Finite-Dimensional Bistable Topological Insulators: From Small to Large

Photonic topological insulators supporting unidirectional topologically protected edge states represent an attractive platform for the realization of disorder- and backscattering-immune transport of edge excitations in both linear and nonlinear regimes. While the properties of the edge states at unclosed interfaces of two bulk media with different topologies are known, the existence of edge states in practical finite-dimensional topological insulators fully immersed in a nontopological environment remains largely unexplored. In this work, using realistic polariton topological insulators built from small-size honeycomb arrays of microcavity pillars as an example, it is shown how topological properties of the system build up upon gradual increase of its dimensionality. To account for the dissipative nature of the polariton condensate forming in the array of microcavity pillars, the impact of losses and resonant pump leading to rich bistability effects in this system is considered. The mechanism is described in accordance with which trivial-phase pump "selects" and excites specific nonlinear topological edge states circulating along the periphery of the structure in the azimuthal direction, dictated by the direction of the external applied magnetic field. The possibility of utilization of vortex pump with different topological charges for selective excitation of different edge currents is also shown.