  Dust in protoplanetary disks is recognized as the building blocks of planets.
In the core accretion scenario, the abundance of dust in disks (or metallicity)
is crucial for forming cores of gas giants. We present our recent progress on
the relationship between the metallicity and planet formation, wherein planet
formation frequencies (PFFs) as well as the critical mass of planetary cores
($M_{c,crit}$) that can initiate gas accretion are statistically examined. We
focus on three different planetary populations that are prominent for observed
exoplanets in the mass-semimajor axis diagram: hot Jupiters, exo-Jupiters that
are densely populated around 1 AU, and low-mass planets in tight orbits. We
show that the resultant PFFs for both Jovian planets are correlated positively
with the metallicity whereas low-mass planets form efficiently for a wide range
of metallicities. This is consistent with the observed Planet-Metallicity
correlation. Examining the statistically averaged value of $M_{c,crit}$
(defined as $<M_{c,crit}>$), we find that the correlation originates from the
behavior of $<M_{c,crit}>$ that increases steadily with metallicity for two
kinds of the Jovian planets while the low-mass planets obtain a rather constant
value for $<M_{c,crit}>$. Such a difference in $<M_{c,crit}>$ can define
transition metallicities (TMs) above which the Jovian planets gain a larger
value of $<M_{c,crit}>$ than the low-mass planets, and hence gas giant
formation takes place more efficiently. We find that TMs are sensitive to the
important parameter that involves $M_{c,crit}$. We show, by comparing with the
observations, that a most likely value of $M_{c,crit}$ is $\simeq 5M_{\oplus}$,
which is smaller than the conventional value in the literature ($\simeq
10M_{\oplus}$). Our results suggest that opacities in planetary atmospheres
play an important role for lowering $M_{c,crit}$.
