  At nonlinear orders in the electric field, the vanishing of the Hall
conductivity does not prevent the nonlinear component of the current from being
transverse for selected field directions. We study electrons on
$\mathcal{C}_{3v}$-symmetric honeycomb lattice for which the Hall conductivity
vanishes at first and second order. Nevertheless, the second-order current
component is transverse for fields perpendicular to the three mirror lines. The
$\mathcal{C}_{3v}$ symmetry constrains the first-order and second-order
conductivity tensors to have only one independent component each, which we
calculate using the quantum kinetic equation. In linearly\hyp{}polarized
oscillating field, the current has a zero\hyp{}frequency component switching
sign upon $\pi/2$-rotation of the polarization angle.
