Probing the Band Structure of Mono-, Bi- and Tri-layer Graphene by Infrared Absorption Spectroscopy

Absorption spectra in the infrared range (0.3 -- 1 eV) were measured for large-area, single-crystal mono-, bi- and tri-layer graphene samples produced by mechanical exfoliation of graphite. A constant absorption independent of photon energy was observed for monolayer samples. For the bi-layer, a strong absorption peak was seen at 0.37eV. The absorption spectrum of tri-layer graphene was found to be well represented by the sum of those of a mono- and a bi-layer, with the latter spectrum scaled by 2$^{1/2}$ in photon energy. These observations can be explained qualitatively within a tight-binding band structure picture and yield an accurate determination of the nearest-layer hopping constant ($\gamma _1 )$. Explicit calculations of the absorption spectra show that an optimal fit to experiment requires a shift of the Fermi energy of approximately 100 meV from the Dirac point and an empirical broadening of tens of meV.