Time-Resolved Photoimaging of Image-Potential States in Carbon Nanotubes

The first experimental evidence for the existence of image-potential states in carbon nanotubes is presented. The observed features constitute a new class of surface image states due to their quantized centrifugal motion. Measurements of binding energies and the temporal evolution of image state electrons were performed using femtosecond time-resolved photoemission. The associated lifetimes are found to be significantly longer than those of $n=1$ image state on graphite, indicating a substantial difference in electron decay dynamics between tubular and planar graphene sheets.

Figure 1

Visualization of an image electron wave function, ${\psi }_{n=3,l=1}(\rho )e^{ikz}$ calculated for a 5 nm MWNT. The angular component of the wave function, $e^{il\varphi }$, [see Eq. (1)] is set to unity.

Figure 2

(a) The energy diagram of a two-photon photoexcitation technique. (b) The experimental photoelectron signal is plotted versus the electron energy relative to the Fermi level. If the IR pulse precedes the UV pulse ($\tau =-100\mathrm{f}\mathrm{s}$), $\overline{e}–h$ pairs (excitons) are created in the vicinity of $E_F$ (taken as zero of the energy scale). Image-potential states are observed just below the vacuum level for a positive delay of 230 fs. (c) The insert shows the change in the UV photoelectron signal induced by the IR probe-pulse.

Figure 3

(a) The photoelectron signal, originating from image-potential states, is plotted versus electron binding energies. Theoretical calculations of binding energies (b) and the associated wave functions, ${\psi }_{n,l}(\rho )$, (c) were performed for a 19-walled carbon nanotube ($d=14.2\mathrm{n}\mathrm{m}$). The model utilizes the jelliumlike potential barrier [17, 26], shown in (d). Different shades of energy bars in (b) represent different electron angular momenta ($0\le l\le 4$).

Figure 4

The temporal evolution of the ${\psi }_{n=1,l}$ image-potential state. The minimum pump-probe delay of 200 fs is used to avoid the background photoemission, generated by the time-reversed pair of laser pulses (IR followed by UV). The energy scale represents the kinetic energy of photoelectrons emitted from image-potential states by the IR probe-pulse.