Model of fragmentation of the exciton inner ring in semiconductor quantum wells

The appearance of nonhomogeneous structures of the indirect exciton density distribution in the region of the quantum well (in the region of the inner ring) is explained. The structure (the fragmentation) occurs due to the exciton condensed phase formation because of the interaction between excitons. The formation of the struc-ture is related with the nonequalibrity of the system, which is caused by the exciton finite lifetime and the presence of the pumping. The structure emerges in the shape of a set of islands or circles of the condensed phase. The structure type depends on the pumping intensity, the size of the laser spot, and disappears with increasing the temperature. The merging of two structures, created by different laser spots, is investigated at decreasing the distance between the centers of the spots.

Figure 1

The distribution of the indirect exciton density in the quantum well plane in the case of the pumping (6) with a changing pumping intensity in the case of narrow laser beams, $G_0$: (a) 0.0015, (b) 0.0055, (c) 0.0075, and (d) 0.035. The shape parameter is $\sigma =10$. The parameters of the system (in dimensionless units) are $d_1=0.1$, $b_1=-2.3$, $\tau =100$. (e) The density profile of the pumping through the center of the system for the set of pumping “a–d.”

Figure 2

The distribution of the exciton density in case of the pumping (6) with changing the pumping intensity $G_0$: (a) 0.0015, (b) 0.0045, and (c) 0.0065. The shape parameter is $\sigma =24$. The parameters of the system are the same as in Fig. 1.

Figure 3

The distribution of the exciton density with increasing the width of the laser beam $\sigma$: (a) 14, (b) 20, (c) 24, and (d) 30. $G_0=0.0055$ is fixed for all images. The parameters of the system are the same as in Fig. 1

Figure 4

The distribution of the exciton density in the plane of the quantum well in the case of the pumping by two spatially separated sources the distance $r_{12}$ between the centers of which is (a) 60.5, (b) 48.5, (c) 36.5, (d) 24.5, (e) 16.5, and (f) 0. The parameters of the system are $G_0=0.0055$, $d_1=0.1$, $\tau =100$, $b_1=-2.3$, $T=2$ K, and $\sigma =28$.

Figure 5

The density distribution of indirect excitons at the same pumping $G_0=0.0055$ and the pumping width $\sigma =24$ with increasing the temperature $T$: (a) 2, (b) 3, (c) 3.5, (d) 4, (e) 5, and (f) 7 K. The critical temperature $T_2=6$ K, the other parameters of the system are the same as in Fig. 3.