  Superclusters, encompassing environments across a wide range of
overdensities, can be regarded as unique laboratories for studying galaxy
evolution. Although numerous supercluster catalogs have been published, none of
them goes beyond redshift $z=0.7$. In this work, we adopt a physically
motivated supercluster definition, requiring that superclusters should
eventually collapse even in the presence of dark energy. Applying a
friends-of-friends (FoF) algorithm to the CAMIRA cluster sample constructed
using the Subaru Hyper Suprime-Cam survey data, we have conducted the first
systematic search for superclusters at $z=0.5-1.0$ and identified $633$
supercluster candidates over an area of 1027 deg$^2$. The FoF algorithm is
calibrated by evolving $N$-body simulations to the far future to ensure high
purity. We found that these high-$z$ superclusters are mainly composed of $2-4$
clusters, suggesting the limit of gravitationally bound structures in the
younger Universe. In addition, we studied the properties of the clusters and
brightest cluster galaxies (BCGs) residing in different large-scale
environments. We found that clusters associated with superclusters are
typically richer, but no apparent dependence of the BCG properties on
large-scale structures is found. We also compared the abundance of observed
superclusters with mock superclusters extracted from halo light cones, finding
that photometric redshift uncertainty is a limiting factor in the performance
of superclusters detection.
