  We report on transport properties of the super-honeycomb lattice, the band
structure of which possesses a flat band and Dirac cones, according to the
tight-binding approximation. This super-honeycomb model combines the honeycomb
lattice and the Lieb lattice and displays the properties of both. The
super-honeycomb lattice also represents a hybrid fermionic and bosonic system,
which is rarely seen in nature. By choosing the phases of input beams properly,
the flat-band mode of the super-honeycomb will be excited and the input beams
will exhibit strong localization during propagation. On the other hand, if the
modes of Dirac cones of the super-honeycomb lattice are excited, one will
observe conical diffraction. Furthermore, if the input beam is properly chosen
to excite a sublattice of the super-honeycomb lattice and the modes of Dirac
cones with different pseudospins, e.g., the three-beam interference pattern,
the pseudospin-mediated vortices will be observed.
