Quantized nonlinear Hall effect from chiral monopole

Abstract: Nonlinear Hall effect arises in materials without inversion symmetry, and the intrinsic contribution is typically from Berry curvature dipole of non-universal Fermi pockets. Here we propose that nonlinear Hall effect can reach quantization in chiral Weyl semimetals without mirror symmetries. The energy shift between a pair of Weyl nodes leads to chirally asymmetric intra-node relaxation, and the net trace of nonlinear Hall conductivity is thus quantized in units of $e^3/\hbar^2$ and determined by sum of monopole charge weighted by the transport relaxation time. Our theory also applies to mirror symmetric Weyl/Dirac semimetals with chiral anomaly. Additionally, besides DC transport probes, we anticipate that nonlinear circular dichroism measurements could detect chiral asymmetry-induced currents.