Topological enhancement of nonlinear transport in unconventional point-node semimetals

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