  The topological singularity of the Bloch states close to the Fermi level
significantly enhances nonlinear electric responses in topological semimetals.
Here, we systematically characterize this enhancement for a large class of
topological nodal-point fermions, including those with linear,
linear-quadratic, and quadratic dispersions. Specifically, we determine the
leading power-law dependence of the nonlinear response functions on the
chemical potential $\mu$ defined relative to the nodal point. We identify two
characteristics that qualitatively improve nonlinear transports compared to
those of conventional Dirac and Weyl fermions. First, the type II (over-tilted)
spectrum leads to the $\log\mu$ enhancement of nonlinear response functions
having zero scaling dimension with respect to $\mu$, which is not seen in a
type-I (moderately or not tilted) spectrum. Second, the anisotropic
linear-quadratic dispersion increases the power of small-$\mu$ divergence for
the nonlinear response tensors along the linearly dispersing direction. Our
work reveals new experimental signatures of unconventional nodal points in
topological semimetals as well as provides a guiding principle for giant
nonlinear electric responses.
