  The full-heavy tetraquarks $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$ are
systematically investigated within the chiral quark model. The meson-meson
structure, diquark-antidiquark structure and K-structure are considered in this
work. There is no bound state for $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$
systems in $ IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$ channels. However, for
$cc\bar{c}\bar{b}$ system, three possible resonance states with energy of $
10079~{\rm MeV} $, $ 10081~{\rm MeV} $ and $ 10177~{\rm MeV} $ are found in $
IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$, respectively, and their decay width $
\Gamma$ are $6.7-8.4~{\rm MeV} $, $1.4-7.2~{\rm MeV} $ and $9.1-11.1~{\rm MeV}
$. For $bb\bar{b}\bar{c}$ system, there also exist three possible resonance
states with energy of $ 16474~{\rm MeV} $, $ 16474~{\rm MeV} $ and $ 16541~{\rm
MeV} $ in $ IJ^{P}=00^{+},01^{+}$ and $ 02^{+}$, respectively, and the decay
widths $ \Gamma$ of them are $2.2-6.1~{\rm MeV} $, $2.2-6.9~{\rm MeV} $ and
$5.3-8.5~{\rm MeV} $. $bc\bar{c}\bar{c}$ and $cb\bar{b}\bar{b}$ systems will
have the same results as $cc\bar{c}\bar{b}$ and $bb\bar{b}\bar{c}$,
respectively. These full-heavy resonance states are worthy to be searched in
the future experiments.
