  The electronic topology is generally related to the Berry curvature, which
can induce the anomalous Hall effect in time-reversal symmetry breaking
systems. Intrinsic monolayer transition metal dichalcogenides possesses two
nonequivalent K and K' valleys, having Berry curvatures with opposite signs,
and thus vanishing anomalous Hall effect in this system. Here we report the
experimental realization of asymmetrical distribution of Berry curvature in a
single valley in monolayer WSe2 through applying uniaxial strain to break C3v
symmetry. As a result, although the Berry curvature itself is still opposite in
K and K' valleys, the two valleys would contribute equally to nonzero Berry
curvature dipole. Upon applying electric field, the emergent Berry curvature
dipole would lead to an out-of-plane orbital magnetization, which further
induces an anomalous Hall effect with a linear response to E^2, known as
nonlinear Hall effect. We show the strain modulated transport properties of
nonlinear Hall effect in monolayer WSe2 with moderate hole-doping by gating.
The second-harmonic Hall signals show quadratic dependence on electric field,
and the corresponding orbital magnetization per current density can reach as
large as 60. In contrast to the conventional Rashba-Edelstein effect with
in-plane spin polarization, such current-induced orbital magnetization is along
the out-of-plane direction, thus promising for high-efficient electrical
switching of perpendicular magnetization.
