Dynamical core-hole screening in the x-ray absorption spectra of hydrogenated carbon nanotubes and graphene

We have calculated the electronic structure and the x-ray absorption (XA) spectrum of a hydrogenated single graphite plane, in order to simulate recent experimental results on hydrogenated single wall carbon nanotubes (SWCNT) as well as hydrogenated graphene. We find that the presence of H induces a substantial component of $s{p}^3$ bonding and as a result the $\pi$ and ${\pi }^{*}$ components to the electronic structure vanish. We have calculated a theoretical x-ray absorption spectrum using a multiband version of the Mahan-Nozières–De Dominicis theory. By making a fitting of the XA signal of C atoms that have H attached to them and C atoms without H in the vicinity we obtain a good representation of the experimental data and we can draw the conclusion that in the experiments [A. Nikitin et al., Phys. Rev. Lett. 95, 225507 (2005)] some 35–50 % H have been absorbed in the SWCNT.

Figure 1

Experimental XA spectrum of SWCNT with H loading (dashed curve), denoted $s_3$, and experimental XA spectrum of SWCNT without H loading (solid curve), denoted $s_2$. The figure is redrawn after Ref. 1.

Figure 2

Theoretical XA spectrum of SWCNT with H (dashed line), denoted $t_1$, and theoretical XA spectrum of SWCNT without H (solid line), denoted $t_2$. Also shown is the experimental spectrum for the clean SWCNT (thin solid line) (Ref. 1).

Figure 3

Calculated geometry of the H and C atoms in close vicinity to each other in a SWCNT. Gray balls represent C atoms that essentially have not modified their bond distances compared to a SWCNT without H, whereas the dark gray atom is a C atom close to the H atom (light gray atom) which moves out of plane due to the occurrence of an $s{p}^3$ component to the chemical bond induced by H.

Figure 4

The upper curves are the symmetry projected DOS of C. The lower curves are the symmetry projected local DOS for an H bounded C atom.

Figure 5

Difference between the experimental XA spectra of clean and H loaded SWCNT (thin line) compared to a theoretically calculated difference spectra where the degree of hydrogenation has been used as a fitting parameter (thick line). For details see text.