  The nonlinear Hall effect due to Berry curvature dipole (BCD) induces
frequency doubling, which was recently observed in time-reversal-invariant
materials. Here we report novel electric frequency doubling in the absence of
BCD on a surface of the topological insulator Bi2Se3 under zero magnetic field.
We observe that the frequency-doubling voltage transverse to the applied ac
current shows a threefold rotational symmetry, whereas it forbids BCD. One of
the mechanisms compatible with the symmetry is skew scattering, arising from
the inherent chirality of the topological surface state. We introduce the Berry
curvature triple, a high-order moment of the Berry curvature, to explain skew
scattering under the threefold rotational symmetry. Our work paves the way to
obtain a giant second-order nonlinear electric effect in high mobility quantum
materials, as the skew scattering surpasses other mechanisms in the clean
limit.
