Transition from a Tomonaga-Luttinger Liquid to a Fermi Liquid in Potassium-Intercalated Bundles of Single-Wall Carbon Nanotubes

We report on the first direct observation of a transition from a Tomonaga-Luttinger liquid to a Fermi-liquid behavior in potassium-intercalated mats of single-wall carbon nanotubes. Using high resolution photoemission spectroscopy, an analysis of the spectral shape near the Fermi level reveals a Tomonaga-Luttinger liquid power law scaling in the density of states for the pristine sample and for low dopant concentration. As soon as the doping is high enough to achieve a filling of the conduction bands of the semiconducting tubes, a distinct transition to metallic single-wall carbon nanotube bundles with the scaling behavior of a normal Fermi liquid occurs.

Figure 1

Doping dependence of the valence band photoemission spectra in the vicinity of the Fermi edge for high doping levels. The numbers correspond to the $\mathrm{C}/\mathrm{K}$ ratio derived from core level photoemission. The dotted lines are guidelines for the evolution of the $S_1,S_2$ and $M_1$ peaks with increasing doping. The arrow highlights the satellite in the photoemission response at high doping levels.

Figure 2

Valence band photoemission spectra in the vicinity of the Fermi level (dotted line) for pristine (upscaled for clarity) and highly doped ($\mathrm{C}/\mathrm{K}\mathrm{=}\mathrm{20}$) SWCNT mats.

Figure 3

Double-logarithmic representation of the photoemission spectra for the analysis of the power law scaling within TLL theory close to the chemical potential. $\alpha$ results from a linear fit between 0.05 and 0.2 eV (solid lines in the figure) and is also shown for the pristine case.

Figure 4

Power law scaling factor $\alpha$ as a function of different doping levels ($e^{-}/\mathrm{C}$).