Hanle model of a spin-orbit coupled Bose-Einstein condensate of excitons in semiconductor quantum wells

We present a theoretical model of a driven-dissipative spin-orbit coupled Bose-Einstein condensate of indirect excitons in semiconductor quantum wells (QW's). Our steady-state solution of the problem shares analogies with the Hanle effect in an optical orientation experiment. The role of the spin pump in our case is played by boson stimulated scattering into the linearly-polarized ground state and the depolarization occurs as a result of long-range exchange interaction between electrons and holes. Our theory agrees with the recent experiment [A. A. High et al., Phys. Rev. Lett. 110, 246403 (2013)], where spontaneous emergence of spatial coherence and polarization texture have been observed. As a complementary test, we discuss a configuration where an external magnetic field is applied in the structure plane.