  Starting from a minimal model for a 2D nodal loop semimetal, we study the
effect of chiral mass gap terms. The resulting Dirac loop anomalous Hall
insulator's Chern number is the phase winding number of the mass gap terms on
the loop. We provide simple lattice models, analyze the topological phases and
generalize a previous index characterizing topological transitions. The
responses of the Dirac loop anomalous Hall and quantum spin Hall insulators to
a magnetic field's vector potential are also studied both in weak and strong
field regimes, as well as the edge states in a ribbon geometry.
