Tuning the topological states in metal-organic bilayers

Abstract

We have investigated the energetic stability and the electronic properties of metal-organic topological insulators bilayers (BLs), (MC4S4)3-BL, with M=Ni and Pt, using first-principles calculations and tight-binding model. Our findings show that (MC4S4)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 (NiC4S4)3-BL presents a Z2-metallic phase, whereas (PtC4S4)3-BL may present both Z2-metallic phase or quantum spin Hall phase. Those non-trivial topological states were confirmed by the formation of chiral edge states in (MC4S4)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.

Quantum anomalous Hall effect in metal-bis(dithiolene), magnetic properties, doping and interfacing graphene

“…In a previous study 17 , we verified that the occupation of the kagome bands, as well as the localization of the non-trivial energy gaps in MOF/MOF interfaces, can be controlled by an external electric field. It is worth to pointing out that the energy bands responsible to the QAH phase are completely spin polarized and separated, with the magnetization out of the MOF plane.…”

“…Further molecular design has been done by building up multilayered systems by stacking MOFs [13][14][15][16] . Very recently, based on firstprinciples calculations, we have found that bilayer sys-tems of (MC 4 S 4 ) 3 , with M=Ni and Pt, present the Z 2metallic phase, where the edge states can be tuned by an EEF ⊥ 17 .…”

Layertronic control of topological states in multilayer metal-organic frameworks

“…For instance, in (NiC 4 S 4 ) 3 bilayers (2ML), the stacking geometry is characterized by the alignment of sites X and Y of the different layers (2ML-XY), with X and Y = A, B, G, and H, as indicated in Fig. 1 In a previous study [26], we have found the 2ML-AA configuration to be the most stable. There, the calculations were performed using the non-local vdW-DF2 [38] correction to describe the vdW interactions.…”

“…Recently, it has been proposed a bending strain perturbation approach to control spin currents in 2DTIs [29]. Meanwhile, ensuing research has shown a) Electronic mail: felipe.lima@ufu.br layer localization control of topological states by an applied external electric field in MOF bilayer nanoribbons [26] and bilayer graphene grain boundaries [30]. Furthermore, the exploration of van de Waals heterostructures allows for designed properties by combining the stacking of two-dimensional materials [31,32].…”

Orbital Pseudospin-Momentum Locking in Two-Dimensional Chiral Borophene

“…Therefore, for zero external field ν = 0, the Hamiltonian commutes with τ x (which coincide with the M z symmetry operator), and the eigenstates reduce to the mirror symmetric and antisymmetric cases g m = ±1. Moreover, for ν = 0 we can still separate the Hamiltonian into two orthogonal subspaces defined by its pseudomirror symmetry [41]…”