Twisted bilayer graphene has recently emerged as a platform for hosting correlated phenomena. For twist angles near θ ≈ 1.1°, the low-energy electronic structure of twisted bilayer graphene features isolated bands with a flat dispersion1,2. Recent experiments have observed a variety of low-temperature phases that appear to be driven by electron interactions, including insulating states, superconductivity and magnetism3,4,5,6. Here we report electrical transport measurements up to room temperature for twist angles varying between 0.75° and 2°. We find that the resistivity, ρ, scales linearly with temperature, T, over a wide range of T before falling again owing to interband activation. The T-linear response is much larger than observed in monolayer graphene for all measured devices, and in particular increases by more than three orders of magnitude in the range where the flat band exists. Our results point to the dominant role of electron–phonon scattering in twisted bilayer graphene, with possible implications for the origin of the observed superconductivity.
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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.
Bistritzer, R. & MacDonald, A. H. Moiré bands in twisted double-layer graphene. Proc. Natl Acad. Sci. USA 108, 12233–12237 (2011).
Surez Morell, E., Correa, J. D., Vargas, P., Pacheco, M. & Barticevic, Z. Flat bands in slightly twisted bilayer graphene: tight-binding calculations. Phys. Rev. B 82, 121407 (2010).
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Cao, Y. et al. Unconventional superconductivity in magic-angle graphene superlattices. Nature 556, 43–50 (2018).
Yankowitz, M. et al. Tuning superconductivity in twisted bilayer graphene. Science 363, 1059–1064 (2019).
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Preprint at https://arxiv.org/abs/1901.03520 (2019).
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).
Wu, F., MacDonald, A. H. & Martin, I. Theory of phonon-mediated superconductivity in twisted bilayer graphene. Phys. Rev. Lett. 121, 257001 (2018).
Lian, B., Wang, Z. & Bernevig, B. A. Twisted bilayer graphene: a phonon-driven superconductor. Phys. Rev. Lett. 122, 257002 (2019).
Choi, Y. W. & Choi, H. J. Strong electron–phonon coupling, electron–hole asymmetry, and nonadiabaticity in magic-angle twisted bilayer graphene. Phys. Rev. B 98, 241412 (2018).
Allen, P. B. in Handbook of Superconductivity (eds Poole, C. P. Jr et al.) 478–489 (Academic Press, 2000).
Emery, V. J. & Kivelson, S. A. Superconductivity in bad metals. Phys. Rev. Lett. 74, 3253–3256 (1995).
Wu, F., Hwang, E. & Das Sarma, S. Phonon-induced giant linear-in-resistivity in magic angle twisted bilayer graphene: ordinary strangeness and exotic superconductivity. Phys. Rev. B 99, 165112 (2019).
Yudhistira, I. et al. Gauge-phonon dominated resistivity in twisted bilayer graphene near magic angle. Phys. Rev. B 99 , 140302(R) (2019).
Kim, Y. et al. Charge inversion and topological phase transition at a twist angle induced van Hove singularity of bilayer graphene. Nano Lett. 16, 5053–5059 (2016).
Cao, Y. et al. Superlattice-induced insulating states and valley-protected orbits in twisted bilayer graphene. Phys. Rev. Lett. 117, 116804 (2016).
Nam, N. N. T. & Koshino, M. Lattice relaxation and energy band modulation in twisted bilayer graphene. Phys. Rev. B 96, 075311 (2017).
Chen, J.-H., Jang, C., Xiao, S., Ishigami, M. & Fuhrer, M. S. Intrinsic and extrinsic performance limits of graphene devices on SiO2. Nat. Nanotechnol. 3, 206–209 (2008).
Dean, C. R. et al. Boron nitride substrates for high-quality graphene electronics. Nat. Nanotechnol. 5, 722–726 (2010).
Hwang, E. H. & Das Sarma, S. Acoustic phonon scattering limited carrier mobility in two-dimensional extrinsic graphene. Phys. Rev. B 77, 115449 (2008).
Efetov, D. K. & Kim, P. Controlling electron–phonon interactions in graphene at ultrahigh carrier densities. Phys. Rev. Lett. 105, 256805 (2010).
Komatsu, K. Interpretation of the specific heat of various graphites at very low temperatures. J. Phys. Chem. Solids 25, 707–712 (1964).
Bloch, F. Zum elektrischen widerstandsgesetz bei tiefen temperaturen. Z. Phys. 59, 208–214 (1930).
Grüneisen, E. Die abhängigkeit des elektrischen widerstandes reiner metalle von der temperatur. Ann. Phys. 408, 530–540 (1933).
Stormer, H. L., Pfeiffer, L. N., Baldwin, K. W. & West, K. W. Observation of a Bloch–Grüneisen regime in two-dimensional electron transport. Phys. Rev. B 41, 1278–1281 (1990).
Gorkov, L. P. Phonon mechanism in the most dilute superconductor n-type SrTiO3. Proc. Natl Acad. Sci. USA 113, 4646–4651 (2016).
McMillan, W. L. Transition temperature of strong-coupled superconductors. Phys. Rev. 167, 331–344 (1968).
Chung, T.-F., Xu, Y. & Chen, Y. P. Transport measurements in twisted bilayer graphene: electron–phonon coupling and Landau level crossing. Phys. Rev. B 98, 035425 (2018).
Wallbank, J. R. et al. Excess resistivity in graphene superlattices caused by umklapp electron–electron scattering. Nat. Phys. 15, 32–36 (2019).
Bruin, J. A., Sakai, H., Perry, R. S. & Mackenzie, A. P. Similarity of scattering rates in metals showing T-linear resistivity. Science 339, 804–807 (2013).
Zaanen, J. Why the temperature is high. Nature 430, 512–513 (2004).
Cao, Y. et al. Strange metal in magic-angle graphene with near Planckian dissipation. Preprint at https://arxiv.org/abs/1901.03710 (2019).
Kim, K. et al. van der Waals heterostructures with high accuracy rotational alignment. Nano Lett. 16, 1989–1995 (2016).
Zibrov, A. A. et al. Tunable interacting composite fermion phases in a half-filled bilayer-graphene Landau level. Nature 549, 360–364 (2017).
Wang, L. et al. One-dimensional electrical contact to a two-dimensional material. Science 342, 614–617 (2013).
The authors thank S. Das Sarma and F. Wu for sharing their unpublished theoretical results, and acknowledge further discussions with L. Balents and T. Senthil. Work at both Columbia and UCSB was funded by the Army Research Office under award W911NF-17-1-0323. Sample device design and fabrication was partially supported by DoE Pro-QM EFRC (DE-SC0019443). A.F.Y. and C.R.D. separately acknowledge the support of the David and Lucile Packard Foundation. K.W. and T.T. acknowledge support from the Elemental Strategy Initiative conducted by the MEXT, Japan and the CREST (JPMJCR15F3), JST. A portion of this work was carried out at the KITP, Santa Barbara, supported by the National Science Foundation under grant number NSF PHY-1748958.
The authors declare no competing interests.
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Supplementary Figs. 1–8 and ref. 1.