ABC stacking faults embedded in Bernal graphite.

Bulk graphite has been studied extensively for the last 70 years [1,2] and has various polytypes: Bernal (AB), rhombohedral (ABC) and mixtures of the two. In nature, Bernal is the most stable and common form, however, weak lateral forces between graphite planes will lead to embedded stacking faults (ABC trilayer). We study two realisations of this system: a single stacking fault in a finite-thickness graphite film, as well as an infinite system with periodic stacking faults. We use the hybrid k · p - tight binding theory which accounts for the full set of Sloczweski-Weiss-McClure parameters for graphite [1, 2] supplemented by self-consistent Hartree computation of potentials near stacking faults. We show that the electronic dispersion of 2D states localized [3] on the stacking faults consists of three Dirac cones shifted away from the K/K’-point. Correspondingly, at the Fermi energy, there are 3 hole Fermi pockets, well isolated from bulk states with distinctive Shubnikov-de Haas oscillation periods and cyclotron resonance frequencies. The computed spectrum in magnetic field confirms the semiclassical picture and reveals explicitly the formation of 2D Landau levels.

[1] J. W. McClure. Phys. Rev., 108:612–618, Nov 1957.

[2] J. C. Slonczewski and P. R. Weiss. Phys. Rev., 109:272–279, Jan 1958.

[3] D. P. Arovas and F. Guinea. Phys. Rev. B, 78:245416, Dec 2008.