Analysis of the Spatial Separation of Carrier Spin by the Valley Hall Effect in Monolayer WSe2 Transistors

Monolayers of semiconducting transition metal dichalcogenides (TMDCs) exhibit a valley Hall effect (VHE) in which the carriers in the K (K’) valley acquire a velocity, v(-v) perpendicular the applied electric field, E [1,2,3]. As the K and K’ bands split by spin, the resulting valley current is also a spin current. For a sample of finite width perpendicular to the direction of an applied electric field E, this leads to a steady-state accumulation of spin and valley polarized carriers at the edges. We have investigated the VHE in ambipolar WSe₂ field-effect transistors in both n- and p- type regimes using spatial imaging of the spin and valley polarization by the optical Kerr rotation (KR) at 20 K. Here we quantitatively interpret the magnitude of the measured KR through a model of the optical response for unequal carrier populations in the valleys to obtain an estimate of the experimental spin/valley imbalance. We compare our findings to predictions of a spin diffusion model. This allows us to infer a spin and valley lifetime compatible with previous time-resolved measurements of spin-polarized carriers [4].
[1] Mak et al. Science 344, 1489-92 (2014).
[2] Xiao et al. PRL 108, 196802 (2012).
[3] Lee et al. Nat. Nano. 11, 421-5 (2016).
[4] Hsu et al. Nat. Comm. 8963 (2015)