Intrinsic orbital origin for the chirality-dependent nonlinear planar Hall effect of topological nodal fermions in chiral crystals

Topological semimetals in chiral crystals, which possess both structural handedness and band crossings (or nodes) with topological chiral charge, exhibit many exotic physical properties. Here we demonstrate that the structural and electronic chirality of these systems can endow them with another fascinating phenomenon---the intrinsic nonlinear planar Hall effect (INPHE), which is prominent around the nodes and reverses sign upon chirality reversal in opposite enantiomers. Taking chiral tellurium as an example, we reveal an intrinsic orbital mechanism, which manifests diverging orbital magnetic moments with hedgehoglike textures around nodes and, therefore, generates a dominant contribution to the INPHE that is proportional to the topological charge. Furthermore, we show that multifold fermions in topological chiral semimetals with B20 structures (e.g., CoSi and PtAl) induce a giant INPHE conductivity reaching the order of $1\ensuremath{\sim}10\phantom{\rule{0.28em}{0ex}}\mathrm{A}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}2}\phantom{\rule{0.16em}{0ex}}{\mathrm{T}}^{\ensuremath{-}1}$, which is detectable in experiments. Our study not only relates nonlinear transport to band topology and enantiomer recognition but also offers a new way to explore the exotic physical properties associated with unconventional chiral fermions.