  We consider the fate of the Dirac points in the spectrum of a honeycomb
optical lattice in the presence of a harmonic confining potential. By
numerically solving the tight binding model we calculate the density of states,
and find that the energy dependence can be understood from analytical
arguments. In addition, we show that the density of states of the harmonically
trapped lattice system can be understood by application of a local density
approximation based on the density of states of the homogeneous lattice. The
Dirac points are found to survive locally in the trap as evidenced by the local
density of states. They furthermore give rise to a distinct spatial profile of
a noninteracting Fermi gas.
