Unraveling van Hove singularities in x-ray absorption response of single-wall carbon nanotubes

X-ray absorption (XAS) and core level photoelectron spectroscopy are versatile tools to site selectively study the unoccupied density of states and bonding environment. Hence, they are widely applied to study single-wall carbon nanotubes (SWCNTs) as archetypes of one-dimensional solids. However, their van Hove singularities (vHs’s) were indiscernible. In this paper, we unravel the vHs in the XAS response of SWCNT. These results pave the way toward a conclusive understanding of the interplay between charge transfer and hybridization versus chemical interaction by tracing the vHs at the carbon site.

Figure 1

(Color online) $\mathrm{C}1s$ photoemission of SWCNT as conducted at $400\mathrm{eV}$ photon energy. The inset shows the $\mathrm{C}1s$ line and line shape analysis on an expanded scale. The arrow marks the shoulder in the spectrum. The ten times blowup shows the line shape analysis after strapping the main $\mathrm{C}1s$ peak. Experimental data are black, envelopes of line shape analysis are thick red lines, and single constituents are slim individually colored lines.

Figure 2

(Color online) (a) $\mathrm{C}1s$ absorption edges in XAS of HOPG at 45° to normal incidence, (b) isotropic $\mathrm{C}1s$ absorption edges in high resolution XAS of SWCNT, and (c) $\mathrm{C}1s$ excitation edges in EELS of SWCNT as reproduced from Ref. 22. Arrows mark the fine structures in the high resolution XAS $\mathrm{C}1s$ resonance of SWCNT.

Figure 3

(Color online) Close-up of the high resolution $\mathrm{C}1s$ ${\pi }^{★}$ absorption edges of (a) HOPG and (b) SWCNT and (c) diameter cumulative tight binding DOS, starting from the photoemission $\mathrm{C}1s$ binding energy. The inset depicts (b) at $16\mathrm{K}$ and ambient temperature. Line shape analysis of (b): experiment are black dots, envelope is the thick red line, and individual constituents are solid or dashed lines as discussed in the text.