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 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.

Figure 1

The simplest possible distributions of momentum-space Weyl-Berry monopoles in a 3D Weyl semimetal. The cones represent the low-energy band structure plotted as a function of $k_x$ and $k_z$, for $k_y=0$. Each crossing (Weyl node) acts as a “Weyl-Berry monopole” in momentum space, i.e., a pointlike source of Berry curvature. The color code indicates the chiral charge $\chi =\pm 1$ of each node. Panels (a) and (b) refer to crystals with a finite Weyl-Berry dipole and quadrupole, respectively. In the former case, time-reversal symmetry is broken. In the latter, inversion symmetry is broken. Note that WSMs with broken inversion symmetry come with a minimum of four nodes.

Figure 2

A cartoon representing the $N=24$ nodes of TaAs-based WSMs, as distributed in three parallel crystal planes in the BZ [46, 47]. Red and blue indicate opposite chiral charge, $\chi =\pm$. The node located at $\mathit{b}=b_{0,x}{\widehat{\mathit{k}}}_x-b_{0,z}{\widehat{\mathit{k}}}_z$, whose chirality is $\chi$, is specified by a dashed yellow circle.