  We predict that the interplay between the spin-orbit coupling, stemming from
the TE-TM energy splitting, and the Zeeman effect in semiconductor
microcavities supporting exci- ton-polariton quasi-particles results in the
appearance of unidirectional linear topological edge states when the top
microcavity mirror is patterned to form a truncated dislocated Lieb lattice of
cylindrical pillars. Periodic nonlinear edge states are found to emerge from
the linear ones. They are strongly localized across the interface and they are
remarkably robust in comparison to their counterparts in hexagonal lattices.
Such robustness makes possible the existence of nested unidirectional dark
solitons that move steadily along the lattice edge.

Mesoscale and Nanoscale Physics;Pattern Formation and Solitons;Optics