Electronic Properties of $\alpha \text{−}{\mathrm{RuCl}}_3$ in Proximity to Graphene

In the pursuit of developing routes to enhance magnetic Kitaev interactions in $\alpha \text{−}{\mathrm{RuCl}}_3$, as well as probing doping effects, we investigate the electronic properties of $\alpha \text{−}{\mathrm{RuCl}}_3$ in proximity to graphene. We study $\alpha \text{−}{\mathrm{RuCl}}_3$/graphene heterostructures via ab initio density functional theory calculations, Wannier projection, and nonperturbative exact diagonalization methods. We show that $\alpha \text{−}{\mathrm{RuCl}}_3$ becomes strained when placed on graphene and charge transfer occurs between the two layers, making $\alpha \text{−}{\mathrm{RuCl}}_3$ (graphene) lightly electron doped (hole doped). This gives rise to an insulator-to-metal transition in $\alpha \text{−}{\mathrm{RuCl}}_3$ with the Fermi energy located close to the bottom of the upper Hubbard band of the $t_{2g}$ manifold. These results suggest the possibility of realizing metallic and even exotic superconducting states. Moreover, we show that in the strained $\alpha \text{−}{\mathrm{RuCl}}_3$ monolayer the Kitaev interactions are enhanced by more than 50% compared to the unstrained bulk structure. Finally, we discuss scenarios related to transport experiments in $\alpha \text{−}{\mathrm{RuCl}}_3$/graphene heterostructures.

Figure 1

van der Waals bilayer $\alpha \text{−}{\mathrm{RuCl}}_3$/graphene in the hexagonal supercell (see text for description). The blue, maroon, and gray spheres represent Ru, Cl, and C atoms, respectively.

Figure 2

(a) Top views of two supercells of $\alpha \text{−}{\mathrm{RuCl}}_3/\mathrm{gr}$ considered in this study (black lines): (a) hexagonal and (b) rectangular. The blue and maroon spheres represent Ru and Cl atoms, respectively. The gray hexagon indicates the graphene monolayer.

Figure 3

(a) Calculated band structure along the high-symmetry points ($\mathrm{\Gamma }$, $K$, $M$) of the hexagonal Brillouin zone for zigzag antiferromagnetic $\alpha \text{−}{\mathrm{RuCl}}_3/\mathrm{gr}$ in the $\mathrm{GGA}+\mathrm{SOC}+U$ scheme with $U=1.5\mathrm{eV}$. The insets show enlarged regions near the Fermi level $E_F$. (b) Atom projected spin-polarized density of states. The $E_F$ lies slightly above of the upper Hubbard band in the $t_{2g}$ manifold. (c),(d) Top of side view of charge difference $\delta \rho$ plot with charge isosurface $5\times {10}^{-4}e/{\AA }^3$. The peach and cyan colors represent regions with charge accumulation and depletion (deficiency), respectively. See text for the definition of $\mathrm{\Delta }\rho$.