Theory of core-level spectra in x-ray photoemission of pristine and doped graphene

Spectra of the C1s core hole, created in x-ray photoemission and screened by electronic excitations in pristine and doped graphene are calculated and discussed. We find that singular effects in the lineshapes are not possible in the pristine graphene, and their observation should be connected with the doping. However, the structure of the low-energy excitation spectrum in the region where the singular behavior is expected leads to asymmetries in the core-hole lineshapes in pristine graphene similar to those in doped graphene. This makes the analysis more complex than in the case of metals and may lead to an incorrect or incomplete interpretation of the experimental results.

Figure 1

Local density approximation (LDA) graphene electronic pseudodensity averaged over $xy$ plane. $L$ is the thickness of one supercell. Scale on the abscissa is the unit cell parameter in $xy$ plane $a=4.651\text{a.u.}$ Red dot represents the core-hole position.

Figure 2

The lowest-order cumulant in the XPS process.

Figure 3

Processes in which the hole interacts with the excited electron-hole pair.

Figure 4

Interacting electrons response function.

Figure 5

Lowest-order process in the expansion of ${\chi }_0$.

Figure 6

Density of electronic excitations $\rho \left(\omega \right)$ in pristine graphene (solid line), doped graphene ($E_F=0.5$ eV) (blue dotted-dashed line), and doped graphene ($E_F=1$ eV) (red dashed line).

Figure 7

Singularity index ${\alpha }_0\left(\omega \right)$ in pristine graphene (solid line), doped graphene ($E_F=0.5$ eV) (blue dotted-dashed line), and doped graphene ($E_F=1$ eV) (red dashed line).

Figure 8

Singularity indices in pristine (black solid line), doped $E_F=0.5$ eV (blue dash-dotted line), and doped $E_F=1$ eV (red dashed line) graphene. The inset shows the behavior of singularity indices in the low-energy ($\omega \approx 0$) limit.

Figure 9

(a) XPS core-hole spectra in pristine graphene (black solid line); DS lineshape (red dashed line); no-loss line (blue dotted line). (b) The same as for (a) for doped graphene ($E_F=0.5$ eV). (c) The same as for (a) for doped graphene ($E_F=1$ eV). Hole decay constant $\gamma$ is taken to be 100 meV.

Figure 10

Comparison between the no-loss line $A_0$ (blue dotted line), first-order spectral function $A_1$ (red dashed line), and full spectral function $A$ (black solid line).

Figure 11

The strength of the no-loss line as function of hole decay constant $\gamma$ for pristine graphene $E_F=0$ (solid line) and doped graphene $E_F=1$ eV (dashed line).

Figure 12

Core-hole energy shift as a function of its $z$ position (black solid line) in (a) pristine graphene, (b) doped graphene $E_F=0.5$ eV, and (c) doped graphene $E_F=1$ eV. Corresponding image potential fit (red dashed line) is taken from Ref. 21 Dotted vertical lines denote the graphene image plane positions, and the black dot represents the core-hole energy shift in the center of graphene.