## Fig xA Extracted inversion layer transport parameters for Sample a

Magnetic-field dependent resistivity and Hall-effect measurements were performed as a function of applied gate bias at room temperature and magnetic field intensities B up to 12 T. For all measurements, the drain of the Hall bridge structures was biased at VDS=1V, which resulted in effective biases as measured at the resistivity probes that Go 6983 did not exceed 0.34 V, whilst the substrate contact to the underlaying p-type layer was biased at 0 V. From the measured sheet resistivity RsRs and Hall coefficient RHRH, the conductivity tensor components σxxσxx and σxyσxy were obtained from:equation(1)σxx=RsRs2+RH2;andσxy=RHBRs2+RH2which, in principle, contain information about all carriers present in the sample according to the discretized mobility transform equations [8], [9] and [10]:equation(2)σxx=∑jSp(μj)+Sn(μj)1+μj2B2equation(3)σxy=∑j[Sp(μj)-Sn(μj)]μjB1+μj2B2where Sp(μ)=qμp(μ) and Sn(μ)=qμn(μ) are the hole and electron conductivities in the mobility domain (i.e., the mobility spectrum ), respectively; p(μ)p(μ) and n(μ)n(μ) are hole and electron sheet densities, respectively, expressed in terms of their mobility distribution, and q is electronic charge. High-resolution mobility spectrum analysis (HR-MSA) was employed to solve the coupled inverse transform problem posed by Eqs. (2) and (3), and thus extract Sp(μ)Sp(μ) and Sn(μ)Sn(μ) [10]. From the mobility spectra, the sheet carrier concentration NsNs and mean mobility μDμD associated with the i-th conductivity peak were calculated from:equation(4)Ns=∑iSn(μi)qμi;andμD=1qNs∑iSn(μi)