  We demonstrate the emergence and dynamics of intra-particle entanglement in
massless Dirac fermions. This entanglement, generated by spin-orbit coupling,
arises between the spin and sublattice pseudospin of electrons in graphene. The
entanglement is a complex dynamic quantity but is generally large, independent
of the initial state. Its time dependence implies a dynamical violation of a
Bell inequality, while its magnitude indicates that large intra-particle
entanglement is a general feature of graphene on a substrate. These features
are also expected to impact entanglement between pairs of particles, and may be
detectable in experiments that combine Cooper pair splitting with nonlocal
measurements of spin-spin correlation in mesoscopic devices based on Dirac
materials.
