High-Energy Limit of Massless Dirac Fermions in Multilayer Graphene using Magneto-Optical Transmission Spectroscopy

We have investigated the absorption spectrum of multilayer graphene in high magnetic fields. The low-energy part of the spectrum of electrons in graphene is well described by the relativistic Dirac equation with a linear dispersion relation. However, at higher energies ($>500\mathrm{meV}$) a deviation from the ideal behavior of Dirac particles is observed. At an energy of 1.25 eV, the deviation from linearity is $\simeq 40\mathrm{meV}$. This result is in good agreement with the theoretical model, which includes trigonal warping of the Fermi surface and higher-order band corrections. Polarization-resolved measurements show no observable electron-hole asymmetry.

Figure 1

(a) Representative differential transmission spectra (the $B=0\mathrm{T}$ spectra has been subtracted) measured at the given magnetic fields. (b) Positions of the absorption lines as a function of the square root of the magnetic field. Stars represent data obtained in near visible range, circles denotes the data measured by FTS. Dashed lines are calculated energy of the transitions between LLs assuming a linear dispersion. On the right-hand side the observed transition $L_{-m(-n)}\to L_{n(m)}$ LLs are denoted.

Figure 2

The deviation from linearity $\Delta E$ [from the data in Fig. 1b, with the same colors] for the different transitions as a function of the energy ${\Delta }_n^0$. The solid lines are the result of the theoretical calculation as described in the text.

Figure 3

(a) The polarization selection rules for optical transitions in graphene. (b) The differential transmission spectra for both circular polarization of the light.