  The breathing honeycomb lattice hosts a topologically non-trivial bulk phase
due to the crystalline-symmetry of the system. Pseudospin-dependent edge states
which emerge at the interface between trivial and non-trivial regions can be
used for directional propagation of energy. Using the plasmonic metasurface as
an example system, we probe these states in the near and far-field using a
semi-analytical model. We give the conditions under which directionality is
observed and show that it is source position dependent. By probing with
circularly-polarized magnetic dipoles out of the plane, we first characterize
modes along the interface in terms of the enhancement of source emission due to
the metasurface. We then excite from the far-field with non-zero orbital
angular momentum beams. The position dependent directionality holds true for
all classical wave systems with a breathing honeycomb lattice. Our results show
that a metasurface in combination with a chiral two-dimensional material could
be used to guide light effectively on the nanoscale.
