Intralayer and interlayer electron–phonon interactions in twisted graphene heterostructures

The understanding of interactions between electrons and phonons in atomically thin heterostructures is crucial for the engineering of novel two-dimensional devices. Electron–phonon (el–ph) interactions in layered materials can occur involving electrons in the same layer or in different layers. Here we report on the possibility of distinguishing intralayer and interlayer el–ph interactions in samples of twisted bilayer graphene and of probing the intralayer process in graphene/h-BN by using Raman spectroscopy. In the intralayer process, the el–ph scattering occurs in a single graphene layer and the other layer (graphene or h-BN) imposes a periodic potential that backscatters the excited electron, whereas for the interlayer process the el–ph scattering occurs between states in the Dirac cones of adjacent graphene layers. Our methodology of using Raman spectroscopy to probe different types of el–ph interactions can be extended to study any kind of graphene-based heterostructure.

1. Although one can refer to electrons being in one layer or another, one cannot do the same about the phonons because phonons are essentially normal vibration modes of the entire crystal. The authors say, for example, "In atomically thin heterostructures, the interaction can involve both electrons and phonons in the same layer (intralayer el-ph interaction) or in adjacent layers (interlayer el-ph interaction)." Although it is perfectly all right to mention interlayer (or intralayer) electron-phonon scattering, the expression such as 'phonons in the same layer' should be avoided.
2. Page 3, 9th line from the bottom of the right column: More explanation is needed for the following claim, '… in the case of TBG, the back-scattering is provided by a periodic potential of the Moire pattern.' Unlike the disorder-induced D and D' bands, the periodic potential of the Moire pattern has a definite orientation. As such, it should be checked whether the momentum conservation would work in this case. 5. There is no description of the sample preparation. Although the details have been published elsewhere, a summary of the sample preparation methods should be given in the Experimental Methods section.
6. There are some grammatical errors in the text. A thorough proofreading is recommended.
Reviewer #2 (Remarks to the Author): The authors report a meticulous study on intralayer and interlayer electron-phonon interactions in twisted bilayer graphene through Raman spectroscopy measurements. They observed additional Raman peaks in twisted bilayer graphene and carefully checked its behaviors in terms of the excitation laser energy and the twisting angle. DFT calculations were done to compare the experimental results with theoretical model. The conclusion is reasonable and the results are meaningful to the research community. However, there are still some concerns which need to be further clarified. I suggest that a major revision is needed.
My comments and concerns are as follows (1) In page 4, "These two maximum are associated with electronic transitions close to K and M points of the graphene, and will be called E^{-} and E^{+}." From only this sentence, it is difficult to make sense. As far as I understand, E^{-} is shown in Fig.2(b). E^{+} is not easy to imagine. To make it clarified, I suggest to show a schematics for E^{+}.
(2) As the authors mentioned in page 5, all of them, L_a, L_e, T_a and T_e, should be active in any twisting angle. However, some peaks were not observed in such condition. Could you explain the reason?
(3) In a same context of comments (2), could you plot I_{L_a}/I_SLG, I_{L_e}/ I_SLG, I_(T_a)/I_SLG and I_{T_e}/I_SLG vs. the twisting angle when the intensity is maximum in such photon energy? I think you can compare these plots to your calculations. These plots can help to confirm your theoretical model. (4) I found minor mistakes in this manuscript. Corrections are needed. a. In Fig.3(c) and (d), green squares should be changed to green circle. b. In Fig. 3(c), the explanation for red and black crosses are missed. c. In reference 18, volume and page numbers are missed.
Reviewer #3 (Remarks to the Author): In the present work, the authors report on the observation of specific Raman peaks related to both intralayer and interlayer electron-phonon interactions in twisted graphene bilayers with different twisting angles. They also propose that the intensity of these extra peaks could provide information relative to the strength of the interaction between graphene and the substrate (h-BN).
This work is scientifically sound, original, and the scientific discussion is quite convincing. This research results in a major conceptual leap forward in the Raman study of electron-phonon interactions in graphene heterostructures. At last, the present work also proposes a novel clear convention for these extra Raman peaks (La, Le, Ta, Te) that is clarifying the previous ambiguous notations (R and R' peaks).
The only minor weak point is the absence of critical scientific background regarding the use of the simple folding of the SLG theoretical calculations to capture the physics of both intralayer and interlayer processes in twisted bilayer graphene. Some additional discussion would have been helpful to understand some observed discrepancies (i.e. Fig.4.g).
To my opinion, the present manuscript meets the guidelines for publication in Nature Communications, and I would thus strongly recommend its publication.

Reviewer #1 (Remarks to the Author):
This is a very interesting piece of work that clarifies the origins of the extra peaks observed in Raman spectra of twisted bilayer graphene (TBG). The authors carried out extensive measurements using many laser lines and compared the data with a theoretical model to justify their conclusion. The analyses are rigorous and technically sound. Although the topic would attract the interest of a relatively small number of researchers specializing in Raman analysis of graphene, the implication and the scientific rigor would justify publication in Nature Communications.
Answer: We thank Reviewer #1 for recognizing the quality and importance of our work.
I only have a few minor comments that the authors need to address when they prepare the final version of the manuscript.
1. Although one can refer to electrons being in one layer or another, one cannot do the same about the phonons because phonons are essentially normal vibration modes of the entire crystal. The authors say, for example, "In atomically thin heterostructures, the interaction can involve both electrons and phonons in the same layer (intralayer el-ph interaction) or in adjacent layers (interlayer el-ph interaction)." Although it is perfectly all right to mention interlayer (or intralayer) electronphonon scattering, the expression such as 'phonons in the same layer' should be avoided.
Answer: We agree with this comment and we have corrected the sentences in the Abstract and in the 1 st paragraph of the manuscript, which is now written as.
"In atomically thin heterostructures, the interaction can involve electrons in the same layer (intralayer el-ph interaction) or in adjacent layers (interlayer el-ph interaction)."

Page 3, 9th line from the bottom of the right column: More explanation is needed for the following claim, '… in the case of TBG, the back-scattering is provided by a periodic potential of the Moire pattern.' Unlike the disorder-induced D and D' bands, the periodic potential of the Moire pattern has a definite orientation. As such, it should be checked whether the momentum conservation would work in this case.
Answer: We have added the following sentence in the Experimental Methods section: The TBG samples were grown by CVD technique using methane (99.99%) on polycrystalline Cu foils [12]. The graphene layers were first covered by a thin layer of polycarbonate, followed by etching in HCl aqueous solution to remove the Cu in the transfer process. The polycarbonate film with attached graphene was then transferred onto different substrates: a 300 nm SiO2/Si, 90 nm SiO2/Si and fused silica. Finally, the polycarbonate film was removed using chloroform. The gr/BN samples were prepared by mechanical exfoliation of graphene and transference to a h-BN substrate 6. There are some grammatical errors in the text. A thorough proofreading is recommended.
Answer: We have made a full revision of the manuscript.

Reviewer #2 (Remarks to the Author):
The authors report a meticulous study on intralayer and interlayer electron-phonon interactions in twisted bilayer graphene through Raman spectroscopy measurements. They observed additional Raman peaks in twisted bilayer graphene and carefully checked its behaviors in terms of the excitation laser energy and the twisting angle. DFT calculations were done to compare the experimental results with theoretical model. The conclusion is reasonable and the results are meaningful to the research community.
Answer: We also thank Reviewer #2 for recognizing the quality and importance of our work.
However, there are still some concerns which need to be further clarified. I suggest that a major revision is needed.
My comments and concerns are as follows.
(1) In page 4, "These two maximum are associated with electronic transitions close to K and M points of the graphene, and will be called E^{-} and E^{+}." From only this sentence, it is difficult to make sense. As far as I understand, E^{-} is shown in Fig.2(b). E^{+} is not easy to imagine. To make it clarified, I suggest to show a schematics for E^{+}.
Answer: We thank Reviewer #2 for this suggestion. We have included an inset in Fig. 3c showing schematically the processes associated to Ea , Ee , E + a and E + e . In order to improve the comprehension of Fig 3c, we changed the color of the previous continuous black curve, that is now presented in dashed green. We added the following sentence in the manuscript: In the caption of Fig. 3c we show the low and high energy intralayer and interlayer processes. Notice that, in the limit of small and large twisting angles, the low energy transitions involve states near the K point of graphene, whereas the high energy transitions involve states near the M point.
(2) As the authors mentioned in page 5, all of them, L_a, L_e, T_a and T_e, should be active in any twisting angle. However, some peaks were not observed in such condition. Could you explain the reason?
Answer: This issue has briefly discussed in the paragraph in the right column of page 5 starting as: "In principle, the interlayer electron-phonon scattering process can also activate LO phonons...". As suggested by Reviewer #2, we have reviewed and extended this paragraph in order to clearly address this point. In fact, in our Raman experiments in TBG using visible light, we have not observed the L e and T a peaks. The absence of L e can be only due to the fact that this peak might appear in spectra where the G band is hugely enhanced. Since the L e peak is expected to appear very close to the G band using visible photons, it is possibly masked by the G band enhancement. The absence of T a is not yet well understood. It is possibly due to the very small Raman cross-section of TO phonons in the intralayer process using visible photons. However, a complete calculation of the cross-section will be needed to explain these results. The new version of the paragraph is now: In principle, the intralayer and interlayer el-ph processes can also activate TO and LO phonons, respectively, and give rise to T_a and L_e peaks for samples with intermediate angles. However, T_a and L_e were not observed in our multiple excitation experiments using visible photons. The lack of observation of L_e can be due to the huge enhancement of the G band. Since the position of the L_e peak is very close to the G band position in samples with intermediate twisting angles, it is possibly masked by the G band enhancement. For samples with θ around 10 • and measured using the 1.96 eV laser line,  reported the observation of a peak at 1622 cm −1 , that might be assigned to the L e . The absence of T_a can be ascribed to the very weak cross-section of TO phonons activated by the intralayer process. Electron-phonon matrix elements calculations would be necessary to better clarify this issue. .
(3) In a same context of comments (2), could you plot I_{L_a}/I_SLG, I_{L_e}/ I_SLG, I_(T_a)/I_SLG and I_{T_e}/I_SLG vs. the twisting angle when the intensity is maximum in such photon energy? I think you can compare these plots to your calculations. These plots can help to confirm your theoretical model. Answer: As suggested by Reviewer 2, we have included a new figure in the Supplementary Material (SM) with the plots I_{L_a}/I_SLG and I_{T_e}/I_SLG vs. the twisting angle. In this work, we only calculated the frequencies and laser energies where the new peaks should appear, but not the intensities of each peak. The calculation of Raman intensities is more challenging, since we need to consider the values of the matrix elements for the electron-phonon and electron-photon interactions. Future calculations will be needed to describe the Raman intensities of the extra peaks. We have added the following sentence in the SM in order to explain the new Fig. 8 of the SM. Figure 8 shows the relative intensities of T a , T e , L a and L e as a function of the twisting angle \theta. Notice that they increase with decreasing values of \theta.