Theory of optically induced Förster coupling in van der Waals coupled heterostructures

We investigate the impact of optically induced Förster coupling in van der Waals heterostructures consisting of graphene and a monolayer transition-metal dichalcogenide (TMD). In particular, we predict the corresponding dephasing rates and a fast energy transfer between the TMD layer and graphene being in the picosecond range. Exemplary we find a transition rate of thermalized excitons of about 4 ${\mathrm{ps}}^{-1}$ in a ${\mathrm{MoSe}}_2$-graphene stack at room temperature. This time scale is in good agreement with the recently measured exciton lifetime in this heterostructure.

Figure 1

Schematic illustration of the Förster coupling. (a) Real-space view: a TMD and a graphene layer with a distance $z$ to each other. Förster coupling between the layers leads to an energy transfer. (b) Momentum space view: excitons in the TMD and in the graphene couple via the Förster mechanism under conservation of energy and momentum. (c) Illustration of the coordinate transformation.

Figure 2

Förster induced broadening and energy renormalization of excitonic resonances. (a) Surface plot of the dephasing rate, Eq. (12), as a function of the excitonic center-of-mass momentum and the distance between the graphene and the TMD layer. Dephasing rate, Eq. (12), (b) as a function of the center-of-mass momentum of the TMD exciton for fixed layer distances and (c) as a function of the interlayer distance for fixed exciton momenta.

Figure 3

(a) Transition rate, Eqs. (12) and (19), as a function of the temperature of the exciton in the TMD for three different layer distances. (b) Transition rate as a function of the interlayer distance for three different exciton momenta.