Tuning the electronic structure of monolayer graphene/$\mathrm{Mo}{\mathrm{S}}_2$ van der Waals heterostructures via interlayer twist

We directly measure the electronic structure of twisted graphene/$\mathrm{Mo}{\mathrm{S}}_2$ van der Waals heterostructures, in which both graphene and $\mathrm{Mo}{\mathrm{S}}_2$ are monolayers. We use cathode lens microscopy and microprobe angle-resolved photoemission spectroscopy measurements to image the surface, determine twist angle, and map the electronic structure of these artificial heterostructures. For monolayer graphene on monolayer $\mathrm{Mo}{\mathrm{S}}_2$, the resulting band structure reveals the absence of hybridization between the graphene and $\mathrm{Mo}{\mathrm{S}}_2$ electronic states. Further, the graphene-derived electronic structure in the heterostructures remains essentially intact, irrespective of the twist angle between the two materials. In contrast, however, the electronic structure associated with the $\mathrm{Mo}{\mathrm{S}}_2$ layer is found to be twist-angle dependent; in particular, the relative difference in the energy of the valence band maximum at $\overline{\mathrm{\Gamma }}$ and $\overline{K}$ of the $\mathrm{Mo}{\mathrm{S}}_2$ layer varies from approximately 0 to 0.2 eV. Our results suggest that monolayer $\mathrm{Mo}{\mathrm{S}}_2$ within the heterostructure becomes predominantly an indirect band-gap system for all twist angles except in the proximity of ${30}^{\circ }$. This result enables potential band-gap engineering in van der Waals heterostructures comprised of monolayer structures.

Figure 1

(a) Schematic of the photoemission process and configuration. (b) Brillouin zone (BZ) of Gr and surface Brillouin zone (SBZ) of $\mathrm{Mo}{\mathrm{S}}_2$ with a twist angle of θ. We define the high-symmetry points of Gr BZ (red) as $M\text{−}\mathrm{\Gamma }\text{−}K$ and those of $\mathrm{Mo}{\mathrm{S}}_2$ SBZ (blue) as $\overline{M}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$. (c) LEED patterns (upper plane) derived mostly from the graphene overlayer at 40 eV, and LEED pattern (middle plane) derived mostly from the $\mathrm{Mo}{\mathrm{S}}_2$ bottom layer at 45 eV. The diffraction spots are projected to the bottom plane to extract the twist angle.

Figure 2

(a) Constant energy map of a graphene overlayer heterostructure at a binding energy of 875 meV. (b) ARPES band map (left) and second-derivative-intensity plot (right) of the graphene-derived Dirac cone along the Γ-$K$ direction. (a) and (b) are acquired from the Gr overlayer with a twist angle of ${19}^{\circ }$ with respect to the $\mathrm{Mo}{\mathrm{S}}_2$ bottom layer. (c), (d) ARPES band map and corresponding second-derivative-intensity plot of a Gr overlayer with a twist angle of ${12}^{\circ }$ and ${28}^{\circ }$, respectively.

Figure 3

(a)–(d) ARPES band map along $\overline{M}\text{−}\overline{\mathrm{\Gamma }}\text{−}\overline{K}$ of the $\mathrm{Mo}{\mathrm{S}}_2$ layer with a twist angle of 5°, ${12}^{\circ },{19}^{\circ }$, and ${28}^{\circ }$, respectively. The green dashed curves are a Gr-derived band in heterostructures acquired from a tight-binding model. (e)–(h) Second-derivative plot of the uppermost valence band in (a)–(d).

Figure 4

Energy difference between $\overline{\mathrm{\Gamma }}$ and $\overline{K}$ versus twist angle in the $\mathrm{Gr}\text{/}\mathrm{Mo}{\mathrm{S}}_2$ (purple) and $\mathrm{Mo}{\mathrm{S}}_2\text{/}\mathrm{Gr}$ (green) heterostructures.