We show that three-dimensional (3D) Dirac semimetals (DSMs) can achieve highly efficient terahertz high-order harmonic generation (HHG) up to the 31st harmonic with input intensities $\approx 10\mathrm{M}\mathrm{W}/{\mathrm{cm}}^2$—over ${10}^5$ times lower than required in conventional terahertz HHG systems. Our theory reveals that this extreme nonlinearity is made possible by the existence of an operation regime that differs from previous demonstrations of lower order harmonic generation. We also reveal an unexpected regime in which emitted harmonics abruptly become negligible beyond the third order. This unprecedented vanishing of higher order nonlinearity has a geometrical origin related to the combination of conical dispersion and extra dimensionality in 3D DSMs, breaking the common notion that 3D DSMs share the essential physics of two-dimensional DSMs. Our findings pave the way to unlocking the full potential of 3D DSMs as efficient platforms for terahertz light sources and optoelectronics at moderate intensities.

中文翻译：

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在三维狄拉克半金属中高效产生太赫兹谐波

我们证明了三维（3D）狄拉克半金属（DSM）可以在输入强度下实现高达31次谐波的高效太赫兹高阶谐波生成（HHG） $\approx 10\mathrm{中号}\mathrm{w\; ^}/{\mathrm{厘米}}^2$-过度 ${10}^5$比传统的太赫兹HHG系统所需的时间低两倍。我们的理论表明，这种极端的非线性是由于存在一种不同于先前的低阶谐波产生示范的工作机制而存在的。我们还揭示了一个出乎意料的情况，在该情况下，发出的谐波突然超出三阶而可以忽略不计。高阶非线性的这种前所未有的消失，其几何起源与3D DSM中的圆锥形色散和额外的维数相结合，打破了3D DSM共享二维DSM基本物理原理的普遍观念。我们的发现为释放3D DSM的全部潜力铺平了道路，这些潜力可作为中等强度太赫兹光源和光电子学的高效平台。