Gate-Dependent Electronic Raman Scattering in Graphene

We report the direct observation of polarization resolved electronic Raman scattering in a gated monolayer graphene device. The evolution of the electronic Raman scattering spectra with gate voltage and its polarization dependence are in full agreement with theoretical expectations for nonresonant Raman processes involving interband electron-hole excitations across the Dirac cone. We further show that the spectral dependence of the electronic Raman scattering signal can be simply described by the dynamical polarizability of graphene in the long wavelength limit. The possibility to directly observe Dirac fermion excitations in graphene opens the way to promising Raman investigations of electronic properties of graphene and other 2D crystals.

Figure 1

(a) Optical microscope image and schematic drawing of the device and Raman setup. ${\omega }_{i,s}$ and ${ϵ}_{i,s}$ are the frequency and polarization of the in-coming and scattered photons. The Raman shift is defined as $\omega ={\omega }_i-{\omega }_s$. (b) Cross-polarization spectra recorded at two different gate voltages: $V_g=0$ and $V_g=-40\mathrm{V}$ in the $0-6000{\mathrm{cm}}^{-1}$ frequency range. The sharp peaks are due to optical phonons (first and higher order process) of Si (below $1100{\mathrm{cm}}^{-1}$) and of graphene (above $1100{\mathrm{cm}}^{-1}$). (c) and (d) Polarization resolved changes in the electronic Raman continuum for parallel polarizations (c) and cross polarizations (d) at three different gate voltages.

Figure 2

(a) Experimental and theoretical gate dependence of $R(\omega ,V_g)$ at $T=30\mathrm{K}$ (see text) [44]. (b) Evolution of the theoretical $I_{\mathrm{ERS}}$ in graphene when the Fermi level is at the Dirac point (dotted straight line), and at finite $E_F$ (solid lines). The solid black curve is for a homogenous sample at $T=0\mathrm{K}$ [Eq. (3)]. The solid red line represents the finite temperature spectrum with a Gaussian distribution of Fermi energy. The insets in (b) show schematics of vertical interband electron-hole excitations which are Pauli blocked for $\omega <2E_F$. (c) Schematic drawing of the nonresonant (${\omega }_i\ne E_M-E_1$) two-step Raman process for interband electron-hole excitations via an intermediate virtual state [33]. $E_1$, $E_M$, and $E_2$ are the energies of the initial, intermediate, and final electronic states. The ordering of the process is indicated explicitly: the first (second) step involves a photon induced vertical transition from the initial (virtual) state to the virtual (final) electronic state. (d) Fermi energy plotted as a function of the square root of the gate voltage. The red line is the theoretical expectation computed using the estimated gate capacitance of the device. The black dots were extracted from the $R$ data in (a) using the midpoint energy as an estimate of the inflection point [45].

Figure 3

Evolution of the ERS intensity at $1580{\mathrm{cm}}^{-1}$ (red dots) and of the $G$-band change in linewidth $\mathrm{\Delta }{\mathrm{\Gamma }}_G={\mathrm{\Gamma }}_G-{\mathrm{\Gamma }}_0$ (black dots) as a function of the Fermi energy. ${\mathrm{\Gamma }}_G$ is the observed linewidth and ${\mathrm{\Gamma }}_0$ a gate voltage independent contribution to the linewidth arising from lattice anharmonicity and disorder effects. The dotted line is the theoretical expectation for $I_{\mathrm{ERS}}(1580{\mathrm{cm}}^{-1})$ after a convolution with a Gaussian distribution of Fermi energy with $\delta E_F\sim 50\mathrm{meV}$. The insets show Feynman diagrams for the ERS intensity (red) and electron-phonon induced $G$-band renormalization (black). See Ref. [33] for details about the ERS vertex.