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# Localization of lattice dynamics in low-angle twisted bilayer graphene

## Abstract

Twisted bilayer graphene is created by slightly rotating the two crystal networks in bilayer graphene with respect to each other. For small twist angles, the material undergoes a self-organized lattice reconstruction, leading to the formation of a periodically repeated domain1,2,3. The resulting superlattice modulates the vibrational3,4 and electronic5,6 structures within the material, leading to changes in the behaviour of electron–phonon coupling7,8 and to the observation of strong correlations and superconductivity9. However, accessing these modulations and understanding the related effects are challenging, because the modulations are too small for experimental techniques to accurately resolve the relevant energy levels and too large for theoretical models to properly describe the localized effects. Here we report hyperspectral optical images, generated by a nano-Raman spectroscope10, of the crystal superlattice in reconstructed (low-angle) twisted bilayer graphene. Observations of the crystallographic structure with visible light are made possible by the nano-Raman technique, which reveals the localization of lattice dynamics, with the presence of strain solitons and topological points1 causing detectable spectral variations. The results are rationalized by an atomistic model that enables evaluation of the local density of the electronic and vibrational states of the superlattice. This evaluation highlights the relevance of solitons and topological points for the vibrational and electronic properties of the structures, particularly for small twist angles. Our results are an important step towards understanding phonon-related effects at atomic and nanometric scales, such as Jahn–Teller effects11 and electronic Cooper pairing12,13,14, and may help to improve device characterization15 in the context of the rapidly developing field of twistronics16.

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## Data availability

The experimental data related to this work, including the raw and processed data, are available at https://doi.org/10.5281/zenodo.4313869. The data related to the theoretical work are available on request to the corresponding authors.

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## Acknowledgements

This work was supported by CNPq (302775/2018-8 and INCT/Nanomaterials de Carbono), CAPES (RELAII and 88881.198744/2018-01) and FAPEMIG, Brazil. V.-H.N. and J.-C.C. acknowledge financial support from the Fédération Wallonie-Bruxelles through the ARC on 3D nano-architecturing of 2D crystals (16/21-077), from the European Union’s Horizon 2020 Research Project and Innovation Program — Graphene Flagship Core3 (881603), from the Flag-Era JTC projects ‘MECHANIC’ (R.50.07.18) and ‘TATTOOS’ (R.8010.19), from the Belgium FNRS through the research projects T.1077.15 and T.0051.18, and from the Francqui-Stichting Foundation. V.M. and M.L. acknowledge support from NY State Empire State Development’s Division of Science, Technology and Innovation (NYSTAR).

## Author information

Authors

### Contributions

Sample preparation: A.C.G., D.M., F.C.S., E.G.S.N., J.S.L., L.C.C., R.N. and V.O.; K.W. and T.T. provided hBN crystals. Nano-Raman measurements: A.C.G., C.R. and T.L.V. Micro-Raman measurements: A.C.G., E.G.S.N., J.S.L. and R.N. Scanning probe microscopy measurements: D.A.A.O. and G.M.-R. Phonon structure computation: B.v.T., M.L. and V.M. Electronic structure computation: D.P., V.-H.N. and J.-C.C. Data analysis: A.J., A.C.G., C.R., E.G.S.N. and J.L.C. Project idealization and guidance: A.J., G.M.-R., L.G.C., L.C.C. and V.M. Paper writing: A.J., A.C.G. and V.M. Some authors contributed to parts of the text and figures. All authors read and agreed on the final version of the manuscript.

### Corresponding authors

Correspondence to Vincent Meunier or Ado Jorio.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

Peer review information Nature thanks Ludger Wirtz and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Peer reviewer reports are available.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

## Extended data figures and tables

### Extended Data Fig. 1 Comparison between micro- and nano-Raman spectra in the rTBG sample.

This figure is a reproduction of Fig. 1c, but with the intensity of the micro-Raman spectrum multiplied by 26 to better visualize and compare the details of the two spectra. The enhancement of the hBN substrate peak is considerably lower, owing to the presence of the graphene sample between the tip and the substrate.

### Extended Data Fig. 2 Representative spectral profiles and images for two other rTBG samples.

a, c, The spectral Raman profiles evidence different frequency values for the $${G}_{{\rm{r}}}^{-}$$ and $${G}_{{\rm{r}}}^{+}$$ peaks observed in two different rTBG samples (black arrows link the profiles to the corresponding images in b and d). The vertical lines indicate the central frequencies for the observed $${G}_{{\rm{r}}}^{-}$$, G and $${G}_{{\rm{r}}}^{+}$$ peaks. b, d, The spectral images are based on the G′-band intensities (colour scale). The arrow in d indicates the where the specrum in c was taken. In Fig. 2f (rTBG with θ = 0.09°), the peaks are observed at $${\omega }_{{G}_{{\rm{r}}}^{-}}=1,522\,{{\rm{cm}}}^{-1}$$ and $${\omega }_{{G}_{{\rm{r}}}^{+}}=1,612\,{{\rm{cm}}}^{-1}$$. The frequency difference between the theoretically predicted $${G}_{{\rm{r}}}^{-}$$ and $${G}_{{\rm{r}}}^{+}$$ peaks is $$\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=45\,{{\rm{cm}}}^{-1}$$ (for θ = 0.987°; already reaching the limit of our computational capability). For the experimentally observed $${G}_{{\rm{r}}}^{-}$$ and $${G}_{{\rm{r}}}^{+}$$ peaks for θ = 0.09°, it is $$\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=90\,{{\rm{cm}}}^{-1}$$. Our ability to experimentally define the θ dependence of the splitting is also limited, by the TERS resolution. We cannot properly image a moiré pattern smaller than 40 nm (twice the TERS resolution), limiting the rTBG samples that we can image to those with θ < 0.3°. The $$\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}$$ splitting is predicted to increase with decreasing twist angle6, consistent with experimental observations: for LM ≈ 160 nm (θ ≈ 0.09°), we observed $${\omega }_{{G}_{{\rm{r}}}^{-}}=1,522\,{{\rm{cm}}}^{-1}$$ and $${\omega }_{{G}_{{\rm{r}}}^{+}}=1,612\,{{\rm{cm}}}^{-1}$$ ($$\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=90\,{{\rm{cm}}}^{-1}$$); for LM ≈ 210 nm (θ ≈ 0.07°), we observed $${\omega }_{{G}_{{\rm{r}}}^{-}}=1,517\,{{\rm{cm}}}^{-1}$$ and $${\omega }_{{G}_{{\rm{r}}}^{+}}=1,616\,{{\rm{cm}}}^{-1}$$ ($$\Delta {\omega }_{{G}_{{\rm{r}}}^{\pm }}=99\,{{\rm{cm}}}^{-1}$$); for LM > 1,000 nm (θ < 0.01), $${\omega }_{{G}_{{\rm{r}}}^{-}}$$ was not observed, but $${\omega }_{{G}_{{\rm{r}}}^{+}}=1,619\,{{\rm{cm}}}^{-1}$$ follows the trend.

### Extended Data Fig. 3 Correlation between G- and G′-band frequencies and FWHMs.

a, b, The frequencies (a) and FWHMs (b) are shown for the data displayed in Fig. 1d. The G′ spectra were fitted using four Lorentzians, as per ref. 26. The results shown here are for the most intense G′ feature (named ‘L02’ in ref. 26). The inset in a shows the behaviour of the four peaks.

### Extended Data Fig. 4 Correlation between G- and G′-band frequencies and FWHMs.

a, b, The frequencies (a) and FWHMs (b) are shown for the data displayed in Fig. 4. The twist angle for each point is labelled. The red curved arrow in b indicates a maximum in FWHM observed near the magic angle.

### Extended Data Fig. 5 Schematics of the sample preparation procedure.

a, We cover the newly developed PDMS tear-and-stack pyramid stamp (TPS) with a polycarbonate (PC) sheet and align the TPS edge with the middle of a graphene flake. b, Next, we make contact between the TPS and graphene, followed by a temperature ramp from 70 °C to 80 °C. c, We then wait for the system to cool down, reaching a temperature of 70 °C, similarly to the pick-up method46, removing a piece of the graphene flake. d, e, We then rotate the base (d) and stack the two parts of graphene together, forming the TBG (e). f, We do the previous temperature ramp and cool-down procedure again to remove the remaining graphene piece. g, Next, we put the TBG in contact with a flat and clean hBN flake at room temperature. h, The van der Waals interactions between them is strong enough for the hBN to pull out the TBG from the TPS.

### Extended Data Fig. 6 TERS imaging of nine different moiré structures from rTBG.

ai, TERS images from various moiré structural formations based on the G′-band intensity (left) and the simultaneously obtained AFM images (right). The solitonic structures are observable only in the TERS images (darker blue lines); they are absent in the AFM images. The contrast discontinuities in b and f are due to the realignment of the tip with the laser during the scan.

### Extended Data Fig. 7 Multi-technique structural characterization of rTBG.

a, b, TERS (a) and sMIM (b) images of the same rTBG region.

## Supplementary information

### Supplementary Information

This file contains brings more details about the theory utilized in our work, including Raman intensity calculations, the lattice strain in the relaxed structure and the electronic structure, including (joint) local density of states analysis.

### Supplementary Figures

This document is provided to the reader under the “data availability” directive. The tables summarize the files on a per-figure basis.

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Gadelha, A.C., Ohlberg, D.A.A., Rabelo, C. et al. Localization of lattice dynamics in low-angle twisted bilayer graphene. Nature 590, 405–409 (2021). https://doi.org/10.1038/s41586-021-03252-5

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• ### Lighting up lattice vibrations

• Ankita Anirban

Nature Reviews Materials (2021)