Stable gray soliton pinned by a defect in a microcavity-polariton condensate

We study the spatially localized dark state, called dark soliton, in a one-dimensional system of the non-resonantly pumped microcavity-polariton condensate (MPC). From the recent work by Xue and Matuszewski [Phys. Rev. Lett. 112, 216401 (2014)], we know that the dark soliton in the pure MPC system is unstable. But we find that a dark soliton pinned by a defect in the impure MPC becomes a gray soliton and can be stabilized by the presence of a defect. Moreover, the stable regime of the gray soliton is given in terms of the defect strength and pump parameter.