Non-linear anomalous Hall effect of two-dimensional spin-3/2 heavy holes

We identify a sizable non-linear anomalous Hall effect in the electrical response of spin-3/2 heavy holes in zincblende semiconductor nanostructures. The response is driven by a quadrupole interaction with the electric field enabled by Td-symmetry. This interaction, until recently believed to be negligible, reflects inversion symmetry breaking and in two dimensions results in an electric-field dependent correction to the in-plane g-factor. The effect can be observed in state-of-the-art heterostructures, either via magnetic doping or by using a vector magnet, where even for small perpendicular magnetic fields it is comparable in magnitude to topological materials.