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.

• Received 15 June 2020
• Revised 19 August 2020
• Accepted 14 October 2020

DOI:https://doi.org/10.1103/PhysRevResearch.2.043252

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Published by the American Physical Society