Interlayer Interaction and Electronic Screening in Multilayer Graphene Investigated with Angle-Resolved Photoemission Spectroscopy

The unusual transport properties of graphene are the direct consequence of a peculiar band structure near the Dirac point. We determine the shape of the $\pi$ bands and their characteristic splitting, and find the transition from two-dimensional to bulk character for 1 to 4 layers of graphene by angle-resolved photoemission. By detailed measurements of the $\pi$ bands we derive the stacking order, layer-dependent electron potential, screening length, and strength of interlayer interaction by comparison with tight binding calculations, yielding a comprehensive description of multilayer graphene’s electronic structure.

Figure 1

Photoemission images revealing the band structure of (a) single and (b) bilayer graphene along high symmetry directions $\Gamma \mathrm{\text{−}}K\mathrm{\text{−}}M\mathrm{\text{−}}\Gamma$. The dashed (blue) lines are scaled DFT band structure of freestanding films [16]. Inset in (a) shows the 2D Brillouin zone of graphene.

Figure 2

(a)–(d) The $\pi$ and ${\pi }^{*}$ bands near $E_F$ for 1–4 graphene layers, respectively. $k_{\parallel }=-1.703\AA {}^{-1}$ corresponds to the $K$ point. The $\Gamma$ point is at $k_{\parallel }=0{\AA }^{-1}$, while the $M$ point is at $-2.555{\AA }^{-1}$. The dashed lines are from a calculated tight binding band structure, with band parameters adjusted to reproduce measured bands. Red and orange (light gray) lines are for Bernal-type ($ABAB$ and $ABAC$) stackings, while blue (dark gray) lines are for rhombohedral-type stackings. (e)–(h) Photoemission intensity oscillation of $\pi$ bands at $E_F-1\mathrm{eV}$ as a function of $k_{\parallel }$ and $k_{\perp }$ momentum for 1–4 layers graphene. The photoemission intensity is normalized by the angle integrated intensity between $E_F$ and $E_F-1.5\mathrm{eV}$ for each photon energy.

Figure 3

Potential and carrier concentration profiles of the multilayer graphene as a function of the layer positions. The electron potentials are shifted in the way that the potential of the outermost graphene layer is at zero.