  The diffusion coefficients around the pulsar $\gamma$-ray halos are highly
suppressed compared with the value in the interstellar medium. It is suggested
in the literature that the $\gamma$-ray halos can be explained by a
ballistic-diffusive (BD) propagation without slow diffusion. However our
calculation shows that the BD propagation can not account for the $\gamma$-ray
halo profile well. Furthermore the transfer efficiency of the pulsar spin down
energy to the high energy electrons and positrons is even larger than 1 in the
BD scenario. Therefore slow diffusion is necessary to account for the pulsar
$\gamma$-ray halos. Taking the slow diffusion into account the contribution of
positron flux originated from nearby pulsars to the AMS-02 data is reexamined.
We may also expect a slow diffusion disk of the Milky Way as many such slow
diffusion regions exist. The positron contribution to the AMS-02 data from dark
matter annihilation in the new propagation model is also reexamined. We find
that the dark matter scenario satisfies all the $\gamma$-ray limits in the new
propagation model.
