  Supplementary Information Content:
  1. Sample preparation;
  2. Background subtraction of Shubnikov-de Haas (SdH) oscillations;
  3. The effect of density inhomogeneity on the quantum scattering time tau_q;
  4. Determine the concentration of charged impurity n_imp at a distance z;
  5. Scattering from charges in the bulk of the SiO_2 substrate.
