  We investigate the rectification of heat current carried by electrons through
a double quantum dot (DQD) system under a temperature bias. The DQD can be
realized by molecules such as suspended carbon nanotube and be described by the
Anderson-Holstein model in presence of electron-phonon interaction. Strong
electron-phonon interaction can lead to formation of polaronic states in which
electronic states are dressed by phonon cloud. Dressed tunneling approximation
(DTA), which is nonperturbative in dealing with strong electron-phonon
interaction, is employed to obtain the heat current expression. In DTA,
self-energies are dressed by phonon cloud operator and are temperature
dependent. The temperature dependency of imaginary part of dressed retarded
self-energy gives rise to the asymmetry of the system and is the necessary
condition of thermal rectification. On top of this, one can either tune DQD
effective energy levels such that $|\bar{\epsilon}_1|\neq |\bar{\epsilon}_2|$
or have asymmetric dot-lead couplings to achieve thermal rectification. We
numerically find that increasing electron-phonon coupling and reducing inter
dot coupling can both improve thermal rectification effect, while the
electronic heat current is reduced.
