We study the second-order nonlinear optical response of a Weyl semimetal (WSM), i.e., a three-dimensional metal with linear band touchings acting as pointlike sources of Berry curvature in momentum space, termed ``Weyl-Berry monopoles.'' We first show that the anomalous second-order photocurrent of WSMs can be elegantly parametrized in terms of Weyl-Berry dipole and quadrupole moments. We then calculate the corresponding charge and node conductivities of WSMs with either broken time-reversal invariance or inversion symmetry. In particular, we predict a dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.
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Rostami et al. (2018) studied this question.
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