  Galaxy clusters are crucial to understanding role of the environment in
galaxy evolution. However, due to their rarity, only a limited number of
clusters have been identified at $z\gtrsim2$. In this paper, we report a
discovery of seven cluster candidates with massive quiescent galaxies at
$z\sim2$ in the $3.5\,\mathrm{deg}^{2}$ area of the XMM-LSS field, roughly
doubling the known cluster sample at this frontier redshift if confirmed. We
construct a photometric redshift catalog based on deep ($i\sim26$,
$K_\mathrm{s}\sim24$) multi-wavelength photometry from $u^*$-band to $K$-band
gathered from the Hyper Suprime-Cam Subaru Strategic Program and other
collaborative/public surveys. We adopt a Gaussian kernel density estimate with
two different spatial scales (10" and 60") to draw a density map of massive
($\log(M_{*}/M_{\odot})>10.5$) and quiescent ($\log(\mathrm{sSFR\,
[\mathrm{yr^{-1}}]})<-10$) galaxies at $z\sim2$. Then, We identify seven
prominent overdensities. These candidates show clear red sequences in
color-magnitude diagrams ($z-H$ vs. $H$). Moreover, one of them shows an
extended X-ray emission with $L_\mathrm{X}=(1.46\pm0.35)\times10^{44}$ erg
s$^{-1}$, suggesting its virialized nature. There is no clear evidence of
enhancement nor suppression of the star formation rate of the main sequence
galaxies in the clusters. We find that cluster galaxies have a higher fraction
of transition population with $-10.5<\log(\mathrm{sSFR\,
[\mathrm{yr^{-1}}]})<-10$ ($12\%$) than the field ($2\%$), which implies the
ongoing star formation quenching. The quiescent fraction in the cluster
candidates also exceeds that in the field. We confirm that the excess of a
quiescent fraction is larger for higher-mass galaxies. This is the first
statistical evidence for the mass-dependent environmental quenching at work in
clusters even at $z\sim2$.
