  We have investigated the energetic stability and the electronic properties of
metal-organic topological insulators bilayers (BLs), $(MC_4S_4)_3$-BL, with
M=Ni and Pt, using first-principles calculations and tight-binding model. Our
findings show that $(MC_4S_4)_3$-BL is an appealing platform to perform
electronic band structure engineering, based on the topologically protected
chiral edge states. The energetic stability of the BLs is ruled by van der
Waals interactions; being the AA stacking the energetically most stable one.
The electronic band structure is characterized by a combination of bonding and
anti-bonding kagome band sets (KBSs), revealing that $(NiC_4S_4)_3$-BL presents
a Z$_2$-metallic phase, whereas $(PtC_4S_4)_3$-BL may present both
Z$_2$-metallic phase or quantum spin Hall phase. Those non-trivial topological
states were confirmed by the formation of chiral edge states in
$(MC_4S_4)_3$-BL nanoribbons. We show that the localization of the edge states
can be controlled with a normal external electric field, breaking the mirror
symmetry. Hence, the sign of electric field selects in which layer each set of
edge states are located. Such a control on the (layer) localization, of the
topological edge states, bring us an additional and interesting degree of
freedom to control the transport properties in layered metal-organic
topological insulator.
