The anomalous Hall effect is an ubiquitous phenomenon in magnetic materials but it vanishes in time reversal systems. Nevertheless, Sodemann and Fu 1 suggested that a second order response in the electric field is allowed in time reversal invariant materials without inversion symmetry, as a consequence of the shift in the Fermi distribution function when the electrons go out of equilibrium. This nonlinear Hall effect is driven by the curvature dipole (BCD), which motivated several experiments 2,3 and encouraged the exploration of numerous platforms to enhance the resulting Hall current. In this context, topological materials such as Weyl semimetals (WSM) are excellent candidates to exhibit large values of nonlinear Hall effect due to monopoles of Berry curvature. In addition, the Fermi arcs that connect Weyl nodes of opposite chirality have a known impact on the anomalous Hall effect, but an extended analysis of the surface states is still missed at the level of the nonlinear Hall effect, especially in the regime when there is an important tilting of the Weyl cones. In this work 4, we reveal the contribution of the surface states to the BCD in WSM. Starting from a two-band model 5,6 and applying a slab construction method 7, we deduce that the topological nature of the surface states does not play a crucial role on the BCD. Besides, the transition between type I and type II WSM uncovers a strong impact of the Fermi pockets' projections because of a higher number of states at the surface rather than at the bulk. In contrast, after comparing to the bulk instance we notice that track states' projections does not show a profound effect on the BCD. We extend our study to the realistic case of WTe2 thin film using a Wannier-projected tight-binding representation, confirming that there is a notorious thickness dependence on the BCD subjected to the slab under consideration.

References 1 I.Sodemann and L.Fu. Physical Review Letters 115, 216806 (2015). 2 K.Kang, T.Li, E.Sohn. Nature Materials 18, p. 324-328 (2019). 3 Q.Ma, S.Xu, H.Shen. Nature 565, p. 337-342 (2019). 4 D.García Ovalle, A.Pezo and A.Manchon. Arxiv 2206.08681 (2022). 5 T. Mc Cormick, I.Kimchi and N.Trivedi. Physical Review B 95, 075133 (2017). 6 C.Zeng, S.Nandy and S.Tewari. Physical Review B 103, 245119 (2021). 7 G. Manchon, S. Ghosh, C. Barreteau. Physical Review B 101, 174423 (2020).