Nonlinear anomalous photocurrents in Weyl semimetals

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 point-like 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 universal dissipationless second-order anomalous node conductivity for WSMs belonging to the TaAs family.