Topological quantum materials exhibit fascinating properties1,2,3, with important applications for dissipationless electronics and fault-tolerant quantum computers4,5. Manipulating the topological invariants in these materials would allow the development of topological switching applications analogous to switching of transistors6. Lattice strain provides the most natural means of tuning these topological invariants because it directly modifies the electron–ion interactions and potentially alters the underlying crystalline symmetry on which the topological properties depend7,8,9. However, conventional means of applying strain through heteroepitaxial lattice mismatch10 and dislocations11 are not extendable to controllable time-varying protocols, which are required in transistors. Integration into a functional device requires the ability to go beyond the robust, topologically protected properties of materials and to manipulate the topology at high speeds. Here we use crystallographic measurements by relativistic electron diffraction to demonstrate that terahertz light pulses can be used to induce terahertz-frequency interlayer shear strain with large strain amplitude in the Weyl semimetal WTe2, leading to a topologically distinct metastable phase. Separate nonlinear optical measurements indicate that this transition is associated with a symmetry change to a centrosymmetric, topologically trivial phase. We further show that such shear strain provides an ultrafast, energy-efficient way of inducing robust, well separated Weyl points or of annihilating all Weyl points of opposite chirality. This work demonstrates possibilities for ultrafast manipulation of the topological properties of solids and for the development of a topological switch operating at terahertz frequencies.

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  1. 1.

    Hasan, M. Z. & Kane, C. L. Colloquium: topological insulators. Rev. Mod. Phys. 82, 3045–3067 (2010).

  2. 2.

    Burkov, A. A. Topological semimetals. Nat. Mater. 15, 1145–1148 (2016).

  3. 3.

    Jia, S., Xu, S. Y. & Hasan, M. Z. Weyl semimetals, Fermi arcs and chiral anomalies. Nat. Mater. 15, 1140–1144 (2016).

  4. 4.

    Roushan, P. et al. Topological surface states protected from backscattering by chiral spin texture. Nature 460, 1106–1109 (2009).

  5. 5.

    Alpichshev, Z. et al. STM imaging of electronic waves on the surface of Bi2Te3: topologically protected surface states and hexagonal warping effects. Phys. Rev. Lett. 104, 016401 (2010).

  6. 6.

    Qian, X. et al. Quantum spin Hall effect in two-dimensional transition metal dichalcogenides. Science 346, 1344–1347 (2014).

  7. 7.

    Cortijo, A. et al. Elastic gauge fields in Weyl semimetals. Phys. Rev. Lett. 115, 177202 (2015).

  8. 8.

    Grushin, A. G. et al. Inhomogeneous Weyl and Dirac semimetals: transport in axial magnetic fields and Fermi arc surface states from pseudo-Landau levels. Phys. Rev. X 6, 041046 (2016).

  9. 9.

    Pikulin, D. I., Chen, A. & Franz, M. Chiral anomaly from strain-induced gauge fields in Dirac and Weyl semimetals. Phys. Rev. X 6, 041021 (2016).

  10. 10.

    Zeljkovic, I. et al. Strain engineering Dirac surface states in heteroepitaxial topological crystalline insulator thin films. Nat. Nanotechnol. 10, 849–853 (2015).

  11. 11.

    Liu, Y. et al. Tuning Dirac states by strain in the topological insulator Bi2Se3. Nat. Phys. 10, 294–299 (2014).

  12. 12.

    Xu, S. Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).

  13. 13.

    Yang, L. X. et al. Weyl semimetal phase in the non-centrosymmetric compound TaAs. Nat. Phys. 11, 728–732 (2015); erratum 11, 879 (2015).

  14. 14.

    Lv, B. Q. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).

  15. 15.

    Ali, M. N. et al. Large, non-saturating magnetoresistance in WTe2. Nature 514, 205–208 (2014).

  16. 16.

    Soluyanov, A. A. et al. Type-II Weyl semimetals. Nature 527, 495–498 (2015).

  17. 17.

    Li, P. et al. Evidence for topological type-II Weyl semimetal WTe2. Nat. Commun. 8, 2150 (2017).

  18. 18.

    Lin, C. L. et al. Visualizing type-II Weyl points in tungsten ditelluride by quasiparticle interference. ACS Nano 11, 11459–11465 (2017).

  19. 19.

    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).

  20. 20.

    Yang, J. et al. Elastic and electronic tuning of magnetoresistance in MoTe2. Sci. Adv. 3, eaao4949 (2017).

  21. 21.

    Weathersby, S. P. et al. Mega-electron-volt ultrafast electron diffraction at SLAC National Accelerator Laboratory. Rev. Sci. Instrum. 86, 073702 (2015).

  22. 22.

    Kim, H.-J. et al. Origins of the structural phase transitions in MoTe2 and WTe2. Phys. Rev. B 95, 180101 (2017).

  23. 23.

    Nicoul, M. et al. Picosecond acoustic response of a laser-heated gold-film studied with time-resolved X-ray diffraction. Appl. Phys. Lett. 98, 191902 (2011).

  24. 24.

    Frigge, T. et al. Optically excited structural transition in atomic wires on surfaces at the quantum limit. Nature 544, 207–211 (2017).

  25. 25.

    Chen, S. Y. et al. Activation of new Raman modes by inversion symmetry breaking in type II Weyl semimetal candidate T′-MoTe2. Nano Lett. 16, 5852–5860 (2016).

  26. 26.

    Zhang, K. et al. Raman signatures of inversion symmetry breaking and structural phase transition in type-II Weyl semimetal MoTe2. Nat. Commun. 7, 13552 (2016).

  27. 27.

    Morimoto, T. & Nagaosa, N. Topological nature of nonlinear optical effects in solids. Sci. Adv. 2, e1501524 (2016).

  28. 28.

    Wu, L. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nat. Phys. 13, 350–355 (2017).

  29. 29.

    Levy, N. et al. Strain-induced pseudo-magnetic fields greater than 300 tesla in graphene nanobubbles. Science 329, 544–547 (2010).

  30. 30.

    Gomes, K. K. et al. Designer Dirac fermions and topological phases in molecular graphene. Nature 483, 306–310 (2012).

  31. 31.

    Shen, X. et al. Femtosecond mega-electron-volt electron microdiffraction. Ultramicroscopy 184, 172–176 (2018).

  32. 32.

    Yang, Z. et al. Large-size bulk and thin-film stilbazolium-salt single crystals for nonlinear optics and THz generation. Adv. Funct. Mater. 17, 2018–2023 (2007).

  33. 33.

    Brunner, F. D. et al. A hydrogen-bonded organic nonlinear optical crystal for high-efficiency terahertz generation and detection. Opt. Express 16, 16496–16508 (2008).

  34. 34.

    Ofori-Okai, B. K. et al. A terahertz pump mega-electron-volt ultrafast electron diffraction probe apparatus at the SLAC Accelerator Structure Test Area facility. J. Instrum. 13, P06014 (2018).

  35. 35.

    Waasmaier, D. & Kirfel, A. New analytical scattering-factor functions for free atoms and ions. Acta Crystallogr. A 51, 416–431 (1995).

  36. 36.

    Su, Z. & Coppens, P. Relativistic X-ray elastic scattering factors for neutral atoms Z = 1–54 from multiconfiguration Dirac–Fock wavefunctions in the 0–12 Å−1sinθ/λ range, and six-Gaussian analytical expressions in the 0–6 Å−1 range. Acta Crystallogr. A 53, 749–762 (1997).

  37. 37.

    De Graef, M. Introduction to Conventional Transmission Electron Microscopy (Cambridge Univ. Press, Cambridge, 2003).

  38. 38.

    Zhu, Z. et al. Quantum oscillations, thermoelectric coefficients, and the Fermi surface of semimetallic WTe2. Phys. Rev. Lett. 114, 176601 (2015).

  39. 39.

    Homes, C. C., Ali, M. N. & Cava, R. J. Optical properties of the perfectly compensated semimetal WTe2. Phys. Rev. B 92, 161109 (2015).

  40. 40.

    Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

  41. 41.

    Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

  42. 42.

    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).

  43. 43.

    Hamada, I. van der Waals density functional made accurate. Phys. Rev. B 89, 121103 (2014).

  44. 44.

    Kresse, G. & Furthmüller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 54, 11169–11186 (1996).

  45. 45.

    Perdew, J. P., Burke, K. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).

  46. 46.

    Blöchl, P. E. Projector augmented-wave method. Phys. Rev. B 50, 17953–17979 (1994).

  47. 47.

    Togo, A. & Tanaka, I. First principles phonon calculations in materials science. Scr. Mater. 108, 1–5 (2015).

  48. 48.

    Grimme, S. et al. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H–Pu. J. Chem. Phys. 132, 154104 (2010).

  49. 49.

    Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).

  50. 50.

    Zhou, Y. et al. Direct synthesis of large-scale WTe2 thin films with low thermal conductivity. Adv. Funct. Mater. 27, 1605928 (2017).

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This work is supported primarily by the US Department of Energy (DOE), Office of Basic Energy Sciences, Division of Materials Sciences and Engineering, under contract number DE-AC02-76SF00515, the Stanford Linear Accelerator (SLAC) National Accelerator Laboratory, the Stanford Institute for Materials and Energy Sciences (E.J.S., C.M.N., C.D.P., E.M., T.P.D., T.F.H., A.M.L.). E.J.S. acknowledges additional support from Stanford GLAM Postdoctoral Fellowship Program. C.M.N. acknowledges additional support from the National Science Foundation (NSF) through a Graduate Research Fellowship (DGE-114747). T.F.H. acknowledges additional funding for analysis from the Gordon and Betty Moore Foundation EPiQS Initiative through grant number GBMF4545. S.J.P. is supported by the US Department of Energy (DE-SC0012375). M.C.H. is supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award number 2015-SLAC-100238-Funding. B.K.O.-O. acknowledges support from the DOE Office of Science, Fusion Energy Science, under grant number FWP 100182. N.F. acknowledges support from the Stewardship Science Graduate Fellowship programme, provided under cooperative agreement number DE-NA0002135. Synthesis of MoTe2 and sample preparation were supported by the US Department of Energy, DE-SC0016703 (D.R., D.C., A.A., J.H.). L.B. acknowledges the US Army Research Office MURI grant W911NF-11-1-0362. The National High Magnetic Field Laboratory is supported by the NSF through NSF/DMR-1157490, NSF/DMR-1644779 and the State of Florida. First-principles calculations by C.D.P. were supported by the TIMES programme at SLAC. Numerical simulations were performed using computational resources at the National Energy Research Scientific Computing Center (NSERC). The UED work was performed at SLAC MeV-UED, which is supported in part by the DOE BES SUF Division Accelerator & Detector R&D programme, the LCLS Facility and SLAC under contracts DE-AC02-05-CH11231 and DE-AC02-76SF00515. The authors thank D. Pikulin and B. Moritz for discussions and G. Stewart for the illustration of the UED setup.

Reviewer information

Nature thanks C. Ropers and the other anonymous reviewer(s) for their contribution to the peer review of this work.

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Author notes

    • Daniel Rhodes

    Present address: Department of Mechanical Engineering, Columbia University, New York, NY, USA

  1. These authors contributed equally: Edbert J. Sie, Clara M. Nyby


  1. Geballe Laboratory for Advanced Materials, Stanford University, Stanford, CA, USA

    • Edbert J. Sie
    •  & Thomas P. Devereaux
  2. SIMES, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    • Edbert J. Sie
    • , C. D. Pemmaraju
    • , Su Ji Park
    • , Thomas P. Devereaux
    • , Tony F. Heinz
    •  & Aaron M. Lindenberg
  3. Department of Chemistry, Stanford University, Stanford, CA, USA

    • Clara M. Nyby
  4. SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    • Xiaozhe Shen
    • , Jie Yang
    • , Matthias C. Hoffmann
    • , B. K. Ofori-Okai
    • , Renkai Li
    • , Alexander H. Reid
    • , Stephen Weathersby
    •  & Xijie Wang
  5. PULSE Institute, SLAC National Accelerator Laboratory, Menlo Park, CA, USA

    • Jie Yang
    • , Tony F. Heinz
    •  & Aaron M. Lindenberg
  6. Department of Chemistry, Massachusetts Institute of Technology, Cambridge, MA, USA

    • B. K. Ofori-Okai
  7. Department of Materials Science and Engineering, Stanford University, Stanford, CA, USA

    • Ehren Mannebach
    •  & Aaron M. Lindenberg
  8. Department of Mechanical Engineering, Columbia University, New York, NY, USA

    • Nathan Finney
    • , Daniel Chenet
    • , Abhinandan Antony
    •  & James Hone
  9. National High Magnetic Field Laboratory, Florida State University, Tallahassee, FL, USA

    • Daniel Rhodes
    •  & Luis Balicas
  10. Department of Physics, Florida State University, Tallahassee, FL, USA

    • Daniel Rhodes
    •  & Luis Balicas
  11. Department of Applied Physics, Stanford University, Stanford, CA, USA

    • Tony F. Heinz


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E.J.S., C.M.N. and A.M.L. conceived the experiments, analysed and interpreted the data; E.J.S. and C.M.N. performed the SHG experiments, analysed and interpreted the data with A.M.L. and T.F.H.; E.J.S., C.M.N., A.M.L. and C.D.P. wrote the manuscript with input from all authors; E.J.S. and C.M.N. performed the UED experiments with S.J.P., X.S., J.Y., R.L., S.W., E.M. and X.J.W.; B.K.O.-O., M.C.H. and A.H.R. implemented the terahertz setup; D.R., L.B., C.M.N., E.J.S., N.F., D.C., A.A., J.H. and T.F.H. synthesized the crystals and prepared the samples; C.D.P. and T.P.D. performed the first-principles calculations; X.J.W. led the SLAC 3-MeV UED and terahertz-pump UED-probe development. All authors discussed the results and contributed to the writing of the manuscript.

Competing interests

E.J.S., C.M.N., C.D.P., X.J.W. and A.M.L. have submitted a patent application (“Fast topological switch using strained Weyl semimetals”; US number 62/726,893) that covers a specific aspect of the manuscript. The other authors declare no competing interests.

Corresponding author

Correspondence to Aaron M. Lindenberg.

Extended data figures and tables

  1. Extended Data Fig. 1 Lattice structure variants of WTe2.

    a, The Td phase has an orthorhombic non-centrosymmetric unit cell with bc angle of 90° and bond length d1 > d3. b, The 1T′(*) phase has an orthorhombic centrosymmetric unit cell with a bc angle of 90° and bond length d1 = d3. c, The 1T′ phase has a monoclinic centrosymmetric unit cell with a bc angle of about 94° and bond length d1 < d3.

  2. Extended Data Fig. 2 Electro-optical sampling data of the terahertz pump pulses.

    a, Time trace of terahertz electric field, generated using OH-1 and DSTMS crystals. Curves in a are offset for clarity. b, Frequency bandwidth of the terahertz field, calculated using the Fourier transform of a.

  3. Extended Data Fig. 3 Calculated phonon dispersion of Td WTe2 and energy potential as a function of lattice deformation.

    a, Dispersions for wave vectors along high-symmetry lines in the kz = 0 plane are shown. The schematic on the right shows the interlayer shear motion as rigid displacements between alternating WTe2 layers. b, Energy as a function of uniaxial strain applied along the a axis. We used two different forms for the dispersion corrections, namely, DFT-D3 (labelled D3) and DFT D3 with Becke–Johnson damping (labelled D3-BJ). These two corrections result in slightly different lattice constants, as shown in Extended Data Table 1c, and yield potential energy surfaces that are too shallow and too steep in the D3 and D3-BJ approximations, respectively. The correct description lies between the two limits represented by D3 and D3-BJ. c, Energy as a function of displacement along the shear-mode coordinate. The red dashed line indicates the displacement at which two pairs of Weyl nodes annihilate at the ky = 0 mirror plane (see Fig. 4).

  4. Extended Data Fig. 4 Transverse acoustic propagation dynamics in Td-WTe2.

    The structure-factor modulation is monitored using a terahertz-pump UED probe.

  5. Extended Data Fig. 5 The emergence of terahertz-induced shear oscillations in Td MoTe2, but not in 1T′ MoTe2.

    The structure-factor modulations are monitored using a terahertz-pump UED probe.

  6. Extended Data Fig. 6 Additional terahertz-pump UED-probe measurements at increasing pump fluence.

    a, Intensity changes of the (130) Bragg peak show the interlayer shear oscillation, which exhibits a phonon softening at larger pump fluences. This demonstrates the evolution towards switching behaviour in the transition region. b, Surface plot of a, where ΔI/I0 is shown by the colour scale. In b we use interpolation to show a clearer picture on the frequency shifting at larger pump fluences.

  7. Extended Data Fig. 7 Optical and structural changes in WTe2 induced by 2.1-µm pump pulses.

    a, The transient reflectivity of the 800-nm probe gives a direct experimental probe to the electronic system. There is an abrupt change in ΔR/R right after the pump pulse arrival (within 5 ps). Afterwards, the ΔR/R signal remains finite and stable for longer than 50 ps. b, Bragg peak intensity changes probed by the electron beam. The intensity changes show oscillations that correspond to the interlayer shear-mode frequency of 0.24 THz, similar to the effect produced by the terahertz pump pulses discussed in the main text. c, Time-resolved SHG of WTe2 at nanosecond time delay. Here, the pump pulse has a wavelength of 2.1 µm (polarized at 45° off the horizontal axis), the incident probe pulse has a wavelength of 800 nm, the crystal a axis is aligned horizontally and the SHG is detected at the ‘S-in, P-out’ configuration. This shows that the light-induced centrosymmetric phase lives for a few nanoseconds, or even tens of nanoseconds, which is consistent with the induced metastable phase discussed in the main text.

  8. Extended Data Table 1 Lattice and electronic structure parameters for DFT calculations

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