Having determined the high-symmetry directions, we characterize χ ijk by performing three of types of scans, the results of which are shown in Fig. 2. The angles at which we observe the peak and the null in Fig. 1b and the null in Fig. 1c allow us to identify the principal axes in the (112) plane of the surface.
MEASURE LATTICE PARAMETERS IN CRYSTALMAKER GENERATOR
Rotating the generator and analyser together produces scans, shown in Fig. 1b, c, which are equivalent to rotation of the sample about the surface normal. To do so, we simultaneously rotated the linear polarization of the generating light (the generator) and the polarizer placed before the detector (the analyser), with their relative angle set at either 0° or 90°. Below, we describe the use of the set-up shown in Fig. 1a to characterize the second-order optical susceptibility tensor, χ ijk, defined by the relation, P i(2 ω) = ε 0 χ ijk(2 ω) E j( ω) E k( ω).Īs a first step, we determined the orientation of the high-symmetry axes in the (112) surface, which are the and directions. In contrast, SHG from a TaAs (001) surface is barely detectable (at least six orders of magnitude lower than the (112) surface). The SH intensity from this surface is very strong, allowing for polarization rotation scans with signal-to-noise ratio above 10 6. 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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