Graphite Landau levels in the presence of trigonal warping

Abstract

The Landau levels for the $\pi$ bands of graphite are calculated using the Slonczewski-Weiss-McClure energy-band model. Bohr-Sommerfeld quantization is used to calculate two new types of magnetic energy levels which trigonal warping introduces. The method is valid for any magnitude of ${\gamma }_3$. The trigonal warping introduces off-axis energy extrema near the band edge $E_3$ and special magnetic energy levels which can exist between these extrema and exhibit an $H^{\frac{1}{2}}$ dependence. The usual majority Landau levels with an $H$ dependence are found outside the region of these off-axis energy extrema.