  Topological materials rely on engineering global properties of their bulk
energy bands called topological invariants. These invariants, usually defined
over the entire Brillouin zone, are related to the existence of protected edge
states. However, for an important class of Hamiltonians corresponding to 2D
lattices with time-reversal and chiral symmetry (e.g. graphene), the existence
of edge states is linked to invariants that are not defined over the full 2D
Brillouin zone, but on reduced 1D sub-spaces. Here, we demonstrate a novel
scheme based on a combined real- and momentum-space measurement to directly
access these 1D topological invariants in lattices of semiconductor
microcavities confining exciton-polaritons. We extract these invariants in
arrays emulating the physics of regular and critically compressed graphene
sucht that Dirac cones have merged. Our scheme provides a direct evidence of
the bulk-edge correspondence in these systems, and opens the door to the
exploration of more complex topological effects, for example involving disorder
and interactions.
