  We show that an electric field applied to a strained topological Dirac
semimetal, such as Na3Bi and Cd3As2, induces a spin Hall current that is
quadratic in the electric field. By regarding the strain as an effective "axial
magnetic field" for the Dirac electrons, we investigate the electron and spin
transport semiclassically in terms of the chiral kinetic theory. The nonlinear
spin Hall effect arises as the cross effect between the regular Hall effect
driven by the axial magnetic field and the anomalous Hall effect coming from
the momentum-space topology. It provides an efficient way to generate a fully
spin-polarized and rectified spin current out of an alternating electric field,
which is sufficiently large and can be directly tuned by the gate voltage and
the strain.
