Quantum metric non-linear Hall effect in an antiferromagnetic topological insulator thin-film EuSn2As2

The quantum geometric structure of electrons introduces fundamental insights into understanding quantum effects in materials. One notable manifestation is the non-linear Hall effect (NLHE), which has drawn considerable interest for its potential to overcome the intrinsic limitations of semiconductor diodes at low input power and high frequency. In this study, we investigate NLHE stemming from the real part of the quantum geometric tensor, specifically the quantum metric, in an antiferromagnetic topological material, EuSn${}_2$As${}_2$, using density functional theory. Our calculations predict a remarkable NLHE arising from a symmetry-protected, single Type-II surface Dirac cone in the even-numbered-layer two-dimensional slab thin-film, yielding a non-linear Hall conductivity exceeding 20 mA/V${}^2$—an order of magnitude larger than previously reported. This single Dirac band dispersion represents the simplest model for generating NLHE, positioning the EuSn${}_2$As${}_2$ thin-film as a “hydrogen atom” for NLHE systems. Additionally, we observe NLHE from band-edge states near the Fermi level. Our findings also reveal that 30% phosphorus (P) doping can double the non-linear Hall conductivity. With its substantial and tunable NLHE, EuSn${}_2$As${}_2$ thin-films present promising applications in antiferromagnetic spintronics and rectification devices.