Resonance energy transfer from a dye molecule to graphene

We study the distance dependence of the rate of resonance energy transfer from the excited state of a dye to the pi system of graphene. Using the tight-binding model for the pi system and the Dirac cone approximation, we obtain the analytic expression for the rate of energy transfer from an electronically excited dye to graphene. While in traditional fluorescence resonance energy transfer, the rate has a (distance)(-6) dependence, we find that the distance dependence in this case is quite different. Our calculation of rate in the case of the two dyes, pyrene and nile blue, shows that the distance dependence is Yukawa type. We have also studied the effect of doping on energy transfer to graphene. Doping does not modify the rate for electronic excitation energy transfer significantly. However, in the case of vibrational transfer, the rate is found to be increased by an order of magnitude due to doping. This can be attributed to the nonzero density of states at the Fermi level that results from doping.