  Quantum thermal transistor is a microscopic thermodynamical device that can
modulate and amplify heat current through two terminals by the weak heat
current at the third terminal. Here we study the common environmental effects
on a quantum thermal transistor made up of three strong-coupling qubits. It is
shown that the functions of the thermal transistor can be maintained and the
amplification rate can be modestly enhanced by the skillfully designed common
environments. In particular,the presence of a dark state in the case of the
completely correlated transitions can provide an additional external channel to
control the heat currents without any disturbance of the amplification rate.
These results show that common environment effect can offer new insight on
improving the performance of quantum thermal devices.
