  We consider an armchair bilayer phosphorene that is connected to two hot and
cold leads from both sides and study the thermoelectric properties of such a
system with periodic vacancies at the middle of nanoribbon and in the armchair
direction. For this purpose, we first analytically show that by creating a
vacancy, a localized state is generated around it. Then we demonstrate that in
the presence periodic vacancies, a new energy band will be formed in the energy
bandstructure, and by changing the distance between the vacancies, the width of
the transmission channel and finally the electric power and thermoelectric
efficiency can be tuned.
