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We study the equilibrium properties of self-bound droplets in two-dimensionalBose mixtures employing the time-dependent Hartree-Fock-Bogoliubov theory. Thistheory allows one to understand both the many-body and temperature effectsbeyond the Lee-Huang-Yang description. We calculate higher-order corrections tothe excitations, the sound velocity, and the energy of the droplet. Our resultsfor the ground-state energy are compared with the diffusion Monte Carlo dataand good agreement is found. The behavior of the depletion and anomalousdensity of the droplet is also discussed. At finite temperature, we show thatthe droplet emerges at temperatures well below theBerezinskii-Kosterlitz-Thouless transition temperature. The criticaltemperature strongly depends on the interspecies interactions. Our study isextended to the finite size droplet by numerically solving the generalizedfinite-temperature Gross-Pitaevskii equation which is obtainedself-consistently from our formalism in the framework of the local densityapproximation.

Many-body and temperature effects in two-dimensional quantum droplets in Bose-Bose mixtures