Topological nodal ring semimetal in graphene

Graphene is a two-dimensional Dirac semimetal showing interesting properties as a result of its dispersion relation with both quasiparticles and quasiholes or matter and antimatter. We introduce a topological nodal ring semimetal in graphene with a robust one-dimensional chiral edge mode similar to the quantum Hall effect and a quadratic Fermi-liquid spectrum for the quasiparticles and quasiholes in the bulk. We describe its realization through circularly polarized light. The bulk band degeneracy at the Fermi energy is protected through a Z2 symmetry related to the two spin polarizations of an electron and a "double-orthogonality"structure in the sublattice and spin quantum numbers of the two crossing eigenstates. The system may have applications in nanoelectronics and in quantum mechanical entanglement applied to band theory.