# Tuning the topological states in metal-organic bilayers

## TL;DR

This study explores the electronic and topological properties of metal-organic bilayers, demonstrating their potential for band structure engineering and controllable edge states via external electric fields.

## Contribution

It introduces a detailed analysis of metal-organic bilayers' topological phases and shows how electric fields can manipulate edge state localization.

## Key findings

- $(NiC_4S_4)_3$-BL is a Z$_2$-metallic phase.
- $(PtC_4S_4)_3$-BL can be Z$_2$-metallic or quantum spin Hall.
- Edge states localization can be controlled by external electric fields.

## Abstract

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.