6 and and Kosterlitz-Thouless temperature can be calculated by using Eq. (4) with the substitution of the renormalized sound velocity from Eq. (7) instead of c$_{s}$ = β ( n, n$_{e}$ ) U$_{0}$n/M for the single quantum well. The calculation of the phenomenological parameters β ( n, n$_{e}$ ) for a single quantum well in the presence of 2DEG and and θ ( n, n$_{e}$, D ) for CQWs with the number of electrons higher than the number of holes is an open question which should be answered by future work. The K-T transition temperature T$_{c}$ obtained in our calculations as a function of the exciton density n in CQWs is presented in Fig. 1. It is shown that T$_{c}$ increases monotonically with increasing exciton density n and the inter-well separation D , which can be explained by the fact that the dipole-dipole repulsion causing the superfluidity increases if D increases. Furthermore, the results of our calculations show that T$_{c}$ increases when β ( n, n$_{e}$ ) for a single well or θ ( n, n$_{e}$, D ) for CQWs increase. According to Fig. 1, analogously to the exciton-electron system a single quantum well at the fixed temperature the superfluidity in CQWs exists at the exciton densities greater than the critical one. This critical exciton density increases, when the temperature increases and the interwell separation D decreases. Increasing β ( n, n$_{e}$ ) for a single quantum well or θ ( n, n$_{e}$, D ) for CQWs results in the decreasing critical exciton density. An experimental observation [13] has been reported on a sharp increase in the average photocurrent at the critical voltage V$_{g}$ = − 36 V and hysteresis in the I-V characteristics with subsequent variation of V$_{g}$ which is indicative of the formation of a photocurrent filament [22] from the undoped GaAs layer into the 2DEG in the SHQW. It has been observed in Ref. [13] that there is concurrent, significant changes in the time-integrated excitonic PL at V$_{g}$ = − 36 V. The data show that shortly after excitation at V$_{g}$ = − 36 V, the PL intensity at the filament position is approximately a factor of 8 larger than the PL intensity observed at the same point and time with V$_{g}$ = 0 V even though the residual laser excitation intensity at the filament position is unchanged. TR PL profile data [13] shows that there is no observed delay between the PL peaks in the photoexcitation and the filament regions indicating that no in-plane transport of excitons from the excitation region to the filament region is observed. However, the transport of excitons in a time less than 0 . 1 ns (the experimental resolution time) cannot be ruled out. The data suggests that an exciton excitation energy transport mechanism is responsible for the fast observation of 1550 meV PL from the filament region. One possibility is that in response to the filament-induced potential, excitons undergo a Kosterlitz-Thouless superfluid transition [19] with a long-range transport of exciton excitation energy. Theory points out that exciton superfluidity does not involve transport of mass; instead it involves a transport of excitation energy [23]. The filament-induced increase in exciton density and lifetime along with efficient electron-exciton scattering [24] in the presence of the 2DEG are conducive to exciton condensation. Using theoretical results [25] we estimate that the peak exciton density