Lieb polariton topological insulators

We predict that the interplay between the spin-orbit coupling, stemming from the transverse electric--transverse magnetic energy splitting, and the Zeeman effect in semiconductor microcavities supporting exciton-polariton quasiparticles, 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 honeycomb lattices. Such robustness makes possible the existence of nested unidirectional dark solitons that move steadily along the lattice edge.