![]() Figure 1b, c shows results from a (112) surface of TaAs. Of these, the most relevant to this work is a theoretical formulation 21 of SHG in terms of the shift vector, which is a quantity related to the difference in Berry connection between two bands that participate in an optical transition.įigure 1a and its caption provide a schematic and description of the optical set-up for measurement of SHG in TMMP crystals. While the best established example is the intrinsic anomalous Hall effect in time-reversal breaking systems 14, several nonlocal 15, 16 and nonlinear effects related to Berry curvature generally 17, 18 and in Weyl semimetals (WSMs) specifically 19, 20 have been predicted in crystals that break inversion symmetry. ![]() The past decade has witnessed an explosion of research investigating the role of band-structure topology, as characterized for example by the Berry curvature in momentum space, in the electronic response functions of crystalline solids 13. 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 GaAs 11 and ZnTe 12, and in fact larger than reported in any crystal to date. Here we report measurements of SHG that reveal a giant, anisotropic χ (2) in the TMMPs TaAs, TaP and NbAs. 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). The TMMPs are polar metals, a rare subset of inversion-breaking crystals that would allow spontaneous polarization, were it not screened by conduction electrons 8, 9, 10. The question that arises now is whether these materials will exhibit novel, enhanced, or technologically applicable electronic properties. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention 5, 6, 7. 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 broken 1, 2, 3, 4. ![]()
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