Seeing Many-Body Effects in Single- and Few-Layer Graphene: Observation of Two-Dimensional Saddle-Point Excitons

Significant excitonic effects were observed in graphene by measuring its optical conductivity in a broad spectral range including the two-dimensional $\pi$-band saddle-point singularities in the electronic structure. The strong electron-hole interactions manifest themselves in an asymmetric resonance peaked at 4.62 eV, which is redshifted by nearly 600 meV from the value predicted by ab initio $GW$ calculations for the band-to-band transitions. The observed excitonic resonance is explained within a phenomenological model as a Fano interference of a strongly coupled excitonic state and a band continuum. Our experiment also showed a weak dependence of the excitonic resonance in few-layer graphene on layer thickness. This result reflects the effective cancellation of the increasingly screened repulsive electron-electron ($e\mathrm{\text{−}}e$) and attractive electron-hole ($e\mathrm{\text{−}}h$) interactions.

Figure 1

Experimental optical conductivity (solid line) and the universal optical conductivity (dashed line) of monolayer graphene in the spectral range of 0.2–5.5 eV. The experimental peak energy is 4.62 eV. Note the deviation of the optical conductivity from the universal value at low energies is attributed to spontaneous doping [16].

Figure 2

Fano theory of saddle-point excitons in graphene. Upper panels: optical conductivity of unperturbed band-to-band transitions ${\sigma }_{\mathrm{cont}}$ and the resultant conductivity from a Fano interference of the exciton state and the continuum; lower panels: Fano line shape of Eq. (1). (a) Illustration of the model using the JDOS near the 2D saddle point for ${\sigma }_{\mathrm{cont}}$ and the Fano parameters as described in the text. (b) Fit of experiment to the Fano model using the optical conductivity obtained from $GW$ calculations [7] for ${\sigma }_{\mathrm{cont}}$. The dashed line is the optical conductivity spectrum obtained from the full $GW$-Bethe-Salpeter calculation [7].

Figure 3

(a) Experimental optical conductivity for single- and few-layer graphene in the spectral range of 0.2–5.3 eV. The dashed line is a guide to the eye of the resonance peak. (b) Dependence of the peak energy of the excitonic resonance on layer thickness: experiment (symbols), values calculated from ab initio LDA, $GW$, and GWBS. The dashed lines show the calculated value for bulk graphite.