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Magnetic field induces giant nonlinear optical response in Weyl semimetals

We study the second-order optical response of Weyl semimetals in the presence of a magnetic field. We consider an idealized model of a perfectly linear Weyl node and use the Kubo formula at zero temperature to calculate the intrinsic contribution to photocurrent and second harmonic generation conductivity components. We obtain exact analytical expressions applicable at arbitrary values of frequency, chemical potential, and magnetic field. Our results show that finite magnetic field significantly enhances the nonlinear optical response in semimetals, while magnetic resonances lead to divergences in nonlinear conductivity. In realistic systems, these singularities are regularized by a finite scattering rate, but result in pronounced peaks which can be detected experimentally, provided the system is clean and interactions are weak. We also perform a semiclassical calculation that complements and confirms our microscopic results at small magnetic fields and frequencies.