We have investigated the energetic stability and the electronic properties of metal-organic topological insulator bilayers (BLs), (MC₄S₄)₃BL, with M = Ni and Pt, using first-principles calculations and tight-binding model. Our findings show that (MC₄S₄)₃BL 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, the AA stacking being the energetically most stable one. The electronic band structure is characterized by a combination of bonding and antibonding kagome band sets, revealing that (NiC₄S₄)₃BL presents a Z₂-metallic phase, whereas (PtC₄S₄)₃BL may present Z₂-metallic phase or quantum spin Hall phase. Those nontrivial topological states were confirmed by the formation of chiral edge states in (MC₄S₄)₃BL 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 brings us an additional and interesting degree of freedom to control the transport properties in layered metal-organic topological insulators.
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Lima et al. (2017) studied this question.