Layer-Selective Proximity Symmetry Breaking Enables Anomalous and Nonlinear Hall Responses in 1H-TMD Metals

Abstract

Nonlinear Hall responses are a direct electrical probe of quantum geometry, but they are symmetry-forbidden in many pristine two-dimensional metals. We show that layer-selective magnetic proximity unlocks intrinsic linear and nonlinear Hall effects in metallic $1H-NbX_2$ ($X=\mathrm{S,Se,Te}$), where native $D_{3h}$ symmetry forces both the anomalous Hall conductivity and the Berry-curvature dipole (BCD) to vanish. Fully relativistic density-functional theory combined with Wannier interpolation reveals that an out-of-plane proximity exchange that preserves $C_3$ generates a sizable sheet anomalous Hall conductivity, $\sigma^{\mathrm{sheet}}_{xy} \sim 10^{-2}(e^2/h)$, while keeping the BCD exactly zero. Breaking $C_3$ by adding an in-plane exchange component (or an orthogonal two-sided exchange texture) produces a strongly tunable BCD and hence a nonlinear Hall conductivity that is odd and approximately linear in the in-plane exchange scale, reaching $|D_y|$ of order $10^{-2}$ angstrom and maximized in NbTe$_2$. These magnitudes imply a readily measurable second-harmonic Hall voltage in micron-scale Hall bars under mA ac drive. We further propose a dual-interface device in which the signs of the first- and second-harmonic Hall voltages provide two-bit readout using the same contacts.