## 2 Experimental Details
The typical size of the Raman maps was 10 \(\times\) 10 \(\upmu\)m\({}^{2}\). For each Raman spectrum, the micro-reflectance was also simultaneously measured. To obtain clean Raman spectra of MLG and buffer layers, a Raman spectrum of a bare 4H-SiC substrate was subtracted. Furthermore, all Raman spectra are normalized to the 4H-SiC substrate. The surface morphology of the MLG and buffer layers was characterized by tapping mode atomic force microscopy (AFM) (Veeco Dimension 3100). Microprobe low-energy electron diffraction (\(\upmu\)-LEED), low energy electron microscopy (LEEM), X-ray photoelectron emission microscopy (XPEEM) and micro-focused X-ray photoelectron spectroscopy (micro-XPS) were used to investigate the structural properties and chemical composition of the buffer layer samples. The experiments were performed using the ELMITEC-LEEM III instrument at the I311 beamline of the MAX-Lab synchrotron radiation facility in Lund, Sweden. Contactless terahertz (THz) cavity-enhanced (CE) optical Hall effect (OHE) measurements were performed for the determination of graphene-free charge carrier properties using the custom-built ellipsometry instrumentation at the THz Materials Analysis Center [37]. The OHE describes the magnetic field induced optical birefringence generated by free charge carriers under the influence of the Lorentz force, and can be measured by Mueller matrix ellipsometry [38]. The CE-OHE measurements were performed at room temperature by placing the sample on either of the two sides of a permanent neodymium magnet with a field strength of \(B=0.548\) T and an external cavity of \(\sim\)100 \(\upmu\)m [39]. In-situ environmental control gas cell was employed to measure the samples in different gases and relative humidity (RH) [37; 40]. Mueller Matrix data collected at magnetic fields \(B=+0.548\) T and \(B=-0.548\) T and their differences were simultaneously analyzed using a stratified optical model with parameterized model dielectric functions (MDFs) assigned to each layer, following the methodology described in Ref. [38]. The model consists of a perfect mirror (magnet), air gap, 4H-SiC substrate and an MLG or a QFS-MLG layer. The dielectric function of 4H-SiC was first determined from measurements of a bare substrate. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Sample** & \(T_{\text{Ar}}\) [ \({}^{\circ}\)C] & \(T_{\text{gr}}\) [ \({}^{\circ}\)C] & \(t_{\text{gr}}\) [min] \\ \hline \multicolumn{4}{c}{\(n\)-type 4H-SiC} \\ \hline BL1 & 800 & 1600 & 0 \\ BL2 & 900 & 1600 & 0 \\ BL3 & 1150 & 1600 & 0 \\ BL4 & 1300 & 1600 & 0 \\ \hline MLG0 & 800 & 2000 & 0 \\ \hline \multicolumn{4}{c}{SI 4H-SiC} \\ \hline BL5 & 800 & 1600 & 0 \\ BL6 & 1300 & 1800 & 0 \\ \hline MLG1 & 640 & 2000 & 0 \\ MLG2 & 800 & 2000 & 0 \\ MLG3 & 1300 & 2000 & 5 \\ \hline QFS-MLG1 & 640 & 1600 & 0 \\ QFS-MLG2 & 800 & 1600 & 0 \\ QFS-MLG3 & 1300 & 1800 & 0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Growth conditions of the samples studied in this work: \(T_{\text{Ar}}\), \(T_{\text{gr}}\) and \(t_{\text{gr}}\) of buffer layer (BL), monolayer graphene (MLG) and quasi-free-standing (QFS)-MLG grown on \(n\)-type and semi-insulating (SI) substrates. The substrate MDF parameters were then kept fixed during the analysis of the graphene samples. The MDF of graphene was described by Drude contribution in the presence of magnetic field [37; 38]. The free charge carrier mobility \(\mu\) and sheet density \(N_{\rm s}\) of graphene were determined by non-linear least-squares fit of the calculated Mueller matrix data to the experimental data. The effective mass \(m^{*}\) was parametrized as \(m^{*}=\sqrt{\left(h^{2}N_{\rm s}\right)/\left(4\pi v_{\rm F}^{2}\right)}\) following Ref. [41], where \(v_{\rm F}=1.02\times 10^{6}\) m s\({}^{-1}\) is the Fermi velocity and \(N_{\rm s}\) is the carrier sheet density.