Probing the electronic structure of bilayer graphene by Raman scattering

The electronic structure of bilayer graphene is investigated from a resonant Raman study of the $G^{\prime }$ band using different laser excitation energies. The values of the parameters of the Slonczewski-Weiss-McClure model for bilayer graphene are obtained from the analysis of the dispersive behavior of the Raman features, and reveal the difference of the effective masses of electrons and holes. The splitting of the two TO phonon branches in bilayer graphene is also obtained from the experimental data. Our results have implications for bilayer graphene electronic devices.

Figure 1

(Color online) (a) Atomic structure of bilayer graphene. The $A$ atoms of the two layers are over each other, whereas the $B$ atoms of the two layers are displaced with respect to each other. The SWM constants ${\gamma }_0$, ${\gamma }_1$, ${\gamma }_3$, and ${\gamma }_4$ label the corresponding pair of atoms associated with the hopping processes. (b) First Brillouin zone of monolayer graphene, showing the high symmetry points $\Gamma$, $K$, $K^{\prime }$, and $M$.

Figure 2

(a) Raman spectrum of the monolayer graphene and (b) Raman spectrum of the bilayer graphene performed with the $2.41\mathrm{eV}$ laser line.

Figure 3

(a) Laser energy dependence of the $G^{\prime }$-band energy for a monolayer graphene. (b) Laser energy dependence of the positions of the four peaks that comprise the $G^{\prime }$ band of bilayer graphene. These four Raman peaks originate from the $P_{11}$, $P_{12}$, $P_{21}$, and $P_{22}$ DR processes illustrated in Fig. 4. The black squares are the experimental data and the full lines are the fitted curves (see discussion in the text).

Figure 4

Schematic view of the electron dispersion of bilayer graphene near the $K$ and $K^{\prime }$ points showing both ${\pi }_1$ and ${\pi }_2$ bands. The four DR processes are indicated: (a) process $P_{11}$, (b) process $P_{22}$, (c) process $P_{12}$, and (d) process $P_{21}$. The wave vectors of the electrons ($k_1$, $k_2$, $k_1^{\prime }$, and $k_2^{\prime }$) involved in each of these four DR processes are also indicated.