Formation Mechanism and Low-Temperature Instability of Exciton Rings

The macroscopic rings observed in the photoluminescence patterns of excitons in coupled quantum wells are explained by a mechanism of carrier imbalance, transport, and recombination. The rings originate from the spatial separation of $p$ and $n$ carriers, and occur at the interface of the $p$ and $n$ domains, where excitons are generated. We explore the states of excitons in the ring over a range of temperatures down to $380\mathrm{mK}$ and report a transition of the ring into a periodic array of aggregates, a new low-temperature ordered exciton state.

Figure 1

Exciton rings at different photoexcitation intensity: The pattern of indirect exciton PL at $T=380\mathrm{mK}$ and $V_{\mathrm{g}}=1.24\mathrm{V}$ for (a) $P_{\mathrm{ex}}=310\mu \mathrm{W}$ and (b) $P_{\mathrm{ex}}=930\mu \mathrm{W}$. The excitation spot size is ca. $30\mu \mathrm{m}$. The area of view is $410\times 330\mu \mathrm{m}$. (c) The carrier distribution as predicted by the transport model, Eq. (1), at two excitation intensities (the scales are in a.u.). (d) The CQW band diagram.

Figure 2

Pattern of indirect exciton PL for two sources at $T=380\mathrm{mK}$, $V_{\mathrm{g}}=1.24\mathrm{V}$, and $P_{\mathrm{ex}}=230\mu \mathrm{W}$ per beam for different separations (a)–(d) between the excitation spots. The area of view is $520\times 240\mu \mathrm{m}$; (e)–(g) theoretical prediction for the electron-hole interface evolution at decreasing distance between the two point sources (the scales are in a.u.). Note the ring attraction in (b),(c),(f).

Figure 3

Shrinkage of exciton rings to localized bright spots at nearly homogeneous excitation: Spatial PL pattern for indirect excitons at $T=1.8\mathrm{K}$, $V_{\mathrm{g}}=1.15\mathrm{V}$, and (a) $P_{\mathrm{ex}}=390\mu \mathrm{W}$ and (b) $P_{\mathrm{ex}}=600\mu \mathrm{W}$. With (a),(b), the area of view is $690\times 590\mu \mathrm{m}$. (c) Theoretical electron-hole interface for a point source of holes and a weaker point source of electrons. Arrows show interface displacement at increasing hole number. Note the ring shrinking around electron source. The shrinkage of ring $A$ (a),(b) of indirect excitons is detailed in (d) for $T=380\mathrm{mK}$, $V_{\mathrm{g}}=1.155\mathrm{V}$, and $P_{\mathrm{ex}}=77–160\mu \mathrm{W}$ (from left to right) with defocused excitation spot maximum moved to a location directly below ring $A$. With (d),(e), the area of view is $67\times 67\mu \mathrm{m}$ for each image. Ring shrinkage is accompanied by the onset of the direct exciton emission (e) indicating hot cores at the center of the collapsed rings.

Figure 4

Fragmented ring and localized spots in the (a) indirect and (b) direct exciton PL image. The area of view is $410\times 340\mu \mathrm{m}$. Note that the hot cores with high energy direct excitons, present in the localized spots, are absent in the ring fragments. (c) Exciton density Fourier transform peak height at the fragmentation period vanishes continuously at a critical temperature. (d) The phase diagram of the states of the external ring. The phase boundary of the modulated state observed at the lowest experimental temperatures (solid line) along with the ring onset region (dashed line) are marked.