Pattern formation in exciton system near quantum degeneracy

We discuss models of the modulational instability in a cold exciton system in coupled quantum wells. One mechanism involves exciton formation in a photoexcited electron–hole system in the presence of stimulated binding processes which build up near exciton degeneracy. It is shown that such processes may give rise to Turing instability leading to a spatially modulated state. The structure and symmetry of resulting patterns depend on dimensionality and symmetry. In the spatially uniform 2d electron–hole system, the instability leads to a triangular lattice pattern while, at an electron–hole interface, a periodic 1d pattern develops. Wavelength selection mechanism is analyzed, revealing that the transition is abrupt (type I) for the uniform 2d system, and continuous (type II) for the electron–hole interface. Another mechanism that could possibly drive the instability involves long-range attraction of the excitons. We illustrate how such an interaction can result from plasmon wind, derive stability criterion, and discuss likelihood of such a scenario.