  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 anti-matter. We introduce a topological nodal ring semimetal in
graphene with a quantized quantum Hall response, a robust one-dimensional
chiral edge mode and a quadratic Fermi-liquid spectrum for the quasiparticles
and quasiholes in the bulk. 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 nano-electronics and in quantum mechanical entanglement applied
to band theory.
