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

## Abstract

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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## 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.

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## Acknowledgements

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).

## Author information

Authors

### Contributions

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.

### Corresponding author

Correspondence to V. I. Fal’ko.

## Ethics declarations

### Competing interests

The authors declare no competing interests.

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## Supplementary information

### 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). https://doi.org/10.1038/s41567-018-0278-6

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• DOI: https://doi.org/10.1038/s41567-018-0278-6

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