  Geminga pulsar is surrounded by a multi-TeV $\gamma$-ray halo radiated by the
high energy electrons and positrons accelerated by the central pulsar wind
nebula (PWN). The angular profile of the $\gamma$-ray emission reported by HAWC
indicates an anomalously slow diffusion for the cosmic-ray electrons and
positrons in the halo region around Geminga. In the paper we study the possible
mechanism for the origin of the slow diffusion. At first, we consider the
self-generated Alfv\'en waves due to the streaming instability of the electrons
and positrons released by Geminga. However, even considering a very optimistic
scenario for the wave growth, we find this mechanism DOES NOT work to account
for the extremely slow diffusion at the present day if taking the proper motion
of Geminga pulsar into account. The reason is straightforward as the PWN is too
weak to generate enough high energy electrons and positrons to stimulate strong
turbulence at the late time. We then propose an assumption that the strong
turbulence is generated by the shock wave of the parent supernova remnant (SNR)
of Geminga. Geminga may still be inside the SNR, and we find that the SNR can
provide enough energy to generate the slow-diffusion circumstance. The TeV
halos around PSR B0656+14, Vela X, and PSR J1826-1334 may also be explained
under this assumption.
