Raman Spectroscopy Study of Rotated Double-Layer Graphene: Misorientation-Angle Dependence of Electronic Structure

We present a systematic Raman study of unconventionally stacked double-layer graphene, and find that the spectrum strongly depends on the relative rotation angle between layers. Rotation-dependent trends in the position, width and intensity of graphene 2D and G peaks are experimentally established and accounted for theoretically. Our theoretical analysis reveals that changes in electronic band structure due to the interlayer interaction, such as rotational-angle dependent Van Hove singularities, are responsible for the observed spectral features. Our combined experimental and theoretical study provides a deeper understanding of the electronic band structure of rotated double-layer graphene, and leads to a practical way to identify and analyze rotation angles of misoriented double-layer graphene.

Figure 1

Suspended rotated double-layer graphene and Raman spectrum. (a) TEM image of misoriented double-layer graphene. The graphene sample is suspended in a hole of $2\mu \mathrm{m}$ diameter. (b) Diffraction pattern of the graphene sample shown in (a). The two sets of hexagonal patterns are relatively rotated by 21°. An electron beam size of $\sim 1\mu \mathrm{m}$ is used for diffraction acquisition. (c) Atomic resolution TEM image of double-layer graphene with rotational-angle of 21° showing a moiré pattern. Inset shows a fast Fourier transform (FFT) of the image. (d) Raman spectra of misoriented double-layer and single-layer graphene measured with 633 nm wavelength laser (1.96 eV). The spectra are shifted vertically for clarity.

Figure 2

Rotational-angle dependence of G-peak intensity. (a) Graphene Raman G-peak for rotated double-layer and single-layer graphene. (b) Dependence of G-peak integral intensity (normalized to the single-layer value) on the rotation angle for 1.96 eV (633 nm) laser excitation. The filled and unfilled symbols show experimental and theoretical calculation values, respectively. The lines are guides to the eye. (c) G-peak integral intensity with 2.41 eV (514 nm) laser excitation. The inset shows measured dependence of critical angle on laser energy.

Figure 3

Rotational-angle dependence of Raman 2D peak. (a) Graphene 2D peak for rotated double-layer and single-layer graphene. The vertical dashed line represents the center of single-layer 2D peak. (b) Rotated double-layer graphene 2D peak FWHM. We have fitted the 2D peaks with a single Lorentzian peak for simplicity. The black squares and red circles are the experimental and theoretical calculation values. The blue horizontal area represents the experimental value from single-layer graphene. The grey (experiment) and red (calculation) areas are guides to the eye. (c) Rotated double-layer graphene 2D peak blue-shift in respective to the value from single-layer graphene. (d) Integral intensity of 2D peak. Experimental and calculation values were normalized to the single-layer value.

Figure 4

Electronic band structure and Raman scattering processes in rotated double-layer graphene. (a) Brillouin zone (BZ) of rotated double-layer graphene misoriented by $\theta$. The circles represent the locations of Dirac cones from the first (black) and second (red) layer. The distance between two near-by Dirac cones is $\Delta k$. (b) Energy dispersion relation in the vicinities of two Dirac cone overlap. Van Hove singularities are induced from band-overlap between two Dirac cones. (c) Sketch of energy dependence of density of states (DOS) near the Fermi level of rotated double-layer graphene without (blue) and with interlayer interactions (red). DOS exhibit distortions from the interlayer interactions showing Van Hove singularities. (d) Some processes that contribute to the Raman G-peak amplitude. (e) Intervalley 2D Raman scattering processes for rotated double-layer graphene in which the laser excitation energy is smaller (blue lines) or larger (black lines) than the energy difference between conduction and valence Van Hove singularities.