  The scotogenic type I and type III seesaw models are good candidates to
explain the existence of neutrino masses and dark matter simultaneously.
However, since triplet fermions have SU(2) gauge interaction, they cannot be
out of equilibrium before the electroweak symmetry breaking. Thus, leptogenesis
seems to be difficult within a framework of the pure type III seesaw model.
Some extension seems to be required to solve this fault. A model extended by
introducing a singlet fermion could be such a simple example. If the singlet
fermion is in the thermal equilibrium even for its extremely small neutrino
Yukawa coupling, leptogenesis could be shown to occur successfully for a rather
low mass of the singlet fermion. The required mass could be lowered to
$10^4$~GeV.
