Multiple satellites in materials with complex plasmon spectra: From graphite to graphene

The photoemission spectrum of graphite is still debated. To help resolve this issue, we present photoemission measurements at high photon energy and analyze the results using a Green's function approach that takes into account the full complexity of the loss spectrum. Our measured data show multiple satellite replicas. We demonstrate that these satellites are of intrinsic origin, enhanced by extrinsic losses. The dominating satellite is due to the $\pi +\sigma$ plasmon of graphite, whereas the $\pi$ plasmon creates a tail on the high-binding energy side of the quasiparticle peak. The interplay between the two plasmons leads to energy shifts, broadening, and additional peaks in the satellite spectrum. We also predict the spectral changes in the transition from graphite towards graphene.

Figure 1

XPS spectrum of HOPG at 800 eV photon energy. The experimental data collected at normal emission (blue dots) are compared to the spectral function $A\left(\omega \right)$ calculated from $GW$ (magenta dashed line) and from a multipole version of Eq. (1) (green dot-dashed line). On top of the latter the black solid line also includes extrinsic and interference effects. The result for $A\left(\omega \right)$ in the single plasmon pole approximation ($N_p=1$) for Eq. (1) (red dotted line) is shown for comparison. All curves are scaled to match the intensity of the main QP peak at $-20$ eV. All theoretical spectra contain photoabsorption cross sections, the calculated secondary electron background, and 0.4 eV Gaussian broadening to account for finite BZ sampling and experimental resolution.

Figure 2

$GW$ spectral function $A\left(\omega \right)$ (solid black line) with imaginary (dotted blue line) and shifted real (dashed green line) parts of the $GW$ self-energy. (a) Lowest valence state at $k=(0.0,0.0,0.25)$. (b) Highest valence state at $k=(0.33,0.33,0.25)$. Inset: Zoom on $A\left(\omega \right)$.

Figure 3

C $1s$ XPS spectrum of HOPG at 800 eV photon energy as measured in the present work (blue line with points), Ref. [25] (black squares), and in Ref. [27] (orange circles). Signatures of the $\pi$ and $\pi +\sigma$ plasmons are clearly visible, as well as the feature termed $P_3$ in Refs. [25, 27].

Figure 4

Comparison of graphite (dot-dashed green line) and graphene (solid black line) spectral functions using GW + C. The QP part of graphene (dotted black line) is reported for comparison. The QP and satellite tail at $-30$ eV do not change going from graphite to graphene, while most of the satellite weight below $-40$ eV disappears. This change stems from the differences in the loss functions. Inset: The calculated loss function $-\mathrm{Im}\left[{\varepsilon }^{-1}\right]$ (arbitrary units vs eV) of graphite (dashed black line) is compared to graphene (solid blue line). The curves are scaled to match the intensity of the $\pi$ plasmon peak.

Figure 5

$\Gamma$-point $G{W}_0$ spectral function $A\left(\omega \right)$ for graphene (solid red line) and graphite (dotted blue line), along with the shifted real-part term of the self-energy for the lowest valence band of graphene (dashed green line) and graphite (dot-dashed magenta line), respectively.