Soliton formation in an exciton-polariton condensate at a bound state in the continuum

Bound states in the continuum (BICs) are of special interest in photonics due to their theoretically infinite radiative lifetime. In this work, we take a specific example (a structure composed of GaN and a ${\mathrm{TiO}}_{2}$ photonic crystal slab), showcasing how the interactions affect BICs. The photonic BIC hosted by the photonic crystal slab couples with the excitons of GaN to form a polaritonic BIC with a negative mass. This allows condensation to be reached with a low threshold in a structure suitable for electrical injection, paving the way for room-temperature polariton microdevices. We study in detail how the repulsive interaction between exciton-polaritons affects the condensate distribution in reciprocal space and, consequently, the condensate's overlap with the BIC resonance and, therefore, the condensate lifetime. We study an intrinsic contribution related to the formation of a bright soliton and the extrinsic contribution related to the interaction with an excitonic reservoir induced by spatially focused nonresonant pumping. We then study the peculiar dynamics of the condensation process in a BIC state for interacting particles using Boltzmann equations and hybrid Boltzmann--Gross-Pitaevskii equations. We find optimal conditions allowing one to benefit from the long lifetime of the BIC for polariton condensation in a real structure.