  We calculate the tunneling density-of-states (DOS) of a disorder-free
two-dimensional interacting electron system with a massless-Dirac band
Hamiltonian. The DOS exhibits two main features: i) linear growth at large
energies with a slope that is suppressed by quasiparticle velocity enhancement,
and ii) a rich structure of plasmaron peaks which appear at negative bias
voltages in an n-doped sample and at positive bias voltages in a p-doped
sample. We predict that the DOS at the Dirac point is non-zero even in the
absence of disorder because of electron-electron interactions, and that it is
then accurately proportional to the Fermi energy. The finite background DOS
observed at the Dirac point of graphene sheets and topological insulator
surfaces can therefore be an interaction effect rather than a disorder effect.
