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We provide a theoretical description of the polarization pattern and phasesingularities experimentally evidenced recently in a condensate of indirectexcitons [H. High et al., Nature 483, 584-588 (2012)]. We show that theaveraging of the electron and hole orbital motion leads to a comparablespin-orbit interaction for both type of carriers. We demonstrate that theinterplay between a radial coherent flux of bright indirect excitons and theDresselhaus spin-orbit interaction results in the formation of spin domains andof topological defects similar to Skyrmions. We reproduce qualitatively all thefeatures of the experimental data and obtain polarization pattern as in theoptical spin Hall effect despite the different symmetry of the spin-orbitinteractions.

Skyrmion Formation and Optical Spin-Hall Effect in an Expanding Coherent Cloud of Indirect Excitons