Polariton topological insulators with disclinations

We introduce polariton topological insulator on aperiodic array of microcavity pillars with disclination. This unique dissipative and nonlinear topological system can have discrete rotational symmetry not achievable in structures constructed on periodic arrays that qualitatively affects the structure of topological modes. In such system resonant optical pump can be used for selective excitation of topological states forming on the disclination core in the center, while imposing vorticity on the pump profile allows to excite not only the simplest disclination states, but also vortex-carrying disclination states. Strong repulsive nonlinearity of polaritonic system leads to increasing with pump amplitude tilt of the resonance curves and bistability, with rich possibilities for control of shapes of nonlinear disclination states within topological gap by pump frequency detuning. Stability analysis predicts remarkable robustness of both vortex-free and vortex-carrying nonlinear disclination states in this system. We show that when topological charge of the pump exceeds maximal allowed charge in the disclination array with a given discrete rotational symmetry, the stationary states form that contain vortex clusters in their phase distributions. Our results extend the concept of topological insulators with disclinations to the realm of nonlinear resonantly driven systems and show that rich bistability effects in them can be observed even for excited vortex-carrying topological states with different topological charges allowed by discrete rotational symmetry of the system.