▎ 摘　　要

Two-dimensional graphene is fascinating because of its unique electronic properties. From a fundamental perspective, one among them is the geometric phase structure near the Dirac points in the Brillouin zone, owing to the SU(2) nature of the Dirac cone wave functions. We ask if there are geometric phase structures in two dimensions which go beyond that of a Dirac cone. Here we write down a family of three-band continuum models of noninteracting fermions which have more intricate geometric phase structures. This is connected to the SU(3) nature of the wave functions near threefold degeneracies. We also give a tight-binding free fermion model on a two-dimensional graphene-like lattice where the threefold degeneracies are realized at fine-tuned points. Away from them, we obtain new "three-band" Dirac cone structures with associated nonstandard Landau level quantization, whose organization is strongly affected by the non-SU(2) or beyond-Dirac geometric phase structure of the fine-tuned points.