  The existence of edge states is one of the most vital properties of
topological insulators. Although tremendous success has been accomplished in
describing and explaining edge states associated with PT symmetry breaking,
little work has been done on PT symmetry preserving cases. Two-dimensional
Schroedinger operators with super honeycomb lattice potentials always have
double Dirac cones at the Gamma point - the zero momentum point on their energy
bands due to C6 symmetry, PT symmetry, and the "folding" symmetry - caused by
an additional translation symmetry. There are two topologically different ways
to deform such a system by PT symmetry preserving but folding symmetry breaking
perturbations. Interestingly, there exist two gapped edge states on the
interface between such two kinds of perturbed materials. In this paper, we
illustrate the existence of such PT preserving edge states rigorously for the
first time. We use a domain wall modulated Schroedinger operator to model the
phenomenon under small perturbations and rigorously prove the existence of two
gapped edge states. We also provide a brief interpretation from the point of
view of "topology" by the parities of degenerate bulk modes. Our work
thoroughly explains the existence of "helical" like edge states in super
honeycomb configurations and lays a foundation for the descriptions of
topologies of such systems.
