Electronic correlations in graphite and carbon nanotubes from Auger spectroscopy

We have determined the screened on-site Coulomb repulsion in graphite and single wall carbon nanotubes by measuring their Auger spectra and performing a theoretical analysis based on an extended Cini-Sawatzky approach [Solid State Commun. 24, 681 (1977); Phys. Rev. Lett. 39, 504 (1977)], where only one fit parameter is employed. The experimental line shape is very well reproduced by the theory, and this allows us to determine the value of the screened on-site repulsion between $2p$ states, which is found to be $2.1\mathrm{eV}$ in graphite and $4.6\mathrm{eV}$ in nanotubes. The latter is robust by varying the nanotube radius from $1\text{to}2\mathrm{nm}$.

Figure 1

(Color online) Experimental KVV Auger spectra of HOPG graphite (bold red/gray curve) and SWCNTs with average diameter of $1.3\mathrm{nm}$ (black curve).

Figure 2

One-particle partial DOS of (10,10) SWCNT (diameter close to $1.3\mathrm{nm}$) obtained by the tight binding method of Ref. 22. The inset shows the same quantity for graphite, taken from Ref. 8. The Fermi level corresponds to zero energy and the antibonding part is not displayed.

Figure 3

(Color online) (a) Theoretical line shape [computed from Eq. (1)] of KVV Auger spectrum for HOPG (bold red/gray) and for SWCNTs (black) curve. (b) Diagonal contributions of the interacting DOS for HOPG (bold red/gray) and for SWCNTs (black), where the two valence holes have the same symmetry. The $D_{{\sigma }_p{\sigma }_p{\sigma }_p{\sigma }_p}$ contribution is understood as the sum $D_{{\sigma }_x{\sigma }_x{\sigma }_x{\sigma }_x}+D_{{\sigma }_y{\sigma }_y{\sigma }_y{\sigma }_y}$. The $x$ axis displays kinetic energy, obtained by shifting the position of the Fermi level in Fig. 2 by $284.6\mathrm{eV}$, which is the binding energy of $1s$ core hole.