We theoretically investigate polariton condensates trapped in pillar microcavities ordered in honeycomb lattices. We consider the system with TE-TM splitting and external non-uniform magnetic field. Two magnetic patterns, PT - symmetric and antisymmetric, are examined. The band structures of two-dimensional lattices and quasi-one-dimensional systems (ribbons) are calculated. Finally, we compute the Chern numbers and demonstrate the possibility to form a polariton Chern topological insulator with zero average magnetic field.
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