Fig. 1: Crystal structure symmetry and band model of NbIrTe_4.

a Crystal structure of NbIrTe₄ exhibiting broken inversion symmetry with a mirror plane (M_a) illustrated as a yellow plane. Top view (b) of the crystal structure of NbIrTe₄ with mirror axis M_a (yellow dashed line). J_NLHE is the generated nonlinear Hall current parallel to M_a, and E_ext is the applied electric field perpendicular to M_a. c Illustrations of Hall devices with an optical image (top left inset). I_ω, V_2ω, E_ω, and J_2ω represent the current, voltage, electric field, and generated nonlinear Hall current, respectively, at frequencies ω and 2ω. The scale bar in the optical image (top left inset) is 1 μm. d Polar plots of Raman modes at 151.33 cm⁻¹. The results are shown as intensity versus angle configuration. e A schematic model picture of band structures with Berry curvature (BC) Ω(k) evolution, including spin–orbit coupling (SOC). The lower panels display momentum-resolved BC, highlighting the emergence of a large dipole hotspot of BC in the presence of SOC.