Fig. 1: The long-distance spin-valley transport in IXs in MoSe₂/WSe₂ HS.

a The circular polarization of IX PL. The blue (red) spectrum is co-polarized (cross-polarized) with the circularly polarized laser excitation. b Co-polarized \({I}_{{\sigma }^{+}}\) (blue) and cross-polarized \({I}_{{\sigma }^{-}}\) (red) IX PL intensity vs. the distance from the laser excitation spot centered at x = 0. The HS active area extends from x ~ − 3 to 10 μm. The polarized IX PL propagates through the entire HS. c The degree of circular polarization of IX PL \(P=({I}_{{\sigma }^{+}}-{I}_{{\sigma }^{-}})/({I}_{{\sigma }^{+}}+{I}_{{\sigma }^{-}})\) vs. the transport distance. No decay is observed for the polarization transport for IXs over the entire HS. The laser excitation power P_ex = 0.2 mW, T = 1.7 K (a–c). d–f Normalized spin density profiles \({I}_{{{{\rm{spin}}}}}={I}_{{\sigma }^{+}}-{I}_{{\sigma }^{-}}\) for the LE-IXs for different P_ex (d, e) and temperatures (f). In (d), P_ex = 2, 10, 50, 200 μW (bottom to top). In (e), P_ex = 0.2, 1, 2, 4 mW (top to bottom). In (c), T = 3.5, 15, 50 K (top to bottom). The spin density transport nonmonotonically varies with increasing P_ex, increases at P_ex ≲ 0.2 mW (d) and reduces at P_ex ≳ 0.2 mW (e), and vanishes at high temperatures (f). The dashed line in (b–f) shows the DX luminescence profile in the MoSe₂ ML, this profile is close to the laser excitation profile for short-range DX transport. The LE-IX spectra are separated from the HE-IX spectra by the spectral integration in the range E < 1.4 eV (b–f). The HE-IXs appear in the spectra at high P_ex ≳ 0.2 mW (Fig. 3). T = 3.5 K (d,e), P_ex = 0.2 mW (f). The  ~ 2 μm laser spot is centered at x = 0 (a–f).