  Using gauge/gravity duality, we first study the string breaking and melting
of doubly heavy baryon at a finite chemical potential and temperature in this
paper. The decay mode $\rm{Q Q q \rightarrow Q q q+Q \bar{q}}$ is investigated
with the presence of temperature and chemical potential in this paper. With the
increase of temperature and chemical potential, string breaking takes place at
a smaller potential energy and the string-breaking distance will increase
slightly. It is also found that the $\rm{QQq}$ melts at small separate distance
with the increase of temperature and chemical potential. Then, we compare the
screening distance of $\rm{QQq}$ with $\rm{Q \bar{Q}}$ under the same
conditions. Finally, we draw the melting diagram of $\rm{QQq}$ and $\rm{Q
\bar{Q}}$ in the $T-\mu$ plane.
