Dielectric screening of the Kohn anomaly of graphene on hexagonal boron nitride

Kohn anomalies in three-dimensional metallic crystals are dips in the phonon dispersion that are caused by abrupt changes in the screening of the ion cores by the surrounding electron gas. These anomalies are also present at the high-symmetry points $\Gamma$ and $K$ in the phonon dispersion of two-dimensional graphene, where the phonon wave vector connects two points on the Fermi surface. The linear slope around the kinks in the highest optical branch is proportional to the electron-phonon coupling. Here, we present a combined theoretical and experimental study of the influence of the dielectric substrate on the vibrational properties of graphene. We show that screening by the dielectric substrate reduces the electron-phonon coupling at the high-symmetry point $K$ and leads to an upshift of the Raman 2D line. This results in the observation of a Kohn anomaly that can be tuned by screening. The exact position of the 2D line can thus be taken also as a signature for changes in the (electron-phonon limited) conductivity of graphene.

Figure 1

(a) Schematic illustration of a graphene sample with incident laser. (b),(c) Optical microscope images of graphene flakes partly resting on hBN (blue) and SiO${}_2$. The flake consists of different regions of single-layer, bilayer, and few-layer graphene. (d) Raman spectrum of single-layer graphene resting on hBN. Inset: Region around the hBN peak at sites marked in panel (c). (e),(f) G (e) and 2D (f) peak of single-layer graphene on hBN (marker A) and SiO${}_2$ (marker D).

Figure 2

(a) 2D FWHM Raman image of the sample shown in Fig. 1c. Where no 2D peak was found, the hBN peak FWHM was plotted making the hBN flake visible (highlighted by white dotted lines). (b) Raman map of the 2D FWHM of the sample shown in Fig. 1b [see white dashed box in Fig. 1b]. Dotted line marks the hBN substrate. (c) Raman map of the same sample: integrated intensity of the hBN peak. (d) Line cut along the solid arrow (path P) in panel (a).

Figure 3

Statistical evaluation of single-layer regions of the Raman map shown in Fig. 2a in terms of G-peak position (a), 2D peak position (b), intensity ratio between G and 2D peak (c), and FWHM of the 2D peak (d).

Figure 4

(a) Geometry employed for the calculation of the electron-phonon coupling in graphene surrounded by hBN. (b) Schematic figure of the differences in the highest-optical phonon branch around $K$ between suspended graphene and graphene surrounded by hBN. (c) Raman spectrum of graphene surrounded on both sides by multilayer hBN. The sample is shown in the left inset. The darker-blue area is the region of graphene on an underlying hBN flake. In the light-blue area, an additional hBN layer is deposited on top of the graphene layers. The spot where the spectrum was measured is marked by the black cross and the scale bar is 5 $\mu$m. (d) Raman 2D line of graphene on SiO${}_2$, graphene on hBN, and graphene surrounded by hBN.