  The valley Hall effect arises from valley contrasting Berry curvature and
requires inversion symmetry breaking. Here, we propose a nonlinear mechanism to
generate a valley Hall current in systems with both inversion and time-reversal
symmetry, where the linear and second-order charge Hall currents vanish along
with the linear valley Hall current. We show that a second-order valley Hall
signal emerges from the electric field correction to the Berry curvature,
provided a valley-contrasting anisotropic dispersion is engineered. We
demonstrate the nonlinear valley Hall effect in tilted massless Dirac fermions
in strained graphene and organic semiconductors. Our work opens up the
possibility of controlling the valley degree of freedom in inversion symmetric
systems via nonlinear valleytronics.
