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## Photonic engineering providing conditions for direct exciton macroscopic coherence at elevated temperatures

The possibility to observe a macroscopically coherent state in a gas of two-dimensional direct excitons at temperatures up to tens of Kelvin is described. The dramatic increase of the exciton lifetime allowing effective thermalization is predicted for the o -resonant cavities that strongly suppress exciton recombination. The material

systems considered are single GaAs quantum wells of di erent thicknesses and a transition metal dichalcogenide

monolayer, embedded in a layered medium with subwavelength period. The quantum hydrodynamic approach

combined with the Bogoliubov description yield the one-body density matrix of the system. Employing the

Kosterlitz-Thouless \dielectric screening" problem to account for vortices, we obtain the superfluid and the condensate densities and the critical temperature of the Berezinskii-Kosterlitz-Thouless crossover, for all geometries in consideration. Experimentally observable manyfold increase of the photoluminescence intensity from the structure as it is cooled below the critical temperature is predicted.