## 5 Intra- and Inter-Layer Phonon Energy Renormalizations
### Isotopes  
One of the challenges regarding few layers graphene systems is the difficulty to address and probe individual layers. This problem can be promptly solved by isotope labeling of individual layers, as has been recently demonstrated [73; 74; 75]. One can easily tune the frequency of the phonons by an exchange of the \({}^{12}\)C isotope with a \({}^{13}\)C isotope with essentially no change to the electronic structure. In this context, while isotopic labeling tunes the phonon properties (tuning, therefore, a gas of Bosons in the system), electronic doping provides an important tool to tune the electronic properties of graphene (tuning, therefore, a gas of Fermions in the system) [65; 76; 77]. The changes in the vibrational structure can be observed directly by Raman spectroscopy [74; 78]. Although the doping of 2 LG [79; 80] and FLG [81] has been reported, the results are difficult to interpret, since it is not clear how the doping charge is distributed in between the various graphene layers. This problem can be overcome for turbostratic 2 LG (t-2 LG), since a special 2 LG sample can be prepared by sequential transfer of \({}^{12}\)C and \({}^{13}\)C graphene layers onto, for example, a SiO\({}_{2}\) substrate, so that the Raman features of the top and bottom layers could be resolved and analyzed separately [73]. In these samples, one can determine the doping charge associated with each individual layer independently when both layers were similarly doped, as reported in Reference [73]. Recently, CVD synthesis was used to obtain AB stacked 2 LG [11] regions where the add-layer is synthesized from \({}^{13}\)C and the continuous layer (primary 1 LG) is synthesized from the \({}^{12}\)C isotope, as shown in Figure 17a. In such a sample, we are able to address individual layers by Raman spectroscopy, follow the effect of phonon self-energy renormalizations for each individual layer separately and further understand how the interlayer (IL) interactions work in these isotopic systems. In the sample from Reference [75], a small central area is composed only from the \({}^{12}\)C isotope and the border area is composed of the \({}^{13}\)C isotope. The continuous layer that formed first is composed of the \({}^{12}\)C isotope [82]. Figure 17a shows a photograph of the resulting graphene sample obtained using an optical microscope after transfer of the so-called 2 LG thus prepared onto a SiO\({}_{2}\)/Si substrate. The hexagonal shaped darker region (delimited by the black dotted line) in Figure 17a corresponds to the 2 LG, while the rest of the area (the background area) of the imaged spot is covered by 1 LG. Figure 17b shows a 2D Raman map plotting the G\({}^{\prime}\) (2D) spectral linewidth. The G\({}^{\prime}\) (2D) lineshape is very sensitive to the 2 LG stacking order as well as to the isotopic composition of the layers [11]. In Figure 17b it is possible to localize the \({}^{12}\)C 1 LG, the \({}^{12/12}\)C AB-2 LG as well as the \({}^{12/13}\)C AB-2 LG. As showed in Section 2 in Figure 3, the Raman spectrum of the \({}^{13}\)C 1 LG sample exhibits the same Raman features as the Raman spectrum of the \({}^{12}\)C 1 LG except for a downshift of all the Raman bands for the \({}^{13}\)C 1 LG sample relative to the \({}^{12}\)C graphene sample [73]. Figure 18b shows the Raman spectra of \({}^{12/13}\)C AB-2 LG at different electrode potentials separated by 0.1 V. Interestingly, the behavior of the Raman spectra for \({}^{12/13}\)C AB-2 LG (Figure 18b) is strongly different from that of \({}^{12/13}\)C t-2 LG (Figure 18a). The Raman features in Figure 18a,b both present two G modes; one with higher frequency (HG mode) and one with lower frequency (LG mode). At first glance, one may identify some similarity  
Figure 17: **(a)** Optical image of the graphene with a \({}^{13}\)C-based add-layer (darker hexagonal area delimited by the dotted line) on the SiO\({}_{2}\)/Si substrate.