• Basov, D. N., Averitt, R. D. & Hsieh, D. Towards properties on demand in quantum materials. Nat. Mater. 16, 1077–1088 (2017).

    Article 
    ADS 

    Google Scholar
     

  • de la Torre, A. et al. Colloquium: nonthermal pathways to ultrafast control in quantum materials. Rev. Mod. Phys. 93, 041002 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Ma, Q., Grushin, A. G. & Burch, K. S. Topology and geometry under the nonlinear electromagnetic spotlight. Nat. Mater. 20, 1601–1614 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Bao, C., Tang, P., Sun, D. & Zhou, S. Light-induced emergent phenomena in 2D materials and topological materials. Nat. Rev. Phys. 4, 33–48 (2022).

    Article 

    Google Scholar
     

  • Karni, O., Esin, I. & Dani, K. M. Through the lens of a momentum microscope: viewing light-induced quantum phenomena in 2D materials. Adv. Mater. 35, 2204120 (2023).

    Article 

    Google Scholar
     

  • Zhai, E. et al. The rise of semi-metal electronics. Nat. Rev. Electr. Eng. 1, 497–515 (2024).

    Article 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Feng, B. et al. Spin texture in type-II Weyl semimetal WTe2. Phys. Rev. B 94, 195134 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Bruno, F. Y. et al. Observation of large topologically trivial Fermi arcs in the candidate type-II Weyl semimetal WTe2. Phys. Rev. B 94, 121112 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Sánchez-Barriga, J. et al. Surface Fermi arc connectivity in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 94, 161401(R) (2016).

    Article 
    ADS 

    Google Scholar
     

  • Sante, D. D. et al. Three-dimensional electronic structure of the type-II Weyl semimetal WTe2. Phys. Rev. Lett. 119, 026403 (2017).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Zhang, Q. et al. Lifshitz transitions induced by temperature and surface doping in type-II Weyl semimetal candidate Td-WTe2. Phys. Status Solidi Rapid Res. Lett. 11, 1700209 (2017).

    Article 
    ADS 

    Google Scholar
     

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

    Article 

    Google Scholar
     

  • Zhang, W. et al. Quasiparticle interference of surface states in the type-II Weyl semimetal WTe2. Phys. Rev. B 96, 165125 (2017).

    Article 
    ADS 

    Google Scholar
     

  • Yuan, Y. et al. Quasiparticle interference of Fermi arc states in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 97, 165435 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Sie, E. J. et al. An ultrafast symmetry switch in a Weyl semimetal. Nature 565, 61–66 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Hein, P. et al. Mode-resolved reciprocal space mapping of electron-phonon interaction in the Weyl semimetal candidate Td-WTe2. Nat. Commun. 11, 2613 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Guan, M.-X., Wang, E., You, P.-W., Sun, J.-T. & Meng, S. Manipulating Weyl quasiparticles by orbital-selective photoexcitation in WTe2. Nat. Commun. 12, 1885 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Das, P. K. et al. Electronic properties of candidate type-II Weyl semimetal WTe2. A review perspective. Electron. Struct. 1, 014003 (2019).

    Article 
    ADS 

    Google Scholar
     

  • Kwon, H. et al. Quasiparticle interference and impurity resonances on WTe2. Nano Res. 13, 2534–2540 (2020).

    Article 

    Google Scholar
     

  • Wu, Y. et al. Observation of Fermi arcs in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 94, 121113 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Caputo, M. et al. Dynamics of out-of-equilibrium electron and hole pockets in the type-II Weyl semimetal candidate WTe2. Phys. Rev. B 97, 115115 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Ji, S., Granas, O. & Weissenrieder, J. Manipulation of stacking order in Td-WTe2 by ultrafast optical excitation. ACS Nano 15, 8826–8835 (2021).

    Article 

    Google Scholar
     

  • Qi, Y. et al. Traversing double-well potential energy surfaces: photoinduced concurrent intralayer and interlayer structural transitions XTe2 (X = Mo, W). ACS Nano 16, 11124–11135 (2022).

    Article 

    Google Scholar
     

  • Drueke, E., Yang, J. & Zhao, L. Observation of strong and anisotropic nonlinear optical effects through polarization-resolved optical spectroscopy in the type-II Weyl semimetal Td-WTe2. Phys. Rev. B 104, 064304 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Soranzio, D. et al. Strong modulation of carrier effective mass in WTe2 via coherent lattice manipulation. npj 2D Mater. Appl. 6, 71 (2022).

    Article 

    Google Scholar
     

  • Tang, S. et al. Quantum spin Hall state in monolayer 1T′-WTe2. Nat. Phys. 13, 683–687 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Fei, Z. et al. Ferroelectric switching of a two-dimensional metal. Nature 560, 336–339 (2018).

    Article 
    ADS 

    Google Scholar
     

  • Yang, Q., Wu, M. & Li, J. Origin of two-dimensional vertical ferroelectricity in WTe2 bilayer and multilayer. J. Phys. Chem. Lett. 9, 7160–7164 (2018).

    Article 

    Google Scholar
     

  • Ni, Z. et al. Mechanically tunable spontaneous vertical charge redistribution in few-layer WTe2. J. Phys. Chem. C 124, 2008–2012 (2020).

    Article 

    Google Scholar
     

  • Xiao, J. et al. Berry curvature memory through electrically driven stacking transitions. Nat. Phys. 16, 1028–1034 (2020).

    Article 

    Google Scholar
     

  • Rossi, A. et al. Two phase transitions driven by surface electron doping in WTe2. Phys. Rev. B 102, 121110(R) (2020).

    Article 
    ADS 

    Google Scholar
     

  • Chen, W.-H. et al. Noncentrosymmetric characteristics of defects on WTe2. Phys. Rev. B 106, 075428 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Tao, Y., Schneeloch, J. A., Aczel, A. A. & Louca, D. Td to 1T′ structural phase transition in the WTe2 Weyl semimetal. Phys. Rev. B 102, 060103 (2020).

    Article 
    ADS 

    Google Scholar
     

  • Zhou, Y. et al. Pressure-induced Td to 1T′ structural phase transition in WTe2. AIP Adv. 6, 075008 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Jelic, V. et al. Ultrafast terahertz control of extreme tunnel currents through single atoms on a silicon surface. Nat. Phys. 13, 591–598 (2017).

    Article 

    Google Scholar
     

  • Peller, D. et al. Quantitative sampling of atomic-scale electromagnetic waveforms. Nat. Photon. 15, 143–147 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Cocker, T. L., Peller, D., Yu, P., Repp, J. & Huber, R. Tracking the ultrafast motion of a single molecule by femtosecond orbital imaging. Nature 539, 263–267 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Cocker, T. L., Jelic, V., Hillenbrand, R. & Hegmann, F. A. Nanoscale terahertz scanning probe microscopy. Nat. Photon. 15, 558–569 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Jelic, V. et al. Atomic-scale terahertz time-domain spectroscopy. Nat. Photon. 18, 898–904 (2024).

    Article 

    Google Scholar
     

  • He, B. et al. Coherent optical phonon oscillation and possible electronic softening in WTe2 crystals. Sci. Rep. 6, 30487 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Cocker, T. L. et al. An ultrafast terahertz scanning tunnelling microscope. Nat. Photon. 7, 620–625 (2013).

    Article 
    ADS 

    Google Scholar
     

  • Ammerman, S. E. et al. Lightwave-driven scanning tunnelling spectroscopy of atomically precise graphene nanoribbons. Nat. Commun. 12, 6794 (2021).

    Article 
    ADS 

    Google Scholar
     

  • Chen, C. J. Introduction to Scanning Tunneling Microscopy 3rd edn (Oxford Univ. Press, 2021).

  • Giessibl, F. J., Hembacher, S., Bielefeldt, H. & Mannhart, J. Subatomic features on the silicon (111)-(7 × 7) surface observed by atomic force microscopy. Science 289, 422–425 (2000).

    Article 
    ADS 

    Google Scholar
     

  • Welker, J. & Giessibl, F. J. Revealing the angular symmetry of chemical bonds by atomic force microscopy. Science 336, 444–449 (2012).

    Article 
    ADS 

    Google Scholar
     

  • Emmrich, M. et al. Subatomic resolution force microscopy reveals internal structure and adsorption sites of small iron clusters. Science 348, 308–311 (2015).

    Article 
    ADS 

    Google Scholar
     

  • Chang, T.-R. et al. Prediction of an arc-tunable Weyl Fermion metallic state in MoxW1–xTe2. Nat. Commun. 7, 10639 (2016).

    Article 
    ADS 

    Google Scholar
     

  • Kim, H.-J., Kang, S.-H., Hamada, I. & Son, Y.-W. Origins of the structural phase transitions in MoTe2 and WTe2. Phys. Rev. B 95, 180101(R) (2017).

    Article 
    ADS 

    Google Scholar
     

  • Erba, A. et al. CRYSTAL23: a program for computational solid state physics and chemistry. J. Chem. Theory Comput. 19, 6891–6932 (2022).

    Article 

    Google Scholar
     

  • Bodo, F., Desmarais, J. K. & Erba, A. Spin current density functional theory of Weyl semimetals. Phys. Rev. B 105, 125108 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Schmucker, S. W. et al. Field-directed sputter sharpening for tailored probe materials and atomic-scale lithography. Nat. Commun. 3, 935 (2012).

    Article 
    ADS 

    Google Scholar
     

  • Nečas, D. & Klapetek, P. Gwyddion: an open-source software for SPM data analysis. Cent. Eur. J. Phys. 10, 181–188 (2012).


    Google Scholar
     

  • Hirori, H., Blanchard, F. & Tanaka, K. Single-cycle terahertz pulses with amplitudes exceeding 1 MV/cm generated by optical rectification in LiNbO3. Appl. Phys. Lett. 98, 091106 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Ammerman, S. E., Wei, Y., Everett, N., Jelic, V. & Cocker, T. L. Algorithm for subcycle terahertz scanning tunneling spectroscopy. Phys. Rev. B 105, 115427 (2022).

    Article 
    ADS 

    Google Scholar
     

  • Lloyd-Hughes, J. et al. The 2021 ultrafast spectroscopic probes of condensed matter roadmap. J. Phys. Condens. Matter 33, 353001 (2021).

    Article 

    Google Scholar
     

  • Adamo, C. & Barone, V. Toward reliable density functional methods without adjustable parameters: the PBE0 model. J. Chem. Phys. 110, 6158–6170 (1999).

    Article 
    ADS 

    Google Scholar
     

  • Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. 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).

    Article 
    ADS 

    Google Scholar
     

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

    Article 
    ADS 

    Google Scholar
     

  • Momma, K. & Izumi, F. VESTA 3 for three-dimensional visualization of crystal, volumetric and morphology data. J. Appl. Crystallogr. 44, 1272–1276 (2011).

    Article 
    ADS 

    Google Scholar
     

  • Xu, S.-Y. et al. Discovery of Lorentz-violating type II Weyl fermions in LaAlGe. Sci. Adv. 3, e1603266 (2017).

    Article 
    ADS 

    Google Scholar
     

  • 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).

    Article 
    ADS 

    Google Scholar
     

  • Rüßmann, P. et al. Universal scattering response across the type-II Weyl semimetal phase diagram. Phys. Rev. B 97, 075106 (2018).

    Article 
    ADS 

    Google Scholar