Intrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets

Abstract

Two-dimensional systems with honeycomb lattice are known to be a paradigmatic platform to explore the various types of Hall effects, owing to that the interplay of lattice geometry, spin-orbit coupling and magnetism can give rise to very rich features in the quantum geometry of wave functions. In this work, we consider honeycomb topological antiferromagets that are effectively described by a $\mathcal{PT}$-symmetric antiferromagnetic Kane-Mele model, and explore the evolution of its nonlinear Hall response with respect to the change of lattice anisotropy, chemical potential, and the direction of the Néel vector. Due to the $\mathcal{PT}$-symmetry, the leading-order Hall effect of quantum geometric origin is the intrinsic nonlinear Hall effect, which is a second-order effect of electric fields and is independent of the scattering time. We investigate the behavior of the intrinsic nonlinear Hall conductivity tensor across topological phase transitions driven by antiferromagnetic exchange field and lattice anisotropy and find that its components do not change sign, which is different from the extrinsic nonlinear Hall effect. In the weakly doped regime, we find that the intrinsic nonlinear Hall effect is valley-polarized. By varying the chemical potential, we find that the nonlinear Hall conductivity tensors exhibit kinks when the Fermi surface undergoes Lifshitz transitions. Furthermore, we find that the existence of spin-orbit coupling to lift the spin-rotation symmetry is decisive for the use of intrinsic nonlinear Hall effect to detect the direction of the Néel vector. Our work shows that the two-dimensional honeycomb topological antiferromagnets are an ideal class of material systems with rich properties for the study of intrinsic nonlinear Hall effect.