Charge carrier density-dependent Raman spectra of graphene encapsulated in hexagonal boron nitride

We present low-temperature Raman measurements on gate tunable graphene encapsulated in hexagonal boron nitride, which allows to study in detail the Raman G and 2D mode frequencies and line widths as function of the charge carrier density. We observe a clear softening of the Raman G mode (of up to 2.5 cm$^{-1}$) at low carrier density due to the phonon anomaly and a residual G~mode line width of $\approx$ 3.5 cm$^{-1}$ at high doping. From analyzing the G mode dependence on doping and laser power we extract an electron-phonon-coupling constant of $\approx$ 4.4 $\times$ 10$^{-3}$ (for the G mode phonon). The ultra-flat nature of encapsulated graphene results in a minimum Raman 2D peak line width of 14.5 cm$^{-1}$ and allows to observe the intrinsic electron-electron scattering induced broadening of the 2D peak of up to 18 cm$^{-1}$ for an electron density of 5$\times$10$^{12}$ cm$^{-2}$ (laser excitation energy of 2.33 eV). Our findings not only provide insights into electron-phonon coupling and the role of electron-electron scattering for the broadening of the 2D peak, but also crucially shows the limitations when it comes to the use of Raman spectroscopy (i.e. the use of the frequencies and the line widths of the G and 2D modes) to benchmark graphene in terms of charge carrier density, strain and strain inhomogenities. This is particularly relevant when utilizing spatially-resolved 2D Raman line width maps to assess substrate-induced nanometer-scale strain variations.