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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 brokencite{WanPRB2011,BurkovPRL2011, WengPRX2015,HuangNatComm2015}. Recently they have been observed in transition metal monopnictides (TMMPs) such as TaAs, a class of noncentrosymmetric materials that heretofore received only limited attention cite{XuScience2015, LvPRX2015, YangNatPhys2015}. 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 electrons cite{anderson1965symmetry,shi2013ferroelectric,kim2016polar}. Despite the absence of spontaneous polarization, polar metals can exhibit other signatures of inversion-symmetry breaking, most notably second-order nonlinear optical polarizability, $chi^{(2)}$, leading to phenomena such as optical rectification and second-harmonic generation (SHG). Here we report measurements of SHG that reveal a giant, anisotropic $chi^{(2)}$ in the TMMPs TaAs, TaP, and NbAs. With the fundamental and second harmonic fields oriented parallel to the polar axis, the value of $chi^{(2)}$ is larger by almost one order of magnitude than its value in the archetypal electro-optic materials GaAs cite{bergfeld2003second} and ZnTe cite{wagner1998dispersion}, and in fact larger than reported in any crystal to date.
Higher-order topology yields intriguing multidimensional topological phenomena, while Weyl semimetals have unconventional properties such as chiral anomaly. However, so far, Weyl physics remain disconnected with higher-order topology. Here, we report
TaAs and NbAs are two of the earliest identified Weyl semimetals that possess many intriguing optical properties, such as chirality-dependent optical excitations and giant second harmonic generation (SHG). Linear and nonlinear optics have been employ
Motivated by the nonlinear Hall effect observed in topological semimetals, we studied the photocurrent by the quantum kinetic equation. We recovered the shift current and injection current discovered by Sipe et al., and the nonlinear Hall current ind
The study of charge-density wave (CDW) distortions in Weyl semimetals has recently returned to the forefront, inspired by experimental interest in materials such as (TaSe4)2I. However, the interplay between collective phonon excitations and charge tr
Topological states of electrons and photons have attracted significant interest recently. Topological mechanical states also being actively explored, have been limited to macroscopic systems of kHz frequency. The discovery of topological phonons of a