Spin Currents in a Coherent Exciton Gas

We report the observation of spin currents in a coherent gas of indirect excitons. The realized long-range spin currents originate from the formation of a coherent gas of bosonic pairs—a new mechanism to suppress the spin relaxation. The spin currents result in the appearance of a variety of polarization patterns, including helical patterns, four-leaf patterns, spiral patterns, bell patterns, and periodic patterns. We demonstrate control of the spin currents by a magnetic field. We also present a theory of coherent exciton spin transport that describes the observed exciton polarization patterns and indicates the trajectories of the spin currents.

Figure 1

Polarization patterns in exciton emission. (a) Diagram of the CQW: $e$, electron; $h$, hole. (b) Schematic of exciton formation in the external ring (left) and LBS ring (right); excitons (red) form on the boundary of hole-rich (blue) and electron-rich (green) areas. Exciton transport is indicated by red arrows. (c) A segment of the emission pattern of indirect excitons showing the external ring (left) and multiple LBS. (d),(e) Patterns of linear $P_{\mathrm{lin}}=(I_x-I_y)/(I_x+I_y)$ (d) and circular $P_{\sigma }=(I_{{\sigma }^{+}}-I_{{\sigma }^{-}})/(I_{{\sigma }^{+}}+I_{{\sigma }^{-}})$ (e) polarization of the emission of indirect excitons in the region shown in (c). $T_{\mathrm{bath}}=0.1\mathrm{K}$.

Figure 2

Control of polarization patterns. Measured (a) and simulated (b) patterns of linear polarization of the emission of indirect excitons $P_{\mathrm{lin}}$ in the region of LBS for different magnetic fields perpendicular to the QW plane $B$. Measured (c) and simulated (d) azimuthal variation of $P_{\mathrm{lin}}$ at a distance from the LBS center $r=9\mu \mathrm{m}$ for $B=0$ (black) and 7 T (red). Angles are measured from the $y$ axis. Measured (e) and simulated (f) patterns of circular polarization of the emission of indirect excitons $P_{\sigma }$ in the region of LBS for different $B$. Measured (g) and simulated (h) cross sections of $P_{\sigma }$ at $x=0$ for $B=0$ (black) and 7 T (red). For all data, $T_{\mathrm{bath}}=0.1\mathrm{K}$; the LBS is at (105,75) in Fig. 1c. See the Supplemental Material [31].

Figure 3

Spin textures. Simulated in-plane exciton polarization (a), electron spin (b), and hole spin (c) patterns. (d) Schematic of exciton momentum (black arrows) and linear polarization (red lines) patterns. Schematic of effective magnetic fields given by the Dresselhaus SO interaction for electrons (e) and holes (f). Exciton polarization (g), electron spin (h), and hole spin (i) patterns in applied magnetic field $B=7\mathrm{T}$. The lines (arrows) and the color visualize the orientation of the linear polarization (spin).