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

Abstract

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 $α$ and $β$ 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 $β$ 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.