Defect-Driven Superfluid Crossover for Two-Dimensional Dipolar Excitons Trapped at Thermodynamic Equilibrium

We study ultra-cold dipolar excitons confined in a 10$\mu$m trap of a double GaAs quantum well. Based on the local density approximation, we unveil for the first time the equation of state of excitons at pure thermodynamic equilibrium. In this regime we show that, below a critical temperature of about $1$ Kelvin, a superfluid forms in the inner region of the trap at a local exciton density $n \sim 2-3 \, 10^{10} \text{cm}^{-2}$, encircled by a more dilute and normal component in the outer rim of the trap. Remarkably, this spatial arrangement correlates directly with the concentration of defects in the exciton density which exhibits a sudden decrease at the onset of superfluidity, thus pointing towards an underlying Berezinskii-Kosterlitz-Thouless mechanism.