Graphene on transition-metal dichalcogenides: A platform for proximity spin-orbit physics and optospintronics

Hybrids of graphene and two-dimensional transition-metal dichalcogenides (TMDCs) have the potential to bring graphene spintronics to the next level. As we show here by performing first-principles calculations of graphene on monolayer ${\mathrm{MoS}}_2$, there are several advantages of such hybrids over pristine graphene. First, Dirac electrons in graphene exhibit a giant global proximity spin-orbit coupling, without compromising the semimetallic character of the whole system at zero field. Remarkably, these spin-orbit effects can be very accurately described by a simple effective Hamiltonian. Second, the Fermi level can be tuned by a transverse electric field to cross the ${\mathrm{MoS}}_2$ conduction band, creating a system of coupled massive and massless electron gases. Both charge and spin transport in such systems should be unique. Finally, we propose to use graphene/TMDC structures as a platform for optospintronics, in particular, for optical spin injection into graphene and for studying spin transfer between TMDCs and graphene.

Figure 1

Calculated electronic and spin properties of graphene on two-dimensional ${\mathrm{MoS}}_2$. (a) The supercell used in first-principles calculations. (b) Calculated band structure along high symmetry lines. The inset is a zoom to the fine structure of the low energy bands at the Fermi level, around the Dirac point. Bands with a positive (negative) $z$ component of the spin are shown in red (blue). The sublattice character ($A$ and $B$) is also indicated. (c) Spin textures for the four bands of the inset in (b).

Figure 2

Field effect on graphene/${\mathrm{MoS}}_2$. (a) Calculated offset ${\mathrm{\Delta }}_{\mathrm{c}}$ from the conduction band minimum of ${\mathrm{MoS}}_2$ to graphene, as a function of an applied transverse electric field. At positive fields electrons are transferred from graphene to ${\mathrm{MoS}}_2$, establishing a massless-massive electrons bilayer. (b) Net Fermi energy for graphene, as the difference of the valence band maximum $E_{\mathrm{gv}}$ of graphene and the system Fermi level $E_{\mathrm{F}}$. At positive fields the valence band of graphene becomes populated. (c) Net Fermi energy for ${\mathrm{MoS}}_2$, as the difference between the system Fermi level $E_{\mathrm{F}}$ and the conduction band minimum $E_{\mathrm{c}}$ of ${\mathrm{MoS}}_2$. The conduction band of ${\mathrm{MoS}}_2$ becomes populated at positive field, reflecting the population of holes in graphene in (b) as the whole system is neutral.

Figure 3

Calculated effective Hamiltonian parameters at the $K$ point: (a) Hybridization gap $\mathrm{\Delta }$, (b) sublattice-resolved intrinsic spin-orbit coupling ${\lambda }_{\mathrm{I}}^{\mathrm{A}}$ and ${\lambda }_{\mathrm{I}}^{\mathrm{B}}$ (they have opposite signs), and (c) Rashba parameter ${\lambda }_{\mathrm{R}}$, as functions of the applied transverse electric field.

Figure 4

Optospintronic schemes for graphene-TMDC hybrids. (a) Optical spin injection into graphene, facilitated by the semiconducting TMDC. A circularly polarized light excites spin-polarized electrons in the semiconductor. The spin is transferred to graphene where it can be detected as a Hanle signal by the ferromagnetic electrode. (b) Spin transfer between two different TMDCs, encapsulating graphene. Circularly polarized light tuned to the band gap of the top material excites electron spins which can tunnel to the lower material, exhibiting a circular luminescence peaked at its band gap frequency.