  We propose theoretically a scheme to get a room-temperature 2D topological
exciton-polariton laser with propagating topological lasing modes. The
structure uses guided modes in a photonic crystal slab. A ZnO layer provides
strong excitonic resonances stable at room temperature. It is capped by a
TiO$_2$ layer pierced by a triangular lattice. The exciton-polariton modes of
the 3D structure are computed by solving numerically Maxwell's equations
including the excitonic response. The designed triangular lattice shows a
transverse electric gap. The triangular lattice is shown to be the limit of a
staggered honeycomb lattice when one of the sub-lattices vanishes. Its topology
can be characterized by symmetry indicators. The interface between two shifted
triangular lattices supports two counter-propagating modes lying in the gap of
the bulk modes. The interface states are analogous to quantum pseudospin Hall
interface states. These modes show orthogonal polarizations. They can be
selectively excited using polarized excitation and are well-protected from
back-scattering. These modes can benefit from the exciton-polariton gain at
room temperature because of their sufficiently large exciton fraction and
favorable position in energy. The strong localization of these propagating
modes makes them suitable to host topological lasing triggered by a
non-resonant pump localized on the interface.
