  Data obtained from Parker Solar Probe (PSP) since 2021 April have shown the
first in situ observation of the solar corona, where the solar wind is formed
and accelerated. Here we investigate the alpha-proton differential flow and its
characteristics across the critical Alfv\'en surface (CAS) using data from PSP
during encounters 8-10 and 12-13. We first show the positive correlation
between the alpha-proton differential velocity and the bulk solar wind speed at
PSP encounter distances. Then we explore how the characteristics of the
differential flow vary across the CAS and how they are affected by Alfv\'enic
fluctuations including switchbacks. We find that the differential velocity
below the CAS is generally smaller than that above the CAS, and the local
Alfv\'en speed well limits the differential speed both above and below the CAS.
The deviations from the alignment between the differential velocity and the
local magnetic field vector are accompanied by large-amplitude Alfv\'enic
fluctuations and decreases in the differential speed. Moreover, we observe that
$V_{\alpha p}$ increases from $M_A < 1$ to $M_A \simeq 2$ and then starts to
decrease, which suggests that alphas may remain preferentially accelerated well
above the CAS. Our results also reveal that in the sub-Alfv\'enic solar wind
both protons and alphas show a strong correlation between their velocity
fluctuations and magnetic field fluctuations, with a weaker correlation for
alphas. In contrast, in the super-Alfv\'enic regime the correlation remains
high for protons, but is reduced for alphas.
