  This work presents the results from our near-infrared spectroscopy of
narrow-band selected H$\alpha$ emitters (HAEs) in two rich over-densities (PKS
1138-262 at $z=2.2$ and USS 1558-003 at $z=2.5$) with the Multi-Object Infrared
Camera and Spectrograph (MOIRCS) on the Subaru telescope. These protoclusters
are promising candidates for the most massive class of galaxy clusters seen
today (Paper I). The confirmed HAEs in the protoclusters at $z>2$ show high
excitation levels as characterized by much higher [OIII]/H$\beta$ or
[OIII]/H$\alpha$ line ratios than those of general galaxies at low-$z$. Such a
high excitation level may not only be driven by high specific star formation
rates (sSFRs) and lower gaseous metallicities, but also be contributed by some
other effects. We investigate the environmental dependence of gaseous
metallicities by comparing the HAEs in the protoclusters with those in the
general field at similar redshifts. We find that the gaseous metallicities of
protocluster galaxies are more chemically enriched than those of field galaxies
at a given stellar mass in the range of M$_\star\lesssim10^{11}$ M$_\odot$.
This can be attributed to many processes, such as intrinsic (or nature)
effects, external (or nurture) effects, and/or some systematic sampling
effects. We also find that the offset of the mass-metallicity relation in dense
environment becomes larger at higher redshifts. This can be naturally
understood by the fact that the in/out-flow rates in star forming galaxies are
much higher at higher redshifts. Therefore the environmental dependence of such
"feeding" and "feedback" mechanisms in galaxy formation are probably playing
major roles in producing the offset of the mass-metallicity relation for the
protocluster galaxies at $z>2$.
