Two possible tunnelling channels under the configuration of Fig. 1d , illustrated here by an on-scale representation of the graphene first Brillouin zone (1BZ; dashed hexagon in the space of parallel wave vector k ∥ ), the surface-projected gold Fermi surface (orange circle, kF^Au is the Fermi wave vector of Au) and the TMD 1BZ (colour plot, showing the non-local surface conductivity for MoSe 2 at 2.1 eV photon energy). The two channels are (1) one-step tunnelling assisted by the creation of indirect TMD excitons (blue arrow) and (2) two-step tunnelling associated with phonon creation (purple arrow) followed by direct-exciton creation (green arrow). Direct excitons produce the intense feature at the Γ point in the TMD conductivity, while indirect excitons show up as maxima at special regions of the TMD 1BZ, such as the Q point (colour plot, showing the non-local surface conductivity (logarithmic scale) for MoSe 2 at 2.1 eV photon energy).
