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Excess resistivity in graphene superlattices caused by umklapp electron–electron scattering


In electronic transport, umklapp processes play a fundamental role as the only intrinsic mechanism that allows electrons to transfer momentum to the crystal lattice and, therefore, provide a finite electrical resistance in pure metals1,2. However, umklapp scattering is difficult to demonstrate in experiment, as it is easily obscured by other dissipation mechanisms1,2,3,4,5,6. Here we show that electron–electron umklapp scattering dominates the transport properties of graphene-on-boron-nitride superlattices over a wide range of temperature and carrier density. The umklapp processes cause giant excess resistivity that rapidly increases with increasing superlattice period and are responsible for deterioration of the room-temperature mobility by more than an order of magnitude as compared to standard, non-superlattice graphene devices. The umklapp scattering exhibits a quadratic temperature dependence accompanied by a pronounced electron–hole asymmetry with the effect being much stronger for holes than electrons. In addition to being of fundamental interest, our results have direct implications for design of possible electronic devices based on heterostructures featuring superlattices.

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Fig. 1: Umklapp scattering and excess resistivity in graphene superlattices.
Fig. 2: Electron–electron scattering and its electron–hole asymmetry in graphene superlattices.
Fig. 3: Characteristics of umklapp electron–electron scattering.

Data availability

The data that support plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.


  1. Bass, J., Pratt, W. P. & Schroeder, P. A. The temperature-dependent electrical resistivities of the alkali metals. Rev. Mod. Phys. 62, 645–744 (1990).

    Article  ADS  Google Scholar 

  2. Gasparov, V. A. & Huguenin, R. Electron–phonon, electron–electron and electron–surface scattering in metals from ballistic effects. Adv. Phys. 42, 393–521 (1993).

    Article  ADS  Google Scholar 

  3. Messica, A. et al. Suppression of conductance in surface superlattices by temperature and electric field. Phys. Rev. Lett. 78, 705–708 (1997).

    Article  ADS  Google Scholar 

  4. Overend, N. et al. Giant magnetoresistance and possible miniband effects in periodic magnetic fields. Physica B 249–251, 326–329 (1998).

    Article  ADS  Google Scholar 

  5. Kato, M., Endo, A., Katsumoto, S. & Iye, Y. Two-dimensional electron gas under a spatially modulated magnetic field: A test ground for electron–electron scattering in a controlled environment. Phys. Rev. B 58, 4876–4881 (1998).

    Article  ADS  Google Scholar 

  6. Kato, M., Endo, A., Sakairi, M., Katsumoto, S. & Iye, Y. Electron–electron Umklapp process in two-dimensional electron gas under a spatially alternating magnetic field. J. Phys. Soc. Jpn 68, 1492–1495 (1999).

    Article  ADS  Google Scholar 

  7. Kashuba, A. B. Conductivity of defectless graphene. Phys. Rev. B 78, 085415 (2008).

    Article  ADS  Google Scholar 

  8. Fritz, L., Schmalian, J., Müller, M. & Sachdev, S. Quantum critical transport in clean graphene. Phys. Rev. B 78, 085416 (2008).

    Article  ADS  Google Scholar 

  9. Nam, Y., Ki, Dong-Keun, K., Soler-Delgado, D. & Morpurgo, A. F. Electron–hole collision limited transport in charge-neutral bilayer graphene. Nat. Phys. 13, 1207–1214 (2017).

    Article  Google Scholar 

  10. Rice, T. M., Robinson, N. J. & Tsvelik, A. M. Umklapp scattering as the origin of T-linear resistivity in the normal state of high-T c cuprate superconductors. Phys. Rev. B 96, 220502 (2017).

    Article  ADS  Google Scholar 

  11. Aleiner, I. L. & Agam, O. Saturation of strong electron–electron umklapp scattering at high temperature. Ann. Phys. 385, 716–728 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  12. Lee, M. et al. Ballistic miniband conduction in a graphene superlattice. Science 353, 1526–1529 (2016).

    Article  ADS  Google Scholar 

  13. Wallbank, J. R., Patel, A. A., Mucha-Kruczyński, M., Geim, A. K. & Fal’ko, V. I. Generic miniband structure of graphene on a hexagonal substrate. Phys. Rev. B 87, 245408 (2013).

    Article  ADS  Google Scholar 

  14. Wallbank, J. R., Mucha-Kruczyński, M., Xi, C. & I., F. V. Moiré superlattice effects in graphene/boron‐nitride van der Waals heterostructures. Ann. Phys. 527, 359–376 (2015).

    Article  Google Scholar 

  15. Yankowitz, M. et al. Emergence of superlattice Dirac points in graphene on hexagonal boron nitride. Nat. Phys. 8, 382–386 (2012).

    Article  Google Scholar 

  16. Krishna Kumar, R. et al. High-temperature quantum oscillations caused by recurring Bloch states in graphene superlattices. Science 357, 181–184 (2017).

    Article  ADS  Google Scholar 

  17. Wang, E. et al. Gaps induced by inversion symmetry breaking and second-generation Dirac cones in graphene/hexagonal boron nitride. Nat. Phys. 12, 1111–1115 (2016).

    Article  Google Scholar 

  18. Wang, E. et al. Electronic structure of transferred graphene/h-BN van der Waals heterostructures with nonzero stacking angles by nano-ARPES. J. Phys. Condens. Matter 28, 444002 (2016).

    Article  Google Scholar 

  19. Hwang, E. H. & Das Sarma, S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Phys. Rev. B 77, 115449 (2008).

    Article  ADS  Google Scholar 

  20. Hwang, E. H. & Das Sarma, S. Dielectric function, screening, and plasmons in two-dimensional graphene. Phys. Rev. B 75, 205418 (2007).

    Article  ADS  Google Scholar 

  21. Ziman, J. M. Electrons And Phonons: The Theory of Transport Phenomena in Solids Sec. 9.14 (Oxford Univ. Press, Oxford, 1960).

  22. Castro Neto, A. H., Guinea, F., Peres, N. M. R., Novoselov, K. S. & Geim, A. K. The electronic properties of graphene. Rev. Mod. Phys. 81, 109–162 (2009).

    Article  ADS  Google Scholar 

  23. DaSilva, A. M., Jung, J., Adam, S. & MacDonald, A. H. Transport and particle–hole asymmetry in graphene on boron nitride. Phys. Rev. B 91, 245422 (2015).

    Article  ADS  Google Scholar 

  24. Chen, J.-H., Jang, C., Xiao, S., Ishigami, M. & Fuhrer, M. S. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nat. Nanotech. 3, 206–209 (2008).

  25. Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).

    Article  ADS  Google Scholar 

  26. Yang, W. et al. Epitaxial growth of single-domain graphene on hexagonal boron nitride. Nat. Mater. 12, 792–797 (2013).

    Article  ADS  Google Scholar 

  27. Lopes dos Santos, J. M. B., Peres, N. M. R. & Castro Neto, A. H. Graphene bilayer with a twist: electronic structure. Phys. Rev. Lett. 99, 256802 (2007).

    Article  ADS  Google Scholar 

  28. Bistritzer, R. & MacDonald, A. H. Transport between twisted graphene layers. Phys. Rev. B 81, 245412 (2010).

    Article  ADS  Google Scholar 

  29. Li, G. et al. Observation of Van Hove singularities in twisted graphene layers. Nat. Phys. 6, 109–113 (2010).

    Article  Google Scholar 

  30. Kim, K. et al. Tunable moiré bands and strong correlations in small-twist-angle bilayer graphene. Proc. Natl Acad. Sci. USA 114, 3364–3369 (2017).

    Article  ADS  Google Scholar 

  31. Sanchez-Yamagishi, J. D. et al. Quantum Hall effect, screening, and layer-polarized insulating states in twisted bilayer graphene. Phys. Rev. Lett. 108, 076601 (2012).

    Article  ADS  Google Scholar 

  32. Rode, J. C., Smirnov, D., Schmidt, H. & Haug, R. J. Berry phase transition in twisted bilayer graphene. 2D Mater. 3, 035005 (2016).

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  34. Mayorov, A. S. et al. Micrometer-scale ballistic transport in encapsulated graphene at room temperature. Nano Lett. 11, 2396–2399 (2011).

    Article  ADS  Google Scholar 

  35. Kretinin, A. V. et al. Electronic properties of graphene encapsulated with different two-dimensional atomic crystals. Nano Lett. 14, 3270–3276 (2014).

    Article  ADS  Google Scholar 

  36. Woods, C. R. et al. Commensurate–incommensurate transition in graphene on hexagonal boron nitride. Nat. Phys. 10, 451–456 (2014).

    Article  Google Scholar 

  37. Ben Shalom, M. et al. Quantum oscillations of the critical current and high-field superconducting proximity in ballistic graphene. Nat. Phys. 12, 318–322 (2015).

    Article  Google Scholar 

  38. Ponomarenko, L. A. et al. Cloning of Dirac fermions in graphene superlattices. Nature 497, 594–597 (2013).

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  40. Hunt, B. et al. Massive Dirac fermions and Hofstadter butterfly in a van der Waals heterostructure. Science 340, 1427–1430 (2013).

    Article  ADS  Google Scholar 

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We would like to thank C. Woods, S. Slizovskiy and F. Guinea for useful discussions. This work was supported by the European Research Council Synergy Grant and Advanced Investigator Grant, Lloyd’s Register Foundation Nanotechnology Grant, EC European Graphene Flagship Project, the Royal Society and EPSRC (including the EPSRC CDT NOWNANO).

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Authors and Affiliations



This study was consummated by J.R.W., V.I.F. and A.K.G.; J.R.W, I.L.A and V.I.F. have developed theory for the studied effect. hBN was provided by T.T. and K.W. The devices were fabricated by M.H., G.H.A. and J.B. Transport measurements were performed by R.K.K., Z.W. and A.M. under the supervision of K.S.N., L.A.P. and A.K.G. All authors have contributed to the discussions of results. The manuscript was written by J.R.W, R.K.K., V.I.F. and A.K.G.

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Correspondence to V. I. Fal’ko.

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Supplementary Information

Supplementary Figures 1–5; Supplementary References 1–18; Additional mathematical derivations

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Wallbank, J.R., Krishna Kumar, R., Holwill, M. et al. Excess resistivity in graphene superlattices caused by umklapp electron–electron scattering. Nature Phys 15, 32–36 (2019).

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