  Using an extended chromomagnetic model, we perform a systematic study of the
masses of the doubly heavy tetraquarks. We find that the ground states of the
doubly heavy tetraquarks are dominated by color-triplet
$\ket{(qq)^{\bar{3}_{c}}(\bar{Q}\bar{Q})^{3_{c}}}$ configuration, which is
opposite to that of the fully heavy tetraquarks. The combined results suggest
that the color-triplet configuration becomes more important when the mass
difference between the quarks and antiquarks increases. We find three stable
states which lie below the thresholds of two pseudoscalar mesons. They are the
$IJ^{P}=01^{+}$ $nn\bar{b}\bar{b}$ tetraquark, the $IJ^{P}=00^{+}$
$nn\bar{c}\bar{b}$ tetraquark and the $J^{P}=1^{+}$ $ns\bar{b}\bar{b}$
tetraquark.
