Figure 1

(a)–(c) Electronic band structure of graphene and (d) experimental setup. (a) $\pi$ and ${\pi }^{*}$ bands of graphene in momentum space. $K$ and $K^{\prime }$ (Dirac points) are the corner points of the first Brillouin zone. For neutral graphene, the $\pi$ band is completely filled, shown as blue shading in this diagram. Near Dirac points, the band structure exhibits isotropic linear dispersion, shown as two cones at $K$ and $K^{\prime }$. (b) shows the region near Dirac points in $n$-type graphene. ${\epsilon }_c$ is the onset energy for vertical electron-hole pair transitions. (c) is like (b) for $p$-type graphene. (d) Upper left is an optical image of the sample.Reuse & Permissions

Figure 2

Low-temperature Raman spectra and their Lorentzian fits (smooth overlapping curves). (a) Evolution of the $G$ band of a graphene monolayer with gate voltage $V_g$. The upper left inset is a schematic representation of carbon atom motion in the $G$ band. The dashed line is a guide to the eye. (b) Spectrum of the $G$ band of a thick ($>10\mathrm{nm}$) graphite layer. (c) Evolution of the $D^{*}$ two-phonon band of a graphene monolayer with $V_g$.Reuse & Permissions

Figure 3

$G$ band energy (squares) and $G$ band width (circles) extracted from Fig. 2a. The vertical dotted line is the approximate position of the charge-neutral Dirac point that is estimated from the symmetry of the data. The upper scale is obtained with $n=C_g(V_g-V_{\mathrm{Dirac}})/e$, where $C_g=115aF/\mu {\mathrm{m}}^2$ [12, 13].Reuse & Permissions

Figure 4

(a)–(c) Graphene $G$ band damping and (d)–(f) energy renormalization. In (a) and (d), dashed blue lines and solid red lines are the fits for ideal and nonuniform graphene, respectively. In all cases, the same electron-phonon coupling strength ($D=12.6\mathrm{eV}/\AA$) is assumed. The vertical dotted lines are the determinations of the Dirac point shown in Fig. 3. The insets are Feynman diagrams for electron-phonon coupling applicable to the case of the $G$ phonon. (b) represents the broadening of the $G$ phonon due to decay into particle-hole pairs. (c) indicates that the $G$-phonon decay into the electron-hole pair is forbidden by the Pauli principle at high EFE-induced charge densities. (e) is for the renormalization of the $G$-phonon energy by interaction with virtual electron-hole pairs. (f) shows that virtual electron-hole pair transitions with energy ranging from 0 to $2|E_F|$ are forbidden. Only the diagrams for $n$-type graphene are shown in (b), (c), (e), and (f). Diagrams for the $p$-type cases are similar.Reuse & Permissions