Characters of graphene’s symmetry group Dg80

Abstract

We have determined the characters of the diperiodic group Dg80—the symmetry group of the honeycomb lattice. We started from the general formula for construction of irreducible representations (irreps) of symmorphic space groups and have found characters by summing diagonal elements of irrep matrices. The result is given for every element of Dg80, not just for generators. We have calculated the Frobenius–Schur indicator for irreps of Dg80 and proved that all of them are equivalent to real representations.