Ultrahigh Magnetic Field Study of Layer Split Bands in Graphite

We report studies of the magnetospectroscopy of graphite into a new regime of high energies and ultrahigh magnetic fields which allows us to perform the first spectroscopic studies of the interlayer split-off bands, $E_1$ and $E_2$. These bands can be well described by an asymmetric bilayer model and have only a small interlayer band gap asymmetry. We show that all of the properties of the electrons and holes can be described by a simple relativistic behavior determined by ${\gamma }_0$ and ${\gamma }_1$.

Figure 1

(a) Schematic view of the experimental system, (b) graphite band structure, (c) typical time dependence of the magnetic field and sample transmission for 1220 nm radiation.

Figure 2

(a) Magnetotransmission as a function of magnetic field (original data and spectra filtered to remove $E_3\pm$ transitions) for a series of wavelengths with arrows shown to denote the transitions to the split-off bands, (b) Fourier transforms as a function of $1/B$ for the traces shown in (a), (c) plots of the values of $1/B_n$ versus (arbitrary) harmonic index for the $E_3^{-}-E_3^{+}$ (right-hand group) and $E_2-E_3^{+}$ (left-hand group) transitions for different photon wavelengths from 1550 to 633 nm, together with linear fits.

Figure 3

Energy momentum relation for interband excitations in graphite deduced from the periodicity of the magneto-oscillations from Fourier transformation (points) and from fitting the values of $1/B_n$ compared with the values from Eq. (8) (lines), low energy (229 meV) data from 26. The $H$-point dispersion comes from $n=1$ to $n=2$ interband transitions giving $v=1.03\times {10}^6\mathrm{m}/\mathrm{s}$ [24].

Figure 4

Transition energies (points) as determined from the Fourier filtered plots shown in Fig. 2 and as calculated (lines) from the ABM for all possible split-off transitions from $n$ to $n\pm 1$, including the asymmetry term $\delta$ and using asymmetric velocities $v$.