title: Existence of Dirac cones in the Brillouin zone of diperiodic atomic crystals according to group theory.
abstract: We have considered non-magnetic materials with weak spin-orbit coupling, that are periodic in two non-collinear directions, and finite in the third, orthogonal direction. In some cases, the combined time-reversal and crystal symmetry of such systems, allows the existence of Dirac cones at certain points in the reciprocal space. We have investigated in a systematic way, all points of the Brillouin zone of all 80 diperiodic groups and have found sufficient conditions for the existence of s  =  1/2 Dirac fermions, with symmetry-provided band touching at the vertex of the Dirac cones. Conversely, complete linear dispersion is forbidden for orbital wave functions belonging to two-dimensional (2D) irreducible representations (irreps) of little groups that do not satisfy certain group theoretical conditions given in this paper. Our results are illustrated by a tight-binding example.
authors.affiliation: Institute of Physics, University of Belgrade, Pregrevica 118, 11080 Belgrade, Serbia.
authors.forename: V
authors.initials: V
authors.lastname: Damljanović
authors.forename: R
authors.initials: R
authors.lastname: Gajić