Probing chiral electronic excitations in bilayer graphene by Raman scattering

We report a symmetry-resolved electronic Raman scattering (ERS) study of a back-gated bilayer graphene device. We show that the ERS continuum is dominated by interband chiral excitations of $A_2$ symmetry and displays a characteristic Pauli-blocking behavior similar to the monolayer case. Crucially, we show that nonchiral excitations make a vanishing contribution to the Raman cross-section due to destructive interference effects in the Raman amplitude matrix elements. This is in marked contrast to the optical absorption measurements and opens interesting prospects for the use of Raman scattering as a selective probe for the detection of the chiral degrees of freedom in graphene, topological materials, and other two-dimensional crystals.

Figure 1

(a) Bernal-stacked bilayer graphene. The unit cell contains four nonequivalent sites, $A1$, $B1$, $A2$, and $B2$. The atoms $A2$ and $B1$ (dimer atoms) are sitting directly on top of each other. The hopping amplitudes ${\gamma }_0$, ${\gamma }_1$, and ${\gamma }_3$ between the atoms are highlighted with arrows. (b) Bilayer graphene electronic bands and allowed vertical interband electron-hole transitions. Sketch of the expected optical conductivity $\omega {\sigma }_1$ at the charge neutrality point (c) $E_F=0$ and at (d) $2E_F=1500{\text{cm}}^{-1}$. In both cases a phenomenological broadening of $\sim 0.05{\gamma }_1$ is used to account for disorder and/or inhomogeneous carrier distribution. Here we do not show the 1–4 interband excitations that have onset energy $E_{On}^{\mathit{1}-\mathit{4}}=2{\gamma }_1\sim 6000{\text{cm}}^{-1}$ and are sensitive to the Pauli blocking for $E_F>{\gamma }_1$.

Figure 2

Two-step Raman processes in bilayer graphene. Indices $i$, $v$, and $f$ correspond to initial, intermediate (virtual), and final electronic states, respectively. ${\mathrm{\Omega }}_I$ is the incoming light frequency and $\omega$ is the Raman shift. The absorption (emission) processes are represented by solid (dashed) lines. They correspond to processes involving (a) zero and (b) two-photon virtual intermediate states.

Figure 3

(a) Optical microscope image of bilayer graphene device and schematic drawing of the setup. ${\mathbf{e}}_{I,S}$ and ${\mathrm{\Omega }}_{I,S}$ are the polarizations and frequencies of incoming and scattered photons. The Raman shift is defined as $\omega ={\mathrm{\Omega }}_I-{\mathrm{\Omega }}_S$. (b) and (c) Polarization-resolved Raman continuum of bilayer graphene recorded at $T=30K$ at five different gate voltage values for (a) parallel and (b) cross polarizations of incoming and scattered photons.

Figure 4

(a) Experimental and theoretical $R(\omega ,V_G)$ at 30 K for the cross polarizations spectra. The theoretical plots are obtained by only considering vertical 2–3 interband transitions, with a Gaussian distribution of Fermi energy with $\delta E_F\sim 35\text{meV}$. (b) Adjusted values of $E_F$ in a function of the gate voltage, superposed to the theoretical curve (11).

Figure 5

(a) Evolution of $G$ band linewidth (blue dots) and energy (red dots) of the bilayer graphene sample as a function of Fermi energy. The Fermi energy was deduced from the gate voltage using the same device capacitance as in the case of the ERS spectra. Theoretical plots are obtained with the same variation of the Fermi energy, $\delta E_F\sim 35\text{meV}$, as the $R(\omega ,V_G)$ theoretical fits [see Fig. 4]. One of the two anomalies is clearly identified at $E_F=-\hslash {\omega }_G/2$. (b) Evolution of the ERS intensity at 1580 ${\text{cm}}^{-1}$ (red dots) and of the $G$ band linewidth (black dots) as a function of the Fermi energy and theoretical expectation (dashed line).

Figure 6

Comparison of $R(\omega ,V_G)$ with normalized infrared transmission measurements $(1-T/T_{\mathrm{CN}})$, where $T_{\mathrm{CN}}$ is the transmission for a Fermi energy at the charge neutrality point. Both were performed on bilayer graphene devices [25] with approximately the same Fermi level shift. The $1-(T\left(V\right)/T_{\mathrm{CN}})$ spectrum is dominated by a peak at around $3000{\text{cm}}^{-1}$, with a magnitude that increases together with the gate voltage. By contrast, the ERS intensity at this frequency is essentially independent of gate voltage.