Random strain fluctuations as dominant disorder source for high-quality on-substrate graphene devices

We have performed systematic investigations of transport through graphene on hexagonal boron nitride (hBN) substrates, together with confocal Raman measurements and a targeted theoretical analysis, to identify the dominant source of disorder in this system. Low-temperature transport measurements on many devices reveal a clear correlation between the carrier mobility $\mu$ and the width $n^*$ of the resistance peak around charge neutrality, demonstrating that charge scattering and density inhomogeneities originate from the same microscopic mechanism. The study of weak-localization unambiguously shows that this mechanism is associated to a long-ranged disorder potential, and provides clear indications that random pseudo-magnetic fields due to strain are the dominant scattering source. Spatially resolved Raman spectroscopy measurements confirm the role of local strain fluctuations, since the line-width of the Raman 2D-peak --containing information of local strain fluctuations present in graphene-- correlates with the value of maximum observed mobility. The importance of strain is corroborated by a theoretical analysis of the relation between $\mu$ and $n^*$ that shows how local strain fluctuations reproduce the experimental data at a quantitative level, with $n^*$ being determined by the scalar deformation potential and $\mu$ by the random pseudo-magnetic field (consistently with the conclusion drawn from the analysis of weak-localization). Throughout our study, we compare the behavior of devices on hBN substrates to that of devices on SiO$_2$ and SrTiO$_3$, and find that all conclusions drawn for the case of hBN are compatible with the observations made on these other materials. These observations suggest that random strain fluctuations are the dominant source of disorder for high-quality graphene on many different substrates, and not only on hexagonal boron nitride.