  Spin-1/2 particles such as the electron are described by the Dirac equation,
which allows for two spin eigenvalues (up or down) and two types of energy
eigenvalues (positive or negative, corresponding to the electron and the
positron). A model of electrons hopping from atom to atom in graphene's
honeycomb lattice gives low-energy electronic excitations that obey a relation
formally identical to a 2+1 dimensional Dirac equation. Graphene's spin
equivalent, "pseudospin", arises from the degeneracy introduced by the
honeycomb lattice's two inequivalent atomic sites per unit cell. Previously it
has been thought that the usual electron spin and the pseudospin indexing the
graphene sublattice state are merely analogues. Here we show that the
pseudospin is also a real angular momentum. This identification explains the
suppression of electron backscattering in carbon nanotubes and the angular
dependence of light absorption by graphene. Furthermore, it demonstrates that
half-integer spin like that carried by the quarks and leptons can derive from
hidden substructure, not of the particles themselves, but rather of the space
in which these particles live.
