  The recent discovery of the quantum nonlinear Hall effect has revived the
field of nonlinear transport. Here, we predict magnetic field-induced nonlinear
Hall effect in time-reversal symmetric Weyl semimetal. We show that the
interplay of the band geometric quantities, such as the Berry curvature, and
the magnetic part of the Lorentz force can give rise to finite nonlinear Hall
conductivity that is linear in the magnetic field. Such nonlinear Hall
conductivity can manifest through nonlinear transport measurement as well as
nonlinear optical phenomena like photocurrent and the second harmonic
generation.
