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

We provide a theoretical description of the polarization pattern and phase singularities experimentally evidenced recently in a condensate of indirect excitons [H. High et al., Nature 483, 584-588 (2012)]. We show that the averaging of the electron and hole orbital motion leads to a comparable spin-orbit interaction for both type of carriers. We demonstrate that the interplay between a radial coherent flux of bright indirect excitons and the Dresselhaus spin-orbit interaction results in the formation of spin domains and of topological defects similar to Skyrmions. We reproduce qualitatively all the features of the experimental data and obtain polarization pattern as in the optical spin Hall effect despite the different symmetry of the spin-orbit interactions.