Figure 3: Low-temperature WAL in graphene on WS₂.

(a–c) Ensemble-averaged MC curves (symbols) obtained from measurements performed in different ranges of V_g (I, II and III, respectively), at several different temperatures below 8 K. The square MC Δσ=σ(B≠0)–σ(B=0) clearly exhibits a peak at zero B in all V_g ranges, whose height decreases as temperature is increased from 250 mK to 8 K, the expected behaviour of WAL due to SOI. Solid lines show the best fits to equation (1) in the main text. (d) Carrier density dependence of the relevant characteristic times. The filled squares represent the elastic scattering time (τ) estimated from the conductivity of our device at zero B; the filled black (red) circles represent the spin relaxation time (τ_so) extracted from the analysis of WAL (non-local spin-Hall effect). For comparison, open up-triangles represent the values of intervalley scattering time (τ_iv) reported in the literature, and extracted from the analysis of weak-localization measured in device similar to ours on different substrates, such as SiO₂ (black²⁷ and red²⁹), hBN (green³⁰) and GaAs (blue³¹). Open circles represent τ_so obtained from spin-valve studies on pristine graphene on SiO₂ (black³⁷ and red³⁸) and hBN (blue⁴⁰). (e) Temperature dependence of the phase-coherence time (τ_φ) of electrons in graphene-on-WS₂ extracted from the analysis of WAL performed in this work, for different gate-voltage ranges. The data clearly exhibit an increase in τ_φ with lowering temperature.