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The weak intrinsic spin-orbit coupling in graphene can be greatly enhanced by proximity coupling. Here, we report on the proximity-induced spin-orbit coupling in graphene transferred by hexagonal boron nitride (hBN) onto the topological insulator Bi1.5 Sb0.5 Te1.7 Se1.3 (BSTS) which was grown on a hBN substrate by vapor solid synthesis. Phase coherent transport measurements, revealing weak localization, allow us to extract the carrier density-dependent phase coherence length lϕ. While lϕ increases with increasing carrier density in the hBN/graphene/hBN reference sample, it decreases in graphene/BSTS due to the proximity coupling of BSTS to graphene. The latter behavior results from D'yakonov-Perel'-type spin scattering in graphene with a large proximity-induced spin-orbit coupling strength of at least 2.5 meV. ; This project has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 785219 (Graphene Flagship), the Virtual Institute for Topological Insulators (Jülich-Aachen-Würzburg-Shanghai), and by the Deutsche Forschungsgemeinschaft (DFG) through SPP 1666 (BE 2441/8-2). ICN2 is supported by the Severo Ochoa program from Spanish MINECO (Grant No. SEV-2013-0295) and funded by the CERCA Programme/Generalitat de Catalunya. Growth of hexagonal boron nitride crystals was supported by the Elemental Strategy Initiative conducted by the MEXT, Japan and JSPS KAKENHI Grants No. JP26248061, No. JP15K21722, and No. JP25106006. ; Peer reviewed

We perform 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 μ 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 with a long-ranged disorder potential and provides clear indications that random pseudomagnetic fields due to strain are the dominant scattering source. Spatially resolved Raman spectroscopy measurements confirm the role of local strain fluctuations, since the linewidth 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 μ 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 μ by the random pseudomagnetic 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 SiO2 and SrTiO3, 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. ; A. F. M. gratefully acknowledges support by the Swiss National Science Foundation (SNF) and by the National Center of Competence in Research on Quantum Science and Technology (NCCR QSIT). F. G. acknowledges support from the Spanish Ministry of Economy (MINECO) through Grant No. FIS2011-23713 and the European Research Council (ERC) Advanced Grant (Contract No. 290846). C. S. and S. E. acknowledge experimental help from F. Buckstegge, J. Dauber, B. Terrés, F. Volmer, and M. Drögeler and financial support from Deutsche Forschungsgemeinschaft (DFG) and European Research Council (ERC) (Contract No. 280140). A. F. M., F. G., and C. S. acknowledge funding from the European Union (EU) under the Graphene Flagship.