Probing plasmons in graphene by resonance energy transfer

We theoretically propose an experimental method to probe electronic excitations in graphene—a monoatomic layer of carbon—by monitoring the fluorescence quenching of a semiconductor quantum dot (or a dye molecule) due to the resonance energy transfer to the graphene sheet. We show how the dispersion relation of plasmons in graphene can be accurately extracted by varying the back-gate voltage and the distance between the quantum dot and graphene.

Figure 1

Density plot of (a) $\mathit{Im}\left[{\Pi }_0^r(q,\epsilon )\right]$ and (b) $\mathit{Im}\left[{\Pi }_{\mathit{RPA}}^r(q,\epsilon )\right]$ in units of $\frac{\mu }{{\hslash }^2{v}_f^2}$. Checkerboard pattern emphasizes regions where the imaginary part of the polarization operator vanishes exactly.

Figure 2

Regimes of asymptotic dependence of quenching efficiency on the QD-graphene distance $z$, at $z\to \infty$ (regimes I, II and III) and at $z\to 0$ (regime IV).

Figure 3

(a) Dependence of the quenching efficiency ${\varphi }_q$ on the QD-graphene distance $z$. (b) The filled area shows where ${\varphi }_q$(z) is between 1000 and 1 at a given excitation energy $\epsilon /\mu$. The red (left) and black (right) circles mark ${\varphi }_q\left(z\right)$=1000 and ${\varphi }_q\left(z\right)$=1 contour lines, respectively.

Figure 4

QE decay rate $q^{*}$ plotted vs $\epsilon /\mu$. Circles (black), squares (red), and triangles (blue) correspond to single-particle approximation, RPA for free-standing graphene (vacuum) and RPA for graphene on substrate (SiO${}_2$, $\kappa$=4), respectively.