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Recent experiments in the topological Weyl semimetal TaAs have observedrecord-breaking second-harmonic generation, a non-linear optical response at$2\omega$ generated by an incoming light source at $\omega$. However, whethersecond-harmonic generation is enhanced in topological semimetals in general isa challenging open question because their band structure entangles thecontributions arising from trivial bands and topological band crossings. Inthis work, we circumvent this problem by studying RhSi, a chiral topologicalsemimetal with a simple band structure with topological multifold fermionsclose to the Fermi energy. We measure second-harmonic generation (SHG) in awide frequency window, $\omega\in [0.27,1.5]$eV and, using first principlecalculations, we establish that, due to their linear dispersion, thecontribution of multifold fermions to SHG is subdominant as compared with otherregions in the Brillouin zone. Our calculations suggest that parts of the bandswhere the dispersion is relatively flat contribute significantly to SHG. As awhole, our results suggest avenues to enhance SHG responses.

Suppression of second-harmonic generation from linear bands in the topological multifold semimetal RhSi