Electric field induced Berry curvature dipole in quasi-one-dimensional Bi${}_4$I${}_4$

The nonlinear Hall effect in time-reversal symmetric materials offers a powerful probe into quantum geometry. Here, we investigate the electric-field-tunable nonlinear Hall response in few-layer ${\text{Bi}}_4{\text{I}}_4$ using comprehensive first-principles calculations across both its $\alpha$ and $\beta$ phases. Guided by symmetry analysis, we track the evolution of the Berry curvature dipole (BCD) tensor from the monolayer to the bilayer configuration under an out-of-plane electric field. While the monolayer features a highly rigid band structure and modest BCD tunability, the bilayer architecture exhibits substantial field-induced band modifications, including a progressive Rashba splitting and eventual gap closure in the $\beta$ phase. Crucially, this field-tunability allows substantial enhancement of the BCD magnitude relative to the monolayer counterpart. Our findings establish quasi-one-dimensional bismuth halogenides as a promising platform for engineering nonlinear Hall response.