Influence of the Surface States on the Nonlinear Hall Effect in Weyl Semimetals

Linear response phenomena have inspired novel applications in nanoelectronics. The most fundamental example is the anomalous Hall effect, where a transverse charge current is generated in presence of an applied electric field. Nevertheless, the Hall effect vanishes in non-magnetic materials. In view of this fact, Sodemann and Fu suggested in 2015 that a second order Hall effect is allowed in systems with time reversal symmetry and non-centrosymmetric structure stemming from the Berry curvature dipole. Several material candidates such as Weyl semimetals have been proposed as ideal platforms to this nonlinear Hall effect because of their highly dispersive energy bands and the presence of Weyl nodes. However, the impact of their surface states on second order Hall transport driven by the Berry curvature dipole is still unclear.

Starting from a two band model we analyze the sensitivity of the Berry curvature dipole to the surface states in a Weyl semimetal. We conclude that whereas in type I regime this nonlinear Hall transport is not affected by the projections of the Fermi arcs on each slab created, an enhancement of the Berry curvature dipole appears at type II regime due to a higher number of states at the surface rather than the bulk. The latter reveals a thickness dependence on the nonlinear Hall effect in one of the slabs into consideration. We compare our predictions with realistic simulations on WTe₂. Our study opens an avenue to engineer more efficiently the nonlinear Hall effect in novel material interfaces.