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Mass-related inversion symmetry breaking and phonon self-energy renormalization in isotopically labeled AB-stacked bilayer graphene

Scientific Reports volume 3, Article number: 2061 (2013) | Download Citation


A mass-related symmetry breaking in isotopically labeled bilayer graphene (2LG) was investigated during in-situ electrochemical charging of AB stacked (AB-2LG) and turbostratic (t-2LG) layers. The overlap of the two approaches, isotopic labeling and electronic doping, is powerful tool and allows to tailor, independently and distinctly, the thermal-related and transport-related phenomena in materials, since one can impose different symmetries for electrons and phonons in these systems. Variations in the system's phonon self-energy renormalizations due to the charge distribution and doping changes could be analyzed separately for each individual layer. Symmetry arguments together with first-order Raman spectra show that the single layer graphene (1LG), which is directly contacted to the electrode, has a higher concentration of charge carriers than the second graphene layer, which is not contacted by the electrode. These different charge distributions are reflected and demonstrated by different phonon self-energy renormalizations of the G modes for AB-2LG and for t-2LG.


Graphene, which is a gapless material, has gathered much attention due to its prospective fascinating applications. However, some of the proposed applications, such as transistor-based applications, cannot be realized in single layer graphene due to fundamental problems related to, for example, a creation of a band-gap. As an alternative, bilayer graphene (2LG) with AB stacked layers (AB-2LG) has different vibrational properties and also a different electronic structure than monolayer graphene (1LG) and might overcome some of the shortcomings of 1LG. For example, in AB-2LG it is possible to tune a bandgap by an external electric field, which enables realization of a field effect transistor with a tunable bandgap1,2. These potential advantages motivated several recent studies involving AB graphene1,3,4,5,6,7.

Another challenge is the difficulty to address and probe individual layers in few layer graphene samples. This problem can be promptly solved by isotope labeling of individual layers, as has been recently demonstrated8,9. One can easily tune the frequency of the phonons by an exchange of the 12C isotope with a 13C 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)10,11,12. It is important to note that, this approach tunes, distinctly and independently, the electronic and vibrational properties of the material. Indeed, by varying the ways one isotopic labels and/or electronic dopes the system, different symmetries can be achieved to describe phonons and electrons in the system, which allow us to control selection rules often important to describe several physics-related phenomena. As a consequence, we gain a powerful method to tailor the thermal-related and transport-related phenomena in the material.

The changes in the vibrational structure can be observed directly by Raman spectroscopy. The larger the amount of 13C isotope that is introduced into the graphene layer, the lower the observed frequency of the Raman bands8,9. If the different layers in a few layer graphene sample contains different amount of 13C isotope, one can distinguish their Raman bands in the isotopically doped spectra relative to that for the corresponding naturally occurring graphene layer containing only 12C 9,13. Also, the electronic doping can be realized by electrostatic gating1, electrochemical charging10,11 or chemical doping14,15 and several reports on charge-induced phenomena in 1LG are found in the literature for each of these doping methods. In few layer graphene (FLG) samples, the situation is more complex. Although the doping of 2LG16,17 and FLG18 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 2LG (t-2LG), since a special 2LG sample can be prepared by sequential transfer of 12C and 13C graphene layers onto, for example, a SiO2 substrate, so that the Raman features of the top and bottom layers could be resolved and analyzed separately8. In these samples one can determine the doping charge associated with each individual layer independently when both layers were similarly doped, as reported in Ref. 8. The experimental results from Ref. 8 suggested that the charge is distributed almost evenly between the top and bottom layers of 2LG when the two constituent layers are randomly stacked on a SiO2 substrate.

As discussed above, the turbostratic FLG can be easily obtained by the subsequent deposition of 12C and 13C individual layers on the target substrate8,9. However, this procedure does not allow one to control the rotation angle between the graphene layers, and for this reason, it is not possible in this way to obtain AB-2LG. Recently, several studies of graphene add-layers (as grown in CVD methods) appeared19,20,21. These add-layers are additional graphene layers formed during the growth of a primary 1LG using a Cu catalyst and in many cases, AB stacked regions are observed for the add-layer relative to the continuous graphene layer. It has been shown that, even though the add-layers grow much slower than the primary 1LG, they continue to grow over the entire growth time19. Therefore, one can, by careful control of the isotope content of the CH4 source and the reaction conditions, reach the situation where the top add-layer contains mostly one type of isotope (either 12C or 13C), while the continuous layer comprises the second type of isotope.

In the present study, we tuned the chemical vapor deposition (CVD) synthesis of the graphene bilayer to form AB stacked regions where the add-layer is synthesized from 13C and the continuous layer (primary 1LG) is synthesized from the 12C isotope, as shown in Fig. 1. 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.

Figure 1: Optical and spectroscopic images of the 2LG.
Figure 1

(a) Optical image of the graphene with a 13C-based add-layer (darker hexagonal area delimited by the dotted line) on the SiO2/Si substrate. The diameter of the hexagon is about 10 μm. Note that the center (small area delimited by the gray dotted lines) of the add-layer forms a 12/12C AB-2LG structure, while the remaining area is formed by 13/12C AB-2LG. (b) G′ (2D) mode Full Width at Half Maximum (FWHM) indentifying the 12C 1LG region (FWHM ~ 30 cm−1), the 12/12C AB-2LG region (FWHM ~ 45 cm−1) and the 12/13C AB-2LG region (FWHM ~ 75 cm−1).


Raman spectra for the 12/13C 2LG systems

The graphene samples were grown on a copper substrate and transferred to a SiO2/Si substrate following the procedure in Ref. 21. During the growth, we changed the carbon isotope as follows: at the beginning of the growth we introduced 12CH4 for 90 s. Next, we changed the carbon source to 13CH4 and we continued the growth for 5 minutes more. Since the growth of the continuous layer is fast and the growth of the add-layer is slow9, we obtained 2LG regions where a small central area is composed only from the 12C isotope and the border area (about 70% of the sample) is composed of the 13C isotope. The continuous layer that formed first is composed of the 12C isotope19. Figure 1(a) shows a photograph of the resulting graphene sample obtained using an optical microscope after transfer of the so-called 2LG thus prepared onto a SiO2/Si substrate. The hexagonal shaped darker region (delimited by the black dotted line) in Fig. 1(a) corresponds to the 2LG, while the rest of the area (the background area) of the imaged spot is covered by 1LG. Figure 1(b) shows a 2D Raman map plotting the G′(2D) spectral linewidth. The G′(2D) lineshape is very sensitive to the 2LG stacking order as well as to the isotopic composition of the layers22. In Fig. 1(b) it is possible to localize the 12C 1LG, the 12/12C AB-2LG as well as the 12/13C AB-2LG.

Figure 2 shows a typical Raman spectrum of the 2LG inner region thus prepared in comparison to that of the 12C 1LG outer region (note that the 12C sample is expected to contain the natural isotopic abundance, which is 1.07% of 13C). Figure 2 also shows the Raman spectrum for a standard CVD-derived 13C 1LG. As expected for isotopic systems, the Raman spectrum of the 13C 1LG sample exhibits the same Raman features as the Raman spectrum of the 12C 1LG except for a downshift of all the Raman bands for the 13C 1LG sample relative to the 12C graphene sample8. The observed experimental downshifts of the D, the G and the G′ bands for the 13C graphene with respect to those of the 12C graphene are about 50 cm−1, 60 cm−1 and 100 cm−1, respectively8. In a continuum model, the frequency shifts of the Raman bands in the 13C enriched material with respect to the 12C counterpart originate from the increased mass of this isotope which is given by equation (1): where ω0 is the frequency of a particular Raman mode in the 12C sample, c = 0.99 is the concentration of 13C in the enriched sample, and c0 = 0.0107 is the natural abundance of 13C in a typical 12C sample. According to equation (1), the downshifts of the D, the G and the G′ bands are expected to be 48 cm−1, 56 cm−1 and 95 cm−1, respectively, which is in good agreement with our previous experimental results8.

Figure 2: Typical 1LG and 2LG Raman spectra.
Figure 2

From the top to the bottom: typical Raman spectrum for the 12C 1LG (black dotted line), typical Raman spectrum for the 13C 1LG (black solid line), typical Raman spectrum for the 12/13C t-2LG (gray dotted line) and typical Raman spectrum for the 12/13C AB-2LG (gray solid line). The spectra are excited using 532 nm laser excitation energy.

In the present work, we analyze the areas of the 2LG sample which comprise the initial 12C 1LG and the 13C regions of the add-layer composing this layered graphene (12/13C 2LG). As expected (see Fig. 2), we observe two G modes in the Raman spectrum, one arising from the 12C layer and the second arising from the 13C layer. The as-grown peak positions of these G bands are at 1587 cm−1 and 1530 cm−1, respectively. Interestingly, in the case of the G′ Raman mode, we obtained only a broad asymmetric band. This is in contrast to the situation in t-2LG prepared by the subsequent transfer of two separately grown graphene single layers8. In the latter case, the layers are misoriented and the phonons of different layers are fully independent since basically no IL interactions take place. In this case, we contemplate the same properties of the 1LG, which has 2 atoms per unit cell and 6 phonons modes. However, for the AB stacked samples, where the IL interactions are significant, one should also consider the interaction of the phonons to form, for example, the G′ mode. In short, when the IL interactions happen, the electronic structure of the AB-2LG departs from two non-interacting Dirac cones (related to the two non-interacting layers) around the K(K′)-point to become a hyperbolic electronic structure with two valence bands (π1 and π2) and two conduction bands (π1* and π2*). Regarding the phonon structure (and starting with the most known case), for a 12/12C AB-2LG we have 4 atoms per unit cell and 12 phonon modes. Thus, the G mode around the Γ-point will appear in two different peaks separated by 3 cm−1, which has to do with the symmetric (S) Eg and anti-symmetric (AS) Eu combinations involving the in-plane longitudinal optical (LO) and the in-plane tangential optical (iTO) modes of the top and bottom layers. Note that, while the S mode is Raman active, the AS is not, and therefore only one peak is seen in the G band region. For the G′ mode, which is a second-order process, in the case of the 12/12C AB-2LG we obtain 4 peaks due to the fact that iTO phonons can connect two different electronic states π1*(π2*) at the K-point with two possible π1*(π2*) states at the K′-point23. For the 12/13C t-2LG, each band can originate from either a 12C or a 13C graphene layer. Due to the different masses of the 12C and 13C atoms, these corresponding phonons observed in the 12C and the 13C graphene layers would differ in energy (frequency)24.

For the 12/13C AB-2LG the situation is slightly different. Likewise the case of 12/12C AB-2LG, the unit cell of a 12/13C AB-2LG is composed of 4 atoms but now the atoms of the top layer are 12C atoms while the atoms in the bottom layer are 13C atoms. This has a very important symmetry consequence: because the 12C and 13C atoms have different masses, the unit cell for the 12/13C AB-2LG system has no inversion symmetry anymore for the phonons (note that for electrons the symmetry is kept) like is observed for the 12/12C AB-2LG system. Therefore, we have a mass-related symmetry breaking and the main consequence is that those S and AS modes discussed for 12/12C AB-2LG are no longer eigenstates of the system. Instead, the new eigenstates are now a mixing of the S and AS modes and the G mode region must comprise two Raman active peaks. A very similar effect happens when one applies an electric field in a 12/12C AB-2LG system23. However, in this case the inversion symmetry is broken for both electrons and phonons, so that we have a band gap opening in the K-point and, the S and AS modes are mixed and the G mode region has two Raman active peaks. Regarding the S and AS iTO phonon resonances, they are no longer unique around K(K′)-point, as is the case for the 12/12C AB-2LG. Due to the mass-related symmetry breaking, we now have two pairs of S and AS iTO mode resonances and the total number of bands contributing to the G′ mode would double giving eight Raman bands. The frequencies of each of these eight bands are close to each other, and therefore only one asymmetric broad band is observed experimentally in the Raman spectrum (Figure 2). It is worth mentioning that, due to its particular mechanism, this somewhat asymmetric G′ mode lineshape is a spectroscopic signature for the 12/13C AB-2LG systems22.

Gate-modulated Raman spectroelectrochemistry

Next, we discuss the Raman spectroelectrochemistry results for the 12/13C AB-2LG systems. Figure 3 gives a schematic illustration of the experimental setup used here in which only the 12C layer is connected to the electrode. Figure 4(b) shows the Raman spectra of 12/13C AB-2LG at different electrode potentials separated by 0.1 V. Interestingly, the behavior of the Raman spectra for 12/13C AB-2LG (Fig. 4(b)) is strongly different from that of 12/13C t-2LG (Fig. 4(a)). From now on, the following convention will be adopted: the Raman features in Figs. 4(a) and (b) both present two G modes; one with higher frequency, which is going to be called the HG mode and one with lower frequency, which is going to be called the LG mode. At first glance, especially in the positive potential regimes, one may identify some similarity between the potential dependent behavior of the HG modes for the 12/13C AB-2LG and t-2LG systems. However, the behavior of the LG mode for the 12/13C AB-2LG is completely different from both G mode lineshapes, that is, different from both the HG and LG modes of the 12/13C t-2LG. Namely, for the LG mode of the 12/13C AB-2LG, we observe small changes in the G mode frequency during negative doping. The LG mode downshifts from 1535 cm−1 to 1528 cm−1 going from 0 to −1.5 V. The corresponding frequency change in the LG mode of the 12/13C t-2LG (Fig. 4(a)) is much larger, and has an opposite direction: from 1528 cm−1 to 1546 cm−1. For positive electrochemical potentials, we observe a larger change from 1535 cm−1 (at 0 V) to 1546 cm−1 (at 1.5 V) for the LG mode in AB-2LG, as seen in Fig. 4(b), but this frequency change is still smaller than in the case of the LG mode in t-2LG for which the change is from 1528 cm−1 (at 0 V) to 1563 cm−1 (at 1.5 V) as shown in Fig. 4(a).

Figure 3: In-situ Raman electrochemistry experimental configuration's scheme.
Figure 3

Note that only the top 12C layer is contacted in the current experimental configuration.

Figure 4: Spectroelectrochemistry experiments.
Figure 4

(a) In-situ Raman spectroelectrochemistry of the 12/13C t-2LG G modes and (b) In-situ Raman spectroelectrochemistry of the 12/13C AB-2LG G modes. The spectra are excited by 2.33 eV laser excitation energy and the electrode potentials range from −1.5 to 1.5 V vs. Ag/Ag+ (from bottom to top) in units of 0.1 V. The red dashed curves are guide to eyes. Note that, due to electrochemistry conventions, positive potentials are filling the system with holes while negative potentials are filling the system with electrons.

In charged graphene, the frequency shift of the G mode, which is a first-order Raman mode around the Γ-point whose phonon momentum is null (q = 0), is related to both, the change in the C-C bond strength and the renormalization of the phonon self-energy associated with many-body effects17. Since for graphene a coupling between the lattice vibrations and the Dirac fermions is allowed (because the energy scales for the electron and phonon dynamics are comparable) the adiabatic Born-Oppenheimer approximation fails to describe phonons in graphene24. As a consequence, the interaction of the carriers in graphene with phonons must be included. These interactions cause electron-hole (e–h) pair creation (annihilation) due to phonon absorption (emission), with a lifetime related to the phonon linewidth (Γ), as observed in the Raman spectrum. This leads to a renormalization of the phonon energy, the phonon lifetime and consequently the energy of the carriers, that is, for both electrons and holes25,26. In charged graphene, every time we have a real creation (annihilation) of e–h pairs, which means that the phonon energy (Eph) is bigger than 2|EF| (EF is the Fermi energy), a decrease of the G mode phonon frequency occurs. When EF is moved away from the Dirac point, the formation of e–h pairs is eventually suppressed by the Pauli principle when the phonon energy (Eph) is smaller than 2|EF|24 resulting in a G mode frequency upshift for both negative and positive electrochemical potentials. It is worth mentioning that when Eph = 2|EF|, the so-called Kohn anomaly takes place and the maximum softening of the G mode frequency occurs24.

Electrochemical doping is a reproducible and precise way to control the graphene doping, and we can easily evaluate the doping effects in graphene systems by monitoring the changes in the frequency of the Raman G mode during electrochemical charging10,11. To better elucidate the changes for both the LG and HG modes in the AB-2LG and t-2LG spectra, we analyzed the spectra in Figs. 4(a) and (b) with Voigt lineshapes. The fitting results are compiled in Fig. 5(a) (for both the LG and HG frequencies and linewidths of the 12/13C t-2LG) and Fig. 5(b) (for both the LG and HG frequencies and linewidths in 12/13C AB-2LG). First, we note that the frequency shifts of the LG and HG modes are observed to be smaller (for both, positive and negative potentials) for 12/13C AB-2LG with comparison to the 12/13C t-2LG. This suggests that different mechanisms are ruling the doping of 12/13C AB-2LG in comparison to the 12/13C t-2LG at the same applied electrode potential (which means the same charge concentration). Indeed, the t-2LG EF will depend on n (n is the charge concentration) according to the following relation: |EF(1LG)| = –h|vF|(πn)1/2 where vF is the Fermi velocity, since the weakly interacting layers composing the t-2LG system keep the 1LG properties, while EF for the AB-2LG will vary with n according to the following expression: |EF(AB-2LG)| = ½(−γ1 + ((4πvF2n)/3 + γ12)1/2), where γ1 = 0.35 eV. By inspecting both, |EF(1LG)| and |EF(AB-2LG)| relations, we see that, for a given change in n, EF for the t-2LG changes more than the EF for the AB-2LG12,17. Consequently, the frequency variations for the t-2LG G modes are expected to be larger than the frequency variations for the AB-2LG.

Figure 5: Fitting analysis of the spectra showed in Fig. 4.
Figure 5

(a) the frequency and linewidth behavior of the LG mode (left panel) and HG (right panel) in t-2LG as a function of the electrode potential. (b) the frequency and linewidth behavior of the LG mode (left panel) and HG (right panel) in AB-2LG as a function of the electrode potential. All insets present information on the intensity dependence with the electrode potential. Note that, due to electrochemistry conventions, positive potentials are filling the system with holes while negative potentials are filling the system with electrons.

Besides the different charging of the layers in both, 12/13C AB-2LG and 12/13C t-2LG, which changes the magnitude of the phonon self-energy renormalizations, the observed experimental results for the G mode frequency and linewidth shifts are quite distinct for both samples, as observed in Figs. 5(a) and (b). Since the G mode occurs close to the Γ-point, in which the phonon wave vector magnitude q is negligible, the G mode is sensitive to each particular graphene layer. In other words, the G mode must reflect the charge associated to each particular layer. The behaviour observed for both the LG and HG modes for the 12/13C t-2LG (Figs. 4(a) and 5(a)) agrees well to the corresponding behavior observed for 1LG in which the frequency (linewidth) hardens (narrows) with increasing |EF|. This behavior is already well understood and can be fully explained within the non-adiabatic phonon self-energy renormalizations11,24. Indeed, as expected for t-2LG systems, the results in Figs. 4(a) and 5(a) reflect that the two layers, 12C and 13C layers, are fully decoupled and the differences in the phonon renormalization magnitudes are due to different charging of each layer constituting the t-2LG. The renormalizations observed are related to Eg modes of each 13C (the LG mode in Fig. 4(a)) and 12C (the HG mode in Fig. 4(a)), separately. At this point, we must note that for the case of the 12/13C AB-2LG we do not observe the standard behavior expected for the dependence of the G mode as a function of EF, in which the frequency (linewidth) hardens (narrows) with increasing |EF|. For the 12/13C AB-2LG, on the other hand, in spite of the inhomogeneous charging of the 12C and 13C to be able to explain the different magnitudes for the frequency change, it cannot fully explain the results in Fig. 4(b) if we consider that the LG and HG modes are originating from the Eg modes from the top and bottom layers separately. Moreover, the results in Figs. 4(b) and 5(b) are also not fully consistent with other results observed for 12/12C AB-2LG available in the literature16,27. This inconsistence is expected since the phonon renormalizations strongly depend on the charge concentration of each of the layers in an AB-2LG.

In previous experiments both the top and bottom layers of the AB stacked 2LG were contacted by an electrode16, and, for this reason, one can assume that EF of both layers in the present case will be equilibrated with each other thermodynamically (in other words, both layers are initially at the same potential). In our present work, the device is formed by the add-layer (the 13C layer) which is located next to the continuous graphene layer, but only the continuous graphene layer is contacted to the electrode, as illustrated in Fig. 3 (in this situation the two layer are at two different potentials). In other words, the charge is transported by the 12C layer to the 12/13C AB-2LG region. In our experimental setup, we must therefore consider a potential barrier due to the different position of EF in the top layer relative to the bottom layer1,28. Therefore the doping of the 13C graphene layer would depend on the efficiency of the charge transfer from the 12C continuous layer to the 13C add-layer. In addition, we should also consider the location of the add-layer with respect to the substrate, e.g., whether the 13C layer is at the top or the bottom of the 12C continuous layer. The injection of the charge carriers is more efficient to the top layer, which is closer to the electrolyte ions than to the bottom layer which is in contact with the substrate. In our case, the add-layer is at the bottom, as commonly expected for CVD-based 2LGs29,30. Therefore, this add-layer is electrically shielded by the top layer, and one can understand the latter observation, in which a smaller amount of charge is located on the add-layer. This is consistent with previous calculations by Das17 and experiments by Fang et al22. We also note that a similar situation happens in the case of double wall carbon nanotubes where both outer and inner tubes are metallic and only the outer tube is contacted by the electrode31. The in-situ Raman spectroelectrochemical measurements on the latter samples also demonstrated that there is more charge located on the outer tube than on inner tube31.


In order to understand the results obtained here for the LG and HG modes in 12/13C AB-2LG, we must, as stated earlier in the text, recall that the unit cell for this systems has 4 atoms, as is the case for 12/12C AB-2LG, with the difference that the bottom atoms of the 2LG unit cell are 13C atoms and the top atoms of the 2LG unit cell are 12C atoms. In this case, the inversion symmetry in 12/13C AB-2LG is naturally broken due to the different 12C and 13C masses. As a result, what we are observing in Figs. 2 and 4(b) is, indeed, a S and AS mixing of the Eg and Eu modes distinctly observed only when the inversion symmetry exists, like is the case for 12/12C AB-2LG. This mixing of the Eg and Eu modes has also been observed for 12/12C AB-2LG when the latter is under the effect of an electric field31. Indeed, this mass-related symmetry breaking is confirmed by the electrochemistry measurements. As reported by Gava et al.3 a signature of the Eg and Eu mixing is that the intensity ratio (IHG/ILG) between the HG (an anti-symmetric combination of Eg and Eu) and the LG modes (a symmetric combination of Eg and Eu) must increase with increasing |EF|. This signature is confirmed by the experimental results, as shown in Fig. 6. Regarding the frequency, linewidth and intensity behavior of the two G band modes, Gava et al.3 described their dependence in terms of the net 2LG charge concentration n = ntop + nbottom. According to the charge concentration for the top (ntop) and bottom (nbottom) layers, the frequency, linewidth and intensity can assume different behaviors3. Here, comparing the dependence of the HG and LG modes on potential voltage with the calculations performed in Ref. 3, we conclude that for the 12/13C AB-2LG, nbottom (which is kept at constant potential) is positive (signifying an excess of electrons) and higher than the initial ntop. Note that to fully explain the frequency and linewidth behaviors, we still need to consider other effects such as the extinction of electron–hole (e–h) pair formation due to a band gap opening related to the application of an external electrical field and also the intraband related renormalizations of the phonon energies32. Both effects will be important for the positive voltages (which means excess of holes in the system) and negative voltages (which means excess of electrons in the system). Note that, due to conventions related to electrochemistry experiments, positive voltages means that the EF is decreasing, so that holes are being injected to the system. On the other hand, negative voltages will mean that EF is increasing, so that electrons are being injected to the system. This electrochemistry convention is opposite to the convention for back-gated experiments.

Figure 6: Intensity ratio (IHG/ILG) between the LG and HG modes for the 12/13C AB-2LG as a function of the electrode potential.
Figure 6

Note that IHG/ILG, which is a spectroscopic signature for the mixing of the Eg and Eu modes, increases with increasing electrode potential. Note that, due to electrochemistry conventions, positive potentials are filling the system with holes while negative potential are filling the system with electrons.

Next, based on the fact that nbottom > ntop, we discuss the existence of an off-set in the change of the LG and HG mode frequencies in their dependence on electrode potential, as observed for the 12/13C AB-2LG. This is, in particular, clear for the case of positive doping. As one can see from Fig. 4(b), there is a small increase in the frequency of the LG mode and almost no changes in the frequency of the HG mode up to an electrode potential of +1 V. Then, for the potentials above +1 V, the G mode frequencies are gradually increased and seem to saturate from the potential +1.3 V on. This behavior is in contrast to 1LG or t-2LG (Fig. 4a) where the frequency starts to change even at very low positive and negative applied potentials (±0.1 V). Besides the competition for the corrections in the phonon frequency between both phenomena, phonon self-energy renormalizations and changes in the chemical C-C bonds (excess of holes hardens the C-C bonds while excess of electrons softens the C-C bonds)24, in AB-2LG, one should also consider subsequent filling (emptying) of the second electronic band in the conduction band π2* (of the second electronic band in the valence band π2) at higher electrode potentials. This band filling (emptying) is important to decide which phenomena will dominate and rule the frequency changes. In particular, it has been shown that the filling of π2* may lead to a kink in the dependence of the Raman frequency on electrode potential17 and this observation is consistent with a sudden change of the slope of the frequency/potential dependence (δωG/δV) during hole doping (positive potentials) as seen in Fig. 4(b)17. Indeed, when EF is at zero, real e–h pairs involving the π1 and π1* bands are being created all time, which contributes to decreasing the phonon frequency. At the same time, virtual e–h pairs are being created between π1 and π2 bands (in the valence band, which contributes to an increase in frequency) while no e–h pairs are being created between π1* and π2* in the conduction band. Note that, because it is a resonant effect, e–h pairs involving the π1 and π1* bands will dominate the virtual processes. Nothing is happening to the bonds since the system is not doped yet.

Let us now understand what happens when the system is doped with holes. In this case, when a first stage takes place (electrochemical potential between 0 and 1 V in Fig. 5(b)), the real e–h pair formation involving the bands π1* and π1 will be halted (since EF is decreasing) and the e–h pairs involving the bands π1 and π2 will change their status from virtual to real e–h pairs. The net effect will be: the phonon self-energy renormalizations will decrease the frequency (broaden the linewidth), since the real e–h pair formation will favor the frequency changes, while the C-C bonds will harden hence increasing the frequency. On average, no (or a small) change in frequency is expected, in accordance with the observations. Precisely speaking, this competition between the phonon self-energy renormalizations versus C-C bond changes will certainly depend on the net charge density n = ntop + nbottom since this charge density will determine the EF behavior in the system33. In our experiment, in which nbottom > ntop, the explanations given so far explain well the behavior observed for the HG mode in the 12/13C AB-2LG but it cannot explain completely the behavior observed for the LG mode, whose frequency slightly increases in the potential range from 0 to 1 V (see Fig. 5(b)). To completely understand the LG mode, we need to consider a band gap opening, as discussed later in the text. Going further in the electrochemical potential, in a second stage, for electrochemical potentials larger than 1 V, the 2LG system is heavily doped with holes and then both, real and virtual e–h creations (annihilations) will be halted and the C-C bonds hardening will favor the frequency changes, resulting in a steep increase of the frequency24.

When the 2LG system is doped with electrons, the virtual e–h pairs created (annihilated) due to phonon absorption (emission) involving the π1 and π2 bands will always exist, which contributes to increase the frequency. Again, in a first stage (electrochemical potential between −1 V and 0), a competition between real and virtual e–h pair formations involving the π1 and π1* bands and the π1 and π2 bands, respectively, will occur. When EF continues to increase, eventually the e–h pair formations involving the π1 and π1* bands and the π1 and π2 bands will be virtual and real e–h pairs involving the π1* and π2* bands start occurring. The net consequence is that the real electron hole pair formation together with the softening of C-C bonds will be dominating (it is worth remembering that when the graphene systems are doped with electrons, the C-C bonds soften, which results in a decrease of phonon frequencies). The net result is a decrease in the frequency, as shown in Fig. 5(b). As we progress to the second stage (electrochemical potential <−1 V), all the e–h pair formations involving all the π1, π2, π1* and π2* will be virtual. However, this virtual e–h pair formation will be a small perturbation favored by the C-C bonds softening. The net effect is still a decrease in the phonon frequency. It is important to comment that the behaviors observed for the phonon linewidths are consistent with our explanations.

As mentioned, the explanations above do not fully explain the behavior of the LG mode for the 12/13C AB-2LG in the range from 0 to 1 V, which requires a band effect to be fully understood. In fact, since the graphene is on the substrate which is known to dope graphene, we can consider this situation as a device with a fixed voltage at the bottom gate and variable voltage at the top gate, which is realized by changing the applied electrode potential. The electrochemical doping method for varying EF has generally been shown to be very efficient for the gating of devices10. Since we gradually increase the gate voltage in our experiment, the bandgap should be opened in the 12/13C AB-2LG electronic structure and, in principle, the charge carriers are no longer injected into the graphene sample, until EF exceeds the band gap magnitude. We note that in contrast to previous studies, we used a potentiostat to control the potential of the gate electrode, and therefore the electric field is expected to be higher and the gap opening can be larger than the phonon energy. The gap opening should therefore be reflected in the Raman spectra of the doped AB-2LG. The situation can be analogous to a semiconducting SWCNT, where one can find an offset in doping which is equal to half the energy of the bandgap34. At this point, it is important to remember that since one of the layers is being kept at a constant potential, the opening of a band gap is accompanied by the respective change of EF. This will make the band gap to be important at positive electrochemical voltages but unimportant for negative electrochemical voltages35. This is discussed as follows: the changes of the Raman G mode features are related to the creation (annihilation) of e–h pairs due to phonon absorption (emission) which hardens (narrows) the Raman band frequency (linewidth) and it is directly connected to the lifetime of the electron–hole pair, in other words, the average time spent by the phonon as an e–h pair. It is worth remembering that, the formation of e–h pairs can be prevented by the injection of charge carriers, to change EF sufficiently so that energy and momentum can no longer be conserved for e–h pair formation due to phonon absorption (emission). Indeed, we discussed that any time the condition Eph < 2|EF| (Eph stands for the phonon energy) is satisfied, the formation of real e–h pairs will be halted and as a consequence the G mode frequency will increase and the respective linewidth will decrease. Alternatively, the formation of real e–h pairs can be prevented by opening a bandgap, since the real e–h pair formation will be halted every time the band gap energy (Egap) is larger than Eph (Eph < Egap). In this case, any change in frequency will be more likely related to changes in the C-C bonds since they major any contribution involving virtual e–h pair creations related to the band-gap (precisely speaking, the formation of e–h pairs involving forbidden states of the bandgap, which can be understood as a virtual e–h pair creation as well, will be unlike since these e–h pairs involve forbidden states of the system). In other words, if the Eph > Egap condition is satisfied, e–h pairs will be formed and the hardening (narrowing) of the G mode frequency (linewidth) should be observed independently of the Egap value.

The bandgap opening, in fact, reflects spectral changes in the positive electrochemical potential values in the LG modes due to the applied gate potential, as shown in Fig. 5(b). Let us start analyzing the range of voltages from −1.5 to 0 V in Figs. 5(a) and (b). In Fig. 5(a), which shows the data for the 12/13C t-2LG, the frequency hardening followed by a saturation at around −1 V for the LG and HG modes is evident and means that the phonon self-energy renormalization is taking place and is a major effect between −1 V and 0 and from −1 V on, the doping-related changes in the C-C bonds, which decrease the phonon frequency, is a major effect. No band gap is introduced since the 2LG in question is turbostratic. Now, as shown in Fig. 5(b), the LG and HG frequencies decrease for the 12/13C AB-2LG, which means that the changes in the C-C bonds are the major changes, as explained above. For negative electrochemical potentials, in which electrons are being injected to the system, EF will be in the conduction band before the condition Eph < Egap occurs35. This means that the band gap will not play an important rule for negative potentials. For the range from 0 to +1 V, the frequency is roughly constant for the HG mode in Fig. 5(b) and slightly increases for the LG mode. This suggests that the band gap is likely affecting the LG mode which is halting the phonon renormalization, since when EF decreases (meaning that the system is doped with holes) the electrons supposedly going from the π1 band to the π1* band will eventually fall into the band gap. During the time this happens, the C-C bond changes will be the major effect in the frequency changes (note that the frequency should increase according to Lazzeri et al.24). Additionally, we believe that the inhomogeneous charging of the top and bottom layers in AB-2LG could explain why the band gap almost does not affect the HG mode17. Finally, at high positive potentials above 1 V, the explanations given above are enough to explain the frequency changes since the gap will not affect the system anymore. Moreover, since the t-2LG system does not open a band gap, its frequency behavior (see Fig. 5(a)) with the electrochemical potential is totally explained within the phonon self-energy formalism and together with C-C bond changes.

In conclusion, we studied 12/13C AB-2LG by Raman spectroscopy and in situ Raman spectroelectrochemistry. A mass-related symmetry breaking is observed where the 12/13C AB-2LG exhibits two distinct G modes, one LG and another HG, which are related to a symmetric (LG) and anti-symmetric (HG) combination of Eg and Eu modes existing in the 12/12C AB-2LG, where no mass-related symmetry breaking takes place. Indeed, this mode mixing happens due to a mass-related symmetry breaking of the inversion symmetry usually present in the unit cell of AB-2LGs. In the case of 12/13C AB-2LG, this symmetry is naturally broken since the top atoms in the unit cell are 12C atoms and the bottom atoms in the unit cell are 13C atoms. This is different from 12/13C t-2LG, where the two distinct LG and HG modes are related to the Eg modes from the 13C and 12C individual layers, respectively. In 12/13C AB-2LG, the electrochemical charging reflects a smaller sensitivity of EF to the electrode potential due to the effect of the modified electronic structure as compared to that for 12/13C t-2LG. In addition, spectroelectrochemical experiments in AB-2LG indicated more charge on the top layer than on the bottom layer.


Graphene flakes synthesis

The AB stacked 2LG was prepared using a modified CVD growth method. A thick copper foil (127 um thick, 99.9%, Alfa Aesar) forming an enclosure over the growth zone was used as a catalyst which was cleaned by dipping the copper into Ni etchant (Nitric acid, Transeneinc.) for 30 seconds. The growth procedure was as follows: the substrate was heated to 1000°C under 10 sccm H2 for 30 min for annealing the substrate. Subsequently, the 12CH4 was introduced for 90 sec, then the line was purged for 5 min using 100 sccmAr/10 sccm H2, and finally 13CH4 (99.5 atom%, Sigma-Aldrich) was introduced for 5 min.

Transfer procedure

To transfer the samples onto the SiO2/Si substrate we used PMMA according to previously reported procedures36. In brief: Graphene on copper was coated with diluted 50:50 Poly(methyl methacrylate) (PMMA, 950 A9, Microchem, 4.5% in anisole) followed by removing the copper from the copper etchant (CE-100, Transene). Then the PMMA/graphene was washed by DI water to remove the residual copper etchant and the PMMA was removed by thermal annealing at 350°C for 3 h under a 200 sccm H2/200 sccmAr atmosphere.

Electrochemistry Raman spectroscopy

For the doping experiments, the graphene samples on a SiO2/Si substrate served as working electrodes and the samples were contacted using Au evaporated on a part of the substrate. The cell was completed with a Pt-counter electrode and an Ag-wire pseudo-reference electrode. The electrolyte solution used was 0.1 M LiClO4 dissolved in dry propylenecarbonate/PMMA (Aldrich). Electrochemical doping of the working graphene electrode was carried out by varying the applied potential between −1.5 and 1.5 V vs. an Ag pseudoreference electrode (PAR potentiostat). We used a three electrode system and carried out measurements in the potentiostatic regime, so that no current was flowing through the reference electrode during the measurements. Care was also taken so that the current flow through the working electrode was minimal. Since the state (potential) of the pseudo-reference electrode is not changed during the measurement, the applied potential on the working electrode is well defined. The Raman spectra were excited by a Nd-YAG laser (Coherent). The spectrometer resolution was about 2.5 cm−1. The spectrometer was interfaced to a microscope (Carl-Zeiss, objective 100×). The size of the laser spot was about 1 μm.


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This work was supported by the Czech Ministry of Education, Youth and sports (LH-13022), and Czech Grant agency (P208-12-1062). The work done at MIT has been supported by NFS-DMR 10-04147. D.L.M. acknowledges the Brazilian agency CNPq.

Author information


  1. Department of Electrical Engineering and Computer Science, MIT, Cambridge, Massachusetts 02139, USA

    • Paulo T. Araujo
    • , Daniela L. Mafra
    • , Wenjing Fang
    • , Jing Kong
    • , Mildred S. Dresselhaus
    •  & Martin Kalbac
  2. J. Heyrovský Institute of Physical Chemistry, Academy of Sciences of the Czech Republic, v.v.i., Dolejškova 3, CZ-18223 Prague 8, Czech Republic

    • Otakar Frank
    •  & Martin Kalbac
  3. Department of Physics, MIT, Cambridge, Massachusetts, 02139, USA

    • Mildred S. Dresselhaus


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M.K. performed measurements. P.T.A. and M.K. analyzed and explained the data. P.T.A. and M.K. wrote the manuscript. O.F., D.L.M., W.F., J.K. and M.S.D. discussed and reviewed the manuscript contents.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Paulo T. Araujo or Martin Kalbac.

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