Abstract
Although Weyl fermions have proven elusive in high-energy physics, their existence as emergent quasiparticles has been predicted in certain crystalline solids in which either inversion or time-reversal symmetry is broken1,2,3,4. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention5,6,7. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons8,9,10. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, χ(2), leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic χ(2) in the TMMPs TaAs, TaP and NbAs. With the fundamental and second-harmonic fields oriented parallel to the polar axis, the value of χ(2) is larger by almost one order of magnitude than its value in the archetypal electro-optic materials GaAs11 and ZnTe12, and in fact larger than reported in any crystal to date.
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References
Wan, X., Turner, A. M., Vishwanath, A. & Savrasov, S. Topological semimetal and Fermi-arc surface states in the electronic structure of pyrochlore iridates. Phys. Rev. B 83, 205101 (2011).
Burkov, A. & Balents, L. Weyl semimetal in a topological insulator multilayer. Phys. Rev. Lett. 107, 127205 (2011).
Weng, H., Fang, C., Fang, Z., Bernevig, B. A. & Dai, X. Weyl semimetal phase in noncentrosymmetric transitionmetal monophosphides. Phys. Rev. X 5, 011029 (2015).
Huang, S.-M. et al. A Weyl Fermion semimetal with surface Fermi arcs in the transition metal monopnictide TaAs class. Nat. Commun. 6, 7373 (2015).
Xu, S.-Y. et al. Discovery of a Weyl fermion semimetal and topological Fermi arcs. Science 349, 613–617 (2015).
Lv, B. et al. Experimental discovery of Weyl semimetal TaAs. Phys. Rev. X 5, 031013 (2015).
Yang, L. et al. Weyl semimetal phase in the noncentrosymmetric compound TaAs. Nat. Phys. 11, 728–732 (2015).
Anderson, P. & Blount, E. Symmetry considerations on martensitic transformations: “ferroelectric” metals? Phys. Rev. Lett. 14, 217 (1965).
Shi, Y. et al. A ferroelectric-like structural transition in a metal. Nat. Mater. 12, 1024–1027 (2013).
Kim, T. et al. Polar metals by geometric design. Nature 533, 68–72 (2016).
Bergfeld, S. & Daum, W. Second-harmonic generation in GaAs: experiment versus theoretical predictions of χ xyz(2) . Phys. Rev. Lett. 90, 036801 (2003).
Wagner, H. P., Kuhnelt, M., Langbein, W. & Hvam, W. Dispersion of the second-order nonlinear susceptibility in ZnTe, ZnSe, and ZnS. Phys. Rev. B 58, 10494 (1998).
Xiao, D., Chang, M.-C. & Niu, Q. Berry phase effects on electronic properties. Rev. Mod. Phys. 82, 1959 (2010).
Nagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H. & Ong, N. P. Anomalous Hall effect. Rev. Mod. Phys. 82, 1939 (2010).
Orenstein, J. & Moore, J. E. Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates. Phys. Rev. B 87, 165110 (2013).
Zhong, S., Orenstein, J. & Moore, J. E. Optical gyrotropy from axion electrodynamics in momentum space. Phys. Rev. Lett. 115, 117403 (2015).
Moore, J. E. & Orenstein, J. Confinement-induced Berry phase and helicity-dependent photocurrents. Phys. Rev. Lett. 105, 165110 (2010).
Sodemann, I. & Fu, L. Quantum nonlinear Hall effect induced by Berry curvature dipole in time-reversal invariant materials. Phys. Rev. Lett. 115, 216806 (2015).
Ishizuka, H., Hayata, T., Ueda, M. & Nagaosa, N. Emergent electromagnetic induction and adiabatic charge pumping in Weyl semimetals. Preprint at http://arXiv.org/abs/1607.06537 (2016).
Chan, C.-K., Lindner, N. H., Refael, G. & Lee, P. A. Photocurrents in Weyl semimetals. Preprint at http://arXiv.org/abs/1607.07839 (2016).
Morimoto, T. & Nagaosa, N. Topological nature of nonlinear optical effects in solids. Sci. Adv. 2, 1501524 (2016).
Boyd, R. W. Nonlinear Optics (Academic, 2003).
Shoji, I., Kondo, T., Kitamoto, A., Shirane, M. & Ito, R. Absolute scale of second-order nonlinear-optical coefficients. JOSA B 14, 2268–2294 (1997).
Miller, R. C. Optical harmonic generation in single crystal BaTiO3 . Phys. Rev. 134, A1313 (1964).
Bloembergen, N. & Pershan, P. Light waves at the boundary of nonlinear media. Phys. Rev. 128, 606 (1962).
Haislmaier, R. C. et al. Large nonlinear optical coefficients in pseudo-tetragonal BiFeO3 thin films. Appl. Phys. Lett. 103, 031906 (2013).
Ju, S., Cai, T.-Y. & Guo, G.-Y. Electronic structure, linear, and nonlinear optical responses in magnetoelectric multiferroic material BiFeO3 . J. Chem. Phys. 130, 214708 (2009).
Young, S. M. & Rappe, A. M. First principles calculation of the shift current photovoltaic effect in ferroelectrics. Phys. Rev. Lett. 109, 116601 (2012).
Hosur, P., Parameswaran, S. & Vishwanath, A. Charge transport in Weyl semimetals. Phys. Rev. Lett. 108, 046602 (2012).
Xu, B. et al. Optical spectroscopy of the Weyl semimetal TaAs. Phys. Rev. B. 93, 121110, (2016).
Boyd, R. W. Nonlinear Optics (Academic, 2003).
Shen, Y.-R. Principles of Nonlinear Optics (Wiley-Interscience, 1984).
Bloembergen, N. & Pershan, P. Light waves at the boundary of nonlinear media. Phys. Rev. 128, 606 (1962).
Acknowledgements
We thank B. M. Fregoso, T. R. Gordillo, J. Neaton and Y. R. Shen for helpful discussions and B. Xu for sharing refractive index data of TaAs. Measurements and modelling were performed at the Lawrence Berkeley National Laboratory in the Quantum Materials program supported by the Director, Office of Science, Office of Basic Energy Sciences, Materials Sciences and Engineering Division, of the US Department of Energy under Contract No. DE-AC02-05CH11231. J.O., L.W. and A.L. received support for performing and analysing optical measurements from the Gordon and Betty Moore Foundation’s EPiQS Initiative through Grant GBMF4537 to J.O. at UC Berkeley. Sample growth was supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative Grant GBMF4374 to J.A. at UC Berkeley. T.M. is supported by the Gordon and Betty Moore Foundation’s EPiQS Initiative Theory Center Grant GBMF4307 to UC Berkeley. J.E.M. received support for travel from the Simons Foundation. The authors would like to thank Nobumichi Tamura for his help in performing crystal diffraction and orientation on beamline 12.3.2 at the Advanced Light Source. N. Tamura and the ALS are supported by the Director, Office of Science, Office of Basic Energy Sciences, of the US Department of Energy under Contract No. DE-AC02-05CH11231. J. A. and N. N. acknowledge support by the Office of Naval Research under the Electrical Sensors and Network Research Division, Award No. N00014-15-1-2674.
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L.W. and J.O. conceived the project. L.W. and S.P. performed and contributed equally to the SHG measurements with assistance from E.T. and A.L. L.W. and J.O. analysed the data. T.M. and J.E.M. performed the model calculation. L.W., T.M. and J.O. performed the frequency scaling analysis. N.L.N. and J.G.A. grew the crystals and characterized the crystal structure. L.W., T.M. and J.O. wrote the manuscript. All authors commented on the manuscript.
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Wu, L., Patankar, S., Morimoto, T. et al. Giant anisotropic nonlinear optical response in transition metal monopnictide Weyl semimetals. Nature Phys 13, 350–355 (2017). https://doi.org/10.1038/nphys3969
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DOI: https://doi.org/10.1038/nphys3969
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