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Group-theoretical analysis of two-dimensional hexagonal materials

Two-dimensional hexagonal materials such as graphene and silicene have highly symmetric crystal structures and Dirac cones at the K point, which induce novel electronic properties. In this report, we calculate their electronic structures by using density functional theory and analyze their band structures on the basis of the group theory. Dirac cones frequently appear when the symmetry at the K point is high; thus, two-dimensional irreducible representations are included. We discuss the relationship between symmetry and the appearance of the Dirac cone.