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Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands

Nature Chemistry volume 14, pages 267–273 (2022)Cite this article

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Abstract

Tailoring electron transfer dynamics across solid–liquid interfaces is fundamental to the interconversion of electrical and chemical energy. Stacking atomically thin layers with a small azimuthal misorientation to produce moiré superlattices enables the controlled engineering of electronic band structures and the formation of extremely flat electronic bands. Here, we report a strong twist-angle dependence of heterogeneous charge transfer kinetics at twisted bilayer graphene electrodes with the greatest enhancement observed near the ‘magic angle’ (~1.1°). This effect is driven by the angle-dependent tuning of moiré-derived flat bands that modulate electron transfer processes with the solution-phase redox couple. Combined experimental and computational analysis reveals that the variation in electrochemical activity with moiré angle is controlled by a structural relaxation of the moiré superlattice at twist angles of <2°, and ‘topological defect’ AA stacking regions, where flat bands are localized, produce a large anomalous local electrochemical enhancement that cannot be accounted for by the elevated local density of states alone.

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Fig. 1: Twisted bilayer graphene moiré superlattices and their electrochemical response.
Fig. 2: Quantifying quantum capacitance effects in interfacial electron transfer in TBG.
Fig. 3: Moiré angle-dependent electron transfer rate.
Fig. 4: Theoretical electron transfer kinetics within a TBG moiré unit cell.
Fig. 5: Lattice relaxation and anomalous enhancement of electron transfer kinetics at AA regions of TBG.

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Data availability

The data supporting the findings of this study are available within the Article and its Supplementary Information files. Source data are provided with this paper. Any additional data are available from the corresponding author.

Code availability

The computer codes used for Delaunay triangulation and quantum capacitance calculations are publicly available at https://github.com/bediakolab/bediakolab_scripts. The computer code used for tight-binding band structure calculations of TBG is publicly available at https://github.com/stcarr/kp_tblg. The computer code used for calculation of theoretical electrochemical rate constants is available in the Github package for calculating Marcus–Hush–Chidsey reaction kinetics incorporating DOS: https://github.com/aced-differentiate/MHC_DOS.

Change history

  • 28 February 2022

    In the version of Fig. 1 initially published, the red probe and blue fill appearing in the Fig. 1g schematic were obscured and have now been restored. Further, in Fig. 4c, the right-hand top label now reading "ϵ = 0.17 eV" was initially a duplicate of the label on the top-left of Fig. 4c.

References

  1. Marcus, R. A. Electron transfer reactions in chemistry: theory and experiment (Nobel Lecture). Angew. Chem. Int. Ed. 32, 1111–1121 (1993).

    Article  Google Scholar 

  2. Seh, Z. W. et al. Combining theory and experiment in electrocatalysis: insights into materials design. Science 355, eaad4998 (2017).

    Article  PubMed  Google Scholar 

  3. Hwang, J. et al. Perovskites in catalysis and electrocatalysis. Science 358, 751–756 (2017).

    Article  CAS  PubMed  Google Scholar 

  4. Boettcher, S. W. & Surendranath, Y. Heterogeneous electrocatalysis goes chemical. Nat. Catal. 4, 4–5 (2021).

    Article  CAS  Google Scholar 

  5. Grimaud, A., Hong, W. T., Shao-Horn, Y. & Tarascon, J.-M. Anionic redox processes for electrochemical devices. Nat. Mater. 15, 121–126 (2016).

    Article  CAS  PubMed  Google Scholar 

  6. Deng, D. et al. Catalysis with two-dimensional materials and their heterostructures. Nat. Nanotechnol. 11, 218–230 (2016).

    Article  CAS  PubMed  Google Scholar 

  7. Jin, H. et al. Emerging two-dimensional nanomaterials for electrocatalysis. Chem. Rev. 118, 6337–6408 (2018).

    Article  CAS  PubMed  Google Scholar 

  8. Chia, X. & Pumera, M. Characteristics and performance of two-dimensional materials for electrocatalysis. Nat. Catal. 1, 909–921 (2018).

    Article  CAS  Google Scholar 

  9. Jaramillo, T. F. et al. Identification of active edge sites for electrochemical H2 evolution from MoS2 nanocatalysts. Science 317, 100–102 (2007).

    Article  CAS  PubMed  Google Scholar 

  10. Zhong, J. H. et al. Quantitative correlation between defect density and heterogeneous electron transfer rate of single layer graphene. J. Am. Chem. Soc. 136, 16609–16617 (2014).

    Article  CAS  PubMed  Google Scholar 

  11. Wang, L. et al. Tunable intrinsic strain in two-dimensional transition metal electrocatalysts. Science 363, 870–874 (2019).

    Article  CAS  PubMed  Google Scholar 

  12. Li, H. et al. Activating and optimizing MoS2 basal planes for hydrogen evolution through the formation of strained sulphur vacancies. Nat. Mater. 15, 48–53 (2016).

    Article  CAS  PubMed  Google Scholar 

  13. Wang, Y., Udyavara, S., Neurock, M. & Frisbie, C. D. Field effect modulation of electrocatalytic hydrogen evolution at back-gated two-dimensional MoS2 electrodes. Nano Lett. 19, 6118–6123 (2019).

    Article  CAS  PubMed  Google Scholar 

  14. Güell, A. G. et al. Redox-dependent spatially resolved electrochemistry at graphene and graphite step edges. ACS Nano 9, 3558–3571 (2015).

    Article  PubMed  Google Scholar 

  15. Mariano, R. G., McKelvey, K., White, H. S. & Kanan, M. W. Selective increase in CO2 electroreduction activity at grain-boundary surface terminations. Science 358, 1187–1192 (2017).

    Article  CAS  PubMed  Google Scholar 

  16. Geim, A. K. & Grigorieva, I. V. Van der Waals heterostructures. Nature 499, 419–425 (2013).

    Article  CAS  PubMed  Google Scholar 

  17. Dean, C. R. et al. Hofstadter’s butterfly and the fractal quantum Hall effect in moiré superlattices. Nature 497, 598–602 (2013).

    Article  CAS  PubMed  Google Scholar 

  18. Balents, L., Dean, C. R., Efetov, D. K. & Young, A. F. Superconductivity and strong correlations in moiré flat bands. Nat. Phys. 16, 725–733 (2020).

    Article  CAS  Google Scholar 

  19. Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).

    Article  CAS  PubMed  Google Scholar 

  20. Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).

    Article  CAS  PubMed  Google Scholar 

  21. Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).

    Article  CAS  PubMed  Google Scholar 

  22. Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).

    Article  CAS  PubMed  Google Scholar 

  23. Lu, X. et al. Superconductors, orbital magnets and correlated states in magic-angle bilayer graphene. Nature 574, 653–657 (2019).

    Article  CAS  PubMed  Google Scholar 

  24. Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  25. Utama, M. I. B. et al. Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist. Nat. Phys. 17, 184–188 (2021).

    Article  CAS  Google Scholar 

  26. Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).

    Article  CAS  PubMed  Google Scholar 

  27. Alden, J. S. et al. Strain solitons and topological defects in bilayer graphene. Proc. Natl Acad. Sci. USA 110, 11256–11260 (2013).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  28. Jiang, Z. et al. MoS2 moiré superlattice for hydrogen evolution reaction. ACS Energy Lett. 4, 2830–2835 (2019).

    Article  CAS  Google Scholar 

  29. Ding, Y. et al. Stacking modes-induced chemical reactivity differences on chemical vapor deposition-grown trilayer graphene. ACS Appl. Mater. Interfaces 10, 23424–23431 (2018).

    Article  CAS  PubMed  Google Scholar 

  30. Ding, Y. et al. Stacking-mode-induced reactivity enhancement for twisted bilayer graphene. Chem. Mater. 28, 1034–1039 (2016).

    Article  CAS  Google Scholar 

  31. Yoo, H. et al. Atomic and electronic reconstruction at the van der Waals interface in twisted bilayer graphene. Nat. Mater. 18, 448–453 (2019).

    Article  CAS  PubMed  Google Scholar 

  32. Kerelsky, A. et al. Maximized electron interactions at the magic angle in twisted bilayer graphene. Nature 572, 95–100 (2019).

    Article  CAS  PubMed  Google Scholar 

  33. Kazmierczak, N. P. et al. Strain fields in twisted bilayer graphene. Nat. Mater. 20, 956–963 (2021).

    Article  CAS  PubMed  Google Scholar 

  34. Trambly de Laissardière, G., Mayou, D. & Magaud, L. Localization of Dirac electrons in rotated graphene bilayers. Nano Lett. 10, 804–808 (2010).

    Article  PubMed  Google Scholar 

  35. Bentley, C. L., Kang, M. & Unwin, P. R. Nanoscale surface structure–activity in electrochemistry and electrocatalysis. J. Am. Chem. Soc. 141, 2179–2193 (2019).

    Article  CAS  PubMed  Google Scholar 

  36. Unwin, P. R., Güell, A. G. & Zhang, G. Nanoscale electrochemistry of sp2 carbon materials: from graphite and graphene to carbon nanotubes. Acc. Chem. Res. 49, 2041–2048 (2016).

    Article  CAS  PubMed  Google Scholar 

  37. Schmickler, W. & Santos, E. Interfacial Electrochemistry 2nd edn (Springer, 2010).

    Book  Google Scholar 

  38. Bard, A. J. & Faulkner, L. R. Electrochemical Methods: Fundamentals and Applications 2nd edn (Wiley, 2001).

    Google Scholar 

  39. Li, J., Pham, P. H. Q., Zhou, W., Pham, T. D. & Burke, P. J. Carbon-nanotube–electrolyte interface: quantum and electric double layer capacitance. ACS Nano 12, 9763–9774 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  40. Heller, I., Kong, J., Williams, K. A., Dekker, C. & Lemay, S. G. Electrochemistry at single-walled carbon nanotubes: the role of band structure and quantum capacitance. J. Am. Chem. Soc. 128, 7353–7359 (2006).

    Article  CAS  PubMed  Google Scholar 

  41. Henstridge, M. C., Laborda, E., Rees, N. V. & Compton, R. G. Marcus–Hush–Chidsey theory of electron transfer applied to voltammetry: a review. Electrochim. Acta 84, 12–20 (2012).

    Article  CAS  Google Scholar 

  42. Kurchin, R. & Viswanathan, V. Marcus–Hush–Chidsey kinetics at electrode–electrolyte interfaces. J. Chem. Phys. 153, 134706 (2020).

    Article  CAS  PubMed  Google Scholar 

  43. Bae, J. H., Yu, Y. & Mirkin, M. V. Diffuse layer effect on electron-transfer kinetics measured by scanning electrochemical microscopy (SECM). J. Phys. Chem. Lett. 8, 1338–1342 (2017).

    Article  CAS  PubMed  Google Scholar 

  44. Fan, L., Liu, Y., Xiong, J., White, H. S. & Chen, S. Electron-transfer kinetics and electric double layer effects in nanometer-wide thin-layer cells. ACS Nano 8, 10426–10436 (2014).

    Article  CAS  PubMed  Google Scholar 

  45. Zhang, K. & Tadmor, E. B. Structural and electron diffraction scaling of twisted graphene bilayers. J. Mech. Phys. Solids 112, 225–238 (2018).

    Article  Google Scholar 

  46. Pavlov, S. V., Nazmutdinov, R. R., Fedorov, M. V. & Kislenko, S. A. Role of graphene edges in the electron transfer kinetics: insight from theory and molecular modeling. J. Phys. Chem. C 123, 6627–6634 (2019).

    Article  CAS  Google Scholar 

  47. Li, H. et al. Rapid and reliable thickness identification of two-dimensional nanosheets using optical microscopy. ACS Nano 7, 10344–10353 (2013).

    Article  CAS  PubMed  Google Scholar 

  48. Ferrari, A. C. et al. Raman spectrum of graphene and graphene layers. Phys. Rev. Lett. 97, 187401 (2006).

    Article  CAS  PubMed  Google Scholar 

  49. Girit, Ç. Ö. & Zettl, A. Soldering to a single atomic layer. Appl. Phys. Lett. 91, 193512 (2007).

    Article  Google Scholar 

  50. Kirkman, P. M. et al. Spatial and temporal control of the diazonium modification of sp2 carbon surfaces. J. Am. Chem. Soc. 136, 36–39 (2014).

    Article  CAS  PubMed  Google Scholar 

  51. Patel, A. N., McKelvey, K. & Unwin, P. R. Nanoscale electrochemical patterning reveals the active sites for catechol oxidation at graphite surfaces. J. Am. Chem. Soc. 134, 20246–20249 (2012).

    Article  CAS  PubMed  Google Scholar 

  52. Carr, S., Fang, S., Zhu, Z. & Kaxiras, E. Exact continuum model for low-energy electronic states of twisted bilayer graphene. Phys. Rev. Res. 1, 013001 (2019).

    Article  CAS  Google Scholar 

  53. Carr, S. et al. Relaxation and domain formation in incommensurate two-dimensional heterostructures. Phys. Rev. B 98, 224102 (2018).

    Article  CAS  Google Scholar 

  54. Carr, S., Fang, S. & Kaxiras, E. Electronic-structure methods for twisted moiré layers. Nat. Rev. Mater. 5, 748–763 (2020).

    Article  CAS  Google Scholar 

  55. Fang, S. & Kaxiras, E. Electronic structure theory of weakly interacting bilayers. Phys. Rev. B 93, 235153 (2016).

    Article  Google Scholar 

  56. Lucignano, P., Alfè, D., Cataudella, V., Ninno, D. & Cantele, G. Crucial role of atomic corrugation on the flat bands and energy gaps of twisted bilayer graphene at the magic angle θ ~ 1.08°. Phys. Rev. B 99, 195419 (2019).

    Article  CAS  Google Scholar 

  57. Huder, L. et al. Electronic spectrum of twisted graphene layers under heterostrain. Phys. Rev. Lett. 120, 156405 (2018).

    Article  CAS  PubMed  Google Scholar 

  58. Bi, Z., Yuan, N. F. Q. & Fu, L. Designing flat bands by strain. Phys. Rev. B 100, 035448 (2019).

    Article  CAS  Google Scholar 

  59. Yang, G. M., Zhang, H. Z., Fan, X. F. & Zheng, W. T. Density functional theory calculations for the quantum capacitance performance of graphene-based electrode material. J. Phys. Chem. C 119, 6464–6470 (2015).

    Article  CAS  Google Scholar 

  60. Xia, J., Chen, F., Li, J. & Tao, N. Measurement of the quantum capacitance of graphene. Nat. Nanotechnol. 4, 505–509 (2009).

    Article  CAS  PubMed  Google Scholar 

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Acknowledgements

We acknowledge discussions with R. Kurchin. This material is based upon work supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, under award no. DE-SC0021049 (experimental studies by Y.Y., K.Z. and D.K.B.) and the Office of Naval Research under award no. N00014-18-S-F009 (computational work by H.P., M.B. and V.V.). S.C. acknowledges support from the National Science Foundation under grant no. OIA-1921199. I.M.C. acknowledges support from a University of California, Berkeley Berkeley Fellowship. M.V.W. acknowledges support from a National Science Foundation Graduate Research Fellowships Program award and University of California, Berkeley Chancellor’s Fellowship. Confocal Raman spectroscopy was supported by a Defense University Research Instrumentation Program grant through the Office of Naval Research under award no. N00014-20-1-2599 (D.K.B.). D.K.B. acknowledges support from the Rose Hills Foundation through the Rose Hills Innovator Program. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the Ministry of Education, Culture, Sports, Science and Technology, Japan (grant no. JPMXP0112101001) and Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research (KAKENHI; grant nos 19H05790, 20H00354 and 21H05233).

Author information

Authors and Affiliations

  1. Department of Chemistry, University of California, Berkeley, CA, USA

    Yun Yu, Kaidi Zhang, Isaac M. Craig, Madeline Van Winkle, Artur Lyssenko & D. Kwabena Bediako

  2. Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, PA, USA

    Holden Parks, Mohammad Babar & Venkatasubramanian Viswanathan

  3. Brown Theoretical Physics Center, Brown University, Providence, RI, USA

    Stephen Carr

  4. International Center for Materials Nanoarchitectonics, National Institute for Materials Science, Tsukuba, Japan

    Takashi Taniguchi

  5. Research Center for Functional Materials, National Institute for Materials Science, Tsukuba, Japan

    Kenji Watanabe

  6. Department of Physics, Carnegie Mellon University, Pittsburgh, PA, USA

    Venkatasubramanian Viswanathan

  7. Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, CA, USA

    D. Kwabena Bediako

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  1. Yun Yu
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Contributions

Y.Y. and D.K.B. conceived the study. Y.Y., K.Z. and A.L. performed the experiments. Y.Y. performed the COMSOL simulations. H.P., M.B., S.C. and V.V. carried out the theoretical calculations. I.M.C. performed the quantum capacitance calculations and STM image analysis. M.V.W. carried out the electron diffraction measurements. T.T. and K.W. provided the hBN crystals. Y.Y., K.Z., I.M.C. and D.K.B. analysed the data. Y.Y. and D.K.B. wrote the manuscript.

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Correspondence to D. Kwabena Bediako.

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Nature Chemistry thanks Prabhakar Bandaru, Patrick Unwin and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Extended data

Extended Data Fig. 1 DOS of twisted bilayer graphene.

Calculated DOS of twisted bilayer graphene with various moiré twist angles, θm. θm = 0° corresponds to Bernal (AB) stacked bilayer graphene.

Source data

Extended Data Fig. 2 In situ conductance measurements of bilayer graphene as a function of the electrochemical bias.

a, Optical micrograph of representative device for in situ conductance measurements. b, Schematic of conductance measurement. The micropipettes are filled with 2 mM Ru(NH3)63+ in 0.1 M KCl aqueous solution. c, Flake resistance as a function of the electrochemical bias obtained from 3 different AB-stacked bilayer graphene samples, showing the position of the charge neutrality point (maximum resistance) relative to the E° values of the three redox couples interrogated in this study.

Source data

Extended Data Fig. 3 Moiré angle dependent electron transfer rate of Ru(NH3)63+/2+ and Co(Phen)33+/2+.

a, k° extracted from the experimental voltammograms as a function of twist angle for the Co(Phen)33+/2+ (blue squares) and Ru(NH3)63+/2+ (red circles) redox couples. b, k° for Co(Phen)33+/2+ extracted from the experimental voltammograms (blue filled circles) as a function of twist angle compared to the values calculated with GM framework (black open circles). The horizontal and vertical error bars represent the standard deviations of θm and k°, respectively.

Source data

Supplementary information

Supplementary Information

Supplementary Figs. 1–23, Tables 1 and 2 and finite-element simulations.

Source data

Source Data Fig. 1

Source data for Fig. 1d,f,h.

Source Data Fig. 2

Source data for Fig. 2b,c.

Source Data Fig. 3

Source data for Fig. 3a–d.

Source Data Fig. 4

Source data for Fig. 4a–c.

Source Data Fig. 5

Source data for Fig. 5a.

Source Data Extended Data Fig. 1

Source data for all shown graphs.

Source Data Extended Data Fig. 2

Source data for Extended Data Fig. 2c.

Source Data Extended Data Fig. 3

Source data for all shown graphs.

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Yu, Y., Zhang, K., Parks, H. et al. Tunable angle-dependent electrochemistry at twisted bilayer graphene with moiré flat bands. Nat. Chem. 14, 267–273 (2022). https://doi.org/10.1038/s41557-021-00865-1

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