Signatures of Dirac-Weyl fermions in long organic molecules

Oligoacenes are molecules which consist of N linearly fused benzene rings. They have been subject of intensive research since they were suspected to support correlated ground states with charge or spin ordering. In addition, they have been considered promising for technological application in organic electronics. We use ab-intio calculations in order to investigate how the optical gap of the molecule decreases with increasing length N. Intriguingly, we find that the limit of a metallic wire is reached with strong oscillations that exhibit periodicity with several periods that are not commensurate with the lattice symmetries. In particular, at certain magical values N*=10, 21, 32,... the gap is (almost) vanishing and revives again at intermediate values. An explanation will be offered in terms of a band-structure argument.