Evolution and crossover from bulk subbands in ABC-stacked graphene to a three-dimensional Dirac cone structure in rhombohedral graphite

Ching-Hong Ho, Cheng-Peng Chang, Ming-Fa Lin

Published 2015-05-21Version 1

The bulk subbands in ABC-stacked $-layer graphene are analytically obtained using a non-perturbative effective Hamiltonian in the bulk subspace. It is for the first times ever that an explicit expression is given for an arbitrary number (N) of layers in this stacking configuration. In the increase of N, the gapped bulk subbands are shown to evolve toward zero energy and in the infinite limit, they touch linearly along a circle. This outcome is a manifestation of the dimensional crossover to a three-dimensional Dirac cone structure having been known to exist in rhombohedral graphite, where the Dirac points form nodal lines in a spiraling fashion and are projected onto the circle. The projection is shown to confine the flat surface subbands, which have been known to be chiral for reasoning the anomalous integer quantum Hall effects discovered in ABC-stacked few-layer graphene. The evolution and crossover indicate the zone-folding relation, which is tenable since the bulk lattice in rhombohedral graphite can be modelled by infinitely many ABC-stacked graphene layers.