  To investigate the role of active galactic nucleus (AGN) X-ray irradiation on
the interstellar medium (ISM), we systematically analyzed Chandra and ALMA
CO($J$=2-1) data for 26 ultra-hard X-ray ($>$ 10 keV) selected AGNs at
redshifts below 0.05. While Chandra unveils the distribution of
X-ray-irradiated gas via Fe-K$\alpha$ emission, the CO($J$=2-1) observations
reveal that of cold molecular gas. At high resolutions $\lesssim$ 1 arcsec, we
derive Fe-K$\alpha$ and CO($J$=2-1) maps for the nuclear 2 arcsec region, and
for the external annular region of 2 arcsec-4 arcsec, where 2 arcsec is $\sim$
100-600 pc for most of our AGNs. First, focusing on the external regions, we
find the Fe-K$\alpha$ emission for six AGNs above 2$\sigma$. Their large
equivalent widths ($\gtrsim$ 1 keV) suggest a fluorescent process as their
origin. Moreover, by comparing 6-7 keV/3-6 keV ratio, as a proxy of
Fe-K$\alpha$, and CO($J$=2-1) images for three AGNs with the highest
significant Fe-K$\alpha$ detections, we find a possible spatial separation.
These suggest the presence of X-ray-irradiated ISM and the change in the ISM
properties. Next, examining the nuclear regions, we find that (1) The 20-50 keV
luminosity increases with the CO($J$=2-1) luminosity. (2) The ratio of
CO($J$=2-1)-to-HCN($J$=1-0) luminosities increases with 20-50 keV luminosity,
suggesting a decrease in the dense gas fraction with X-ray luminosity. (3) The
Fe-K$\alpha$-to-X-ray continuum luminosity ratio decreases with the molecular
gas mass. This may be explained by a negative AGN feedback scenario: the mass
accretion rate increases with gas mass, and simultaneously, the AGN evaporates
a portion of the gas, which possibly affects star formation.
