  Cross-correlations between galaxy weak lensing (WL) and Cosmic Microwave
Background (CMB) lensing are a powerful tool to probe matter fluctuations at
intermediate redshifts and to detect residual systematics in either probe. In
this paper, we study the cross-correlation of galaxy WL from the Hyper
Suprime-Cam Subaru Strategic Program (HSC) first data release and CMB lensing
from the final Planck data release, for HSC source galaxies at 0.3< z < 1.5.
HSC is the deepest Stage-III galaxy WL survey, and provides both a great
opportunity to study the high-redshift universe and new challenges related to
its exceptionally high source density, such as source blending. The
cross-correlation signal is measured at a significance level of 3.1$\sigma$.
The amplitude of our best-fit model with respect to the best-fit 2018 Planck
cosmology is $A = 0.81\pm 0.25$, consistent with $A=1$. Our result is also
consistent with previous CMB lensing and galaxy WL cross-correlation studies
using different surveys. We perform tests with respect to the WL $B$-modes, the
point-spread-function, photometric redshift errors, and thermal
Sunyaev-Zel'dovich leakage, and find no significant evidence of residual
systematics.
