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Article https://doi.org/10.1038/s41467-023-35986-3 scattering mechanisms underlying the activated resistivity, in SI (Figs. S7 and S8) we discuss additional data at lower temperature (down to 50 K) and magnetic field (down to 1 T). We find that ρD drastically increases toward low T, with the activated resistivity exceeding the e-ph limit by more than one order of magnitude in a clean sample. However, as the temperature and magnetic field are increased, ρD progressively drops (i.e., the activated resistivity tends toward the e-ph limit), suggesting a temperature-driven crossover between regimes dominated by either disorder or e-ph interaction (the latter being realized only close to RT). While it is not surprising that the e-ph limit works as a lower bound to the activated resistivity of real samples, the non-universality (i.e., the sample and temperature dependence) of the disorder contribution deserves particular atten- tion in future theoretical treatments of the RT-QH in graphene. Discussion The physics of graphene is essentially determined by its deviations from flatness (that is, ripples), due to either thermal fluctuations associated to flexural phonons for freely suspended samples or to roughness of substrate like for graphene on SiO215. In both cases, rip- ples induce inhomogeneity of electron density with electron and hole puddles in the vicinity of the CNP38,39. In particular, for the case of graphene on SiO2 the amplitude of induced inhomogeneity of charge- carrier density is estimated as 3 × 1011 cm–239, in agreement with the above cited experimental values of n*. This makes the system strongly disordered, and any intrinsic scattering mechanisms become irrele- vant. Oppositely, the hBN substrate is atomically flat1 and at the same time suppresses intrinsic ripples which increases the RT carrier mobility by an order of magnitude and makes intrinsic scattering mechanisms dominant15. Indeed, experimentally measured n* for our samples is an order-of-magnitude smaller than what is supposed to be induced by ripples at RT. This results in an essentially different picture of QH physics at high enough temperatures. In conclusion, we showed experimental evidence of predominant e-ph scattering in the QH regime. This is realized by uniquely com- bining strong magnetic fields, high temperatures and hBN- encapsulation of graphene. Although the RT-QH in graphene has long been known, we showed that mitigation of disorder via van der Waals engineering provides novel insights on the transport mechan- isms in this phenomenon. Methods Graphene-hBN van der Waals assembly and device fabrication hBN/graphene/hBN samples D1-3 are assembled using the standard van der Waals dry pick-up5, starting from micromechanically exfoliated graphene flakes previously identified by optical and Raman micro- scopy. Sample D4 is obtained by CVD growth on Cu foil and direct hBN- mediated pick-up after controlled decoupling via Cu surface oxidation31. All the devices are fabricated making use of electron beam lithography, reactive ion etching and e-beam evaporation of Cr/Au 1D edge contacts5. Magnetotransport measurements We use standard lock-in acquisition at low frequency (13 Hz), with simultaneous ρxx and ρxy measurements in four-probe configuration, either under a constant current excitation (12.5 nA, sample D1-D3) or a constant voltage bias (300 μV, sample D4). The devices are mounted in a VTI system with low-pressure 4He serving as exchange gas, coupling the samples to a liquid-N2 reservoir. The cryogenic system is accom- modated in the access bore of a resistive Bitter magnet at HFML-EMFL, with a maximum field of 33 T. Reporting summary Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article. 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