "publisher",
      "first-page": "685",
      "DOI": "10.1016/j.cpc.2007.11.016",
      "volume": "178",
      "author": "AA Mostofi",
      "year": "2008",
      "unstructured": "Mostofi, A. A. et al. wannier90: A tool for obtaining maximally-localised Wannier functions. Comput. Phys. Commun. 178, 685\u2013699 (2008).",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "6518_CR67",
      "doi-asserted-by": "publisher",
      "first-page": "405",
      "DOI": "10.1016/j.cpc.2017.09.033",
      "volume": "224",
      "author": "Q Wu",
      "year": "2018",
      "unstructured": "Wu, Q., Zhang, S., Song, H.-F., Troyer, M. & Soluyanov, A. A. WannierTools: an open-source software package for novel topological materials. Comput. Phys. Commun. 224, 405\u2013416 (2018).",
      "journal-title": "Comput. Phys. Commun."
    },
    {
      "key": "6518_CR68",
      "doi-asserted-by": "publisher",
      "first-page": "1205",
      "DOI": "10.1088/0305-4608/14/5/016",
      "volume": "14",
      "author": "ML Sancho",
      "year": "1984",
      "unstructured": "Sancho, M. L., Sancho, J. L. & Rubio, J. Quick iterative scheme for the calculation of transfer matrices: application to Mo (100). J. Phys. F 14, 1205\u20131215 (1984).",
      "journal-title": "J. Phys. F"
    },
    {
      "key": "6518_CR69",
      "doi-asserted-by": "publisher",
      "first-page": "851",
      "DOI": "10.1088/0305-4608/15/4/009",
      "volume": "15",
      "author": "ML Sancho",
      "year": "1985",
      "unstructured": "Sancho, M. L., Sancho, J. L., Sancho, J. L. & Rubio, J. Highly convergent schemes for the calculation of bulk and surface Green functions. J. Phys. F 15, 851\u2013858 (1985).",
      "journal-title": "J. Phys. F"
    }
  ],
  "container-title": "Nature Communications",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://www.nature.com/articles/s41467-018-06518-1.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://www.nature.com/articles/s41467-018-06518-1",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://www.nature.com/articles/s41467-018-06518-1.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2022,
        12,
        20
      ]
    ],
    "date-time": "2022-12-20T18:33:05Z",
    "timestamp": 1671561185000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://www.nature.com/articles/s41467-018-06518-1"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2018,
        9,
        28
      ]
    ]
  },
  "references-count": 69,
  "journal-issue": {
    "issue": "1",
    "published-online": {
      "date-parts": [
        [
          2018,
          12
        ]
      ]
    }
  },
  "alternative-id": [
    "6518"
  ],
  "URL": "http://dx.doi.org/10.1038/s41467-018-06518-1",
  "relation": {},
  "ISSN": [
    "2041-1723"
  ],
  "subject": [],
  "container-title-short": "Nat Commun",
  "published": {
    "date-parts": [
      [
        2018,
        9,
        28
      ]
    ]
  },
  "assertion": [
    {
      "value": "22 May 2018",
      "order": 1,
      "name": "received",
      "label": "Received",
      "group": {
        "name": "ArticleHistory",
        "label": "Article History"
      }
    },
    {
      "value": "10 September 2018",
      "order": 2,
      "name": "accepted",
      "label": "Accepted",
      "group": {
        "name": "ArticleHistory",
        "label": "Article History"
      }
    },
    {
      "value": "28 September 2018",
      "order": 3,
      "name": "first_online",
      "label": "First Online",
      "group": {
        "name": "ArticleHistory",
        "label": "Article History"
      }
    },
    {
      "value": "The authors declare no competing interests.",
      "order": 1,
      "name": "Ethics",
      "group": {
        "name": "EthicsHeading",
        "label": "Competing interests"
      }
    }
  ],
  "article-number": "3990"
}