## 3 Results
### Raman Spectroscopy
This downshift of the Raman wavenumber bands directly comes from the increase of the isotope mass as is reported in Equation (2), assuming random isotope repartition and equal bond force constants [36]:  
\[\Delta\omega_{\mathrm{i}}=(\omega_{0}-\omega)_{i}=(\omega_{0})_{i}\cdot\{1-[(12 +c_{0})/(12+c)]^{1/2}\} \tag{2}\]  
where \(\omega_{0}\) is the frequency of the given Raman mode i in the \({}^{12}\)C implanted sample, c and c\({}_{0}\) are the \({}^{13}\)C concentrations in the \({}^{13}\)C and \({}^{12}\)C samples (\({}^{13}\)C natural abundance = 0.0107), respectively. The amplitude of this downshift has been experimentally confirmed on \({}^{12}\)C\({}^{-13}\)C bilayer graphene [33]. The wavenumber shift (cm\({}^{-1}\)), as a function of the \({}^{13}\)C concentration calculated according to Equation (2), is reported in Figure 10. It can be seen that the correlation is quasi linear. \((\omega_{0})_{\mathrm{i}}\) is quoted.as 1581 cm\({}^{-1}\) in Figure 9b (blue line). Moreover, we noted that generally \(\Delta\omega_{\mathrm{2D}}\approx\Delta\omega_{\mathrm{G}}\). We have undergone Raman mappings over a 170 \(\upmu\)m\({}^{2}\) area. The following procedures have been achieved with the ratio I\({}_{\mathrm{2D}}\)/I\({}_{\mathrm{G}}\) displayed in Figure 9d, as we must account for the absence of carbon over part of the surface. A minimal intensity of each Raman mode \(i\) (\(i\) = G, D, 2G) is evaluated (A\({}_{\mathrm{cutoff}}\))\({}_{i}\). All the pixels with an intensity lower than this cutoff intensity (A\({}_{\mathrm{cutoff}}\))\({}_{i}\) are set to zero. Any ratio (I\({}_{\mathrm{2D}}\)/I\({}_{\mathrm{G}}\))\({}_{i}\) is equally set to zero when the denominator is lower than the cutoff intensity. The 2D downshift (named as P\({}_{\mathrm{2D}}\) in Figure 9c) clearly points out to heterogeneities of the \({}^{13}\)C concentration inside a single TLG. The \({}^{13}\)C concentrations are in the range 20%-40%. Few of them display weaker \({}^{13}\)C concentrations. Figure 9: Raman spectroscopy on the \({}^{13}\)C implanted sample. **(a)** Optical micrograph; **(b)** experimental Raman spectra of \({}^{12}\)C (blue) and \({}^{13}\)C (red) implanted samples and theoretical Raman spectra of pure \({}^{13}\)C (green); **(c,d)** Raman mappings of the downward wavenumber shift of the 2D band (P\({}_{\mathrm{2D}}\)) and I\({}_{\mathrm{2D}}\)/I\({}_{\mathrm{G}}\) ratio, respectively. Pixel size is around 0.3 \(\times\) 0.3 \(\upmu\)m\({}^{2}\). The red dot in Figure 9a corresponds to the red spectrum in Figure 9b. The blue and red arrows in Figure 9c correspond to domains of low and high \({}^{13}\)C concentrations, respectively. The elliptic region in Figure 9a,c,d is a guide for the eye. The I\({}_{\rm 2D}\)/I\({}_{\rm G}\) ratio is expected to be sensitive to the thickness of the TLG [23]. The I\({}_{\rm 2D}\)/I\({}_{\rm G}\) mapping given in Figure 9d also displays some heterogeneity inside a single one. Generally it is larger on the center. If the I\({}_{\rm 2D}\) intensity line is correlated to the thickness of the TLG, this infers that the thickness of the TLG is also varying, even inside a single fragment. The Full Width at Half Maximum (FWHM) of the G band typically ranges around 55-60 cm\({}^{-1}\), instead of 35-55 cm\({}^{-1}\) for the \({}^{12}\)C implanted sample [20]. The large FWHM values are indicative of partial graphitic organization, which is expected for TLG not heated to more than 600 \({}^{\circ}\)C. Furthermore the broadening of the FWHM observed on the mixed (\({}^{13}\)C-\({}^{12}\)C) sample can be related to the mixing of \({}^{12}\)C and \({}^{13}\)C atoms inside a single fragment, in agreement with the absence of any splitting of the Raman mode. The lowest \({}^{13}\)C concentrations are generally observed inside or at the sides of the fragment (blue arrows in Figure 9c), whereas the highest \({}^{13}\)C concentrations are observed at the sides of the fragment (red arrows in Figure 9c).