Graphite from the Viewpoint of Landau Level Spectroscopy: An Effective Graphene Bilayer and Monolayer

We describe an infrared transmission study of a thin layer of bulk graphite in magnetic fields up to $B=34\mathrm{T}$. Two series of absorption lines whose energy scales as $\sqrt{B}$ and $B$ are present in the spectra and identified as contributions of massless holes at the $H$ point and massive electrons in the vicinity of the $K$ point, respectively. We find that the optical response of the $K$ point electrons corresponds, over a wide range of energy and magnetic field, to a graphene bilayer with an effective interlayer coupling $2{\gamma }_1$, twice the value for a real graphene bilayer, which reflects the crystal ordering of bulk graphite along the $c$ axis. The $K$ point electrons thus behave as massive Dirac fermions with a mass enhanced twice in comparison to a true graphene bilayer.

Figure 1

Transmission spectra of a thin graphite layer at selected magnetic fields. The plotted energy is scaled as $E/\sqrt{B}$ to emphasize the Dirac fermion-like features in spectra (indicated by dashed vertical lines). Arrows denote transitions arising at the $K$ point which evolve (nearly linearly) with $B$. Data above $B=23\mathrm{T}$ were taken on second sample with a higher density of graphite flakes.

Figure 2

(a) Positions of the absorption lines related to the $H$ point as a function of $\sqrt{B}$. The solid and dashed lines represent expected positions of absorption lines for $\tilde{c}=1.02\times {10}^6\mathrm{m}/\mathrm{s}$ (${\gamma }_0=3.2\mathrm{eV}$). (b) Positions of the absorption lines related to the $K$ point as a function of $B$. The solid lines show expected dipole-allowed transitions in a graphene bilayer with an effective coupling $2{\gamma }_1$ calculated using Eq. (1) for ${\gamma }_0=3.2\mathrm{eV}$ and ${\gamma }_1=0.375\mathrm{eV}$. Grey data points were taken on highly oriented pyrolytic graphite, which exhibit a behavior nearly identical to natural graphite [21]. The inset schematically shows the observed interband transitions in the effective bilayer.