Trivial and inverted Dirac bands and the emergence of quantum spin Hall states in graphene on transition-metal dichalcogenides

Abstract

Proximity orbital and spin-orbital effects of graphene on monolayer transition-metal dichalcogenides (TMDCs) are investigated from first-principles. The Dirac band structure of graphene is found to lie within the semiconducting gap of TMDCs for sulfides and selenides, while it merges with the valence band for tellurides. In the former case, the proximity-induced staggered potential gaps and spin-orbit couplings (all on the meV scale) of the Dirac electrons are established by fitting to a phenomenological effective Hamiltonian. While graphene on MoS 2 , MoSe 2 , and WS 2 has a topologically trivial band structure, graphene on WSe 2 exhibits inverted bands. Using a realistic tight-binding model we find topologically protected helical edge states for graphene zigzag nanoribbons on WSe 2 , demonstrating the quantum spin Hall effect. This model also features "half-topological states," which are protected against time-reversal disorder on one edge only.

Spin Hall Effect and Weak Antilocalization in Graphene/Transition Metal Dichalcogenide Heterostructures

“…31,32 The first element is a Rashba SOC with strength λ R due to the broken out-of-plane symmetry, where d i,j is a normalized vector pointing from site i to its nearest neighbor at site j, and s is the normalized spin operator. The second is a sublattice-dependent PIA SOC, 31,32 where λ (A) PIA and λ for each sublattice. We use parameters provided in reference, 31 which were extracted from fitting to DFT band structures and spin textures.…”

Mass inversion in graphene by proximity to dichalcogenide monolayer

“…We explore the consequences of such relative voltage on the effective band structure on graphene, assuming that the other parameters (hopping integrals and lattice constants) remain unchanged with voltage. One could obtain the appropriate parameters from first principles calculations, although the van der Waals nature of the bonding between layers, as well as the rather fine-scale of the relevant fea-tures make those calculations quite challenging [21,22]. Results for a nearly zero relative shift of the neutrality points are in Fig.…”

“…Although the effective Hamiltonian of the system can be obtained by a variety of methods [21,22], its topological phases remain unexplored. We focus on the Berry curvature and associated valley Chern number and identify different quantum phases that may appear as Hamiltonian parameters vary.…”

“…An interesting family of 2D crystals, transition metal dichalcogenides (TMD) can be used as substrates for graphene [19][20][21][22][23]. Monolayer semiconductor TMD such as MoS 2 and WS 2 have a direct band gap and honeycomb crystal structure [24].…”

Proximity-induced spin-valley polarization in silicene or germanene on F-doped WS2

“…Without SOC we obtain band gaps of 29 and 38 meV, [31]. The enhancement mechanism by proximity SOC is similar to the case of graphene on transition-metal dichalcogenides [32], but due to the buckling of silicene or germanene the magnitude of spin splitting here is different in the valence and conduction bands. As a consequence of the lifted spin degeneracy, we obtain reduced band gaps of 23 and 14 meV for silicene and germanene on WS 2 , respectively.…”