Theory of exciton-polariton condensation in gap-confined eigenmodes

Exciton-polaritons are bosoniclike elementary excitations in semiconductors, which have been recently shown to display large occupancy of topologically protected polariton bound states in the continuum in suitably engineered photonic lattices [V. Ardizzone et al., Nature (London) 605, 447 (2022)], compatible with the definition of polariton condensation. However, a full theoretical description of such condensation mechanism that is based on a driven-dissipative framework like the nonequilibrium Gross-Pitaevskii equation (NEGPE) is still missing. Here, we report on a general multimode theory inspired to the standard NEGPE, showing that it allows to fully interpret the recent experimental findings in patterned photonic lattices, including emission characteristics and condensation thresholds. Beyond that, it is shown that the polariton condensation in these systems is actually the result of an interplay between negative mass confinement of polariton eigenstates (e.g., due to the photonic gap originated from the periodic pattern in plane) and polariton losses. We are then able to show that polariton condensation can also occur in gap-confined bright modes, i.e., coupling of quantum well excitons to a dark photonic mode is not necessarily required to achieve a macroscopic occupation with low population threshold.