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

摘要

Rhombohedral graphite behaves like a topological semimetal, possessing flat surface subbands while being semimetallic in the bulk. The bulk-surface correspondence arises from the ABC-stacking configuration of graphene layers. The bulk subbands in rhombohedral graphite can be interpreted as a three-dimensional Dirac cone structure, whose Dirac points form continuous lines spiraling in momentum space. In this paper, we study the evolution of gapped bulk subbands in ABC-stacked N-layer graphene with an increase of N, and their dimensional crossover to the three-dimensional Dirac cone structure in the bulk limit, where the bulk gap closes up at the Dirac-point spirals. To clarify the effect of coupling to the surface subbands, we use a nonperturbative effective Hamiltonian closed in the bulk subspace. As a consequence, the wavelength of the standing-wave function across the stack of layers depends on the in-plane Bloch momentum. In the bulk limit, the coupling vanishes and hence the wavelength is irrelevant to the surface.