Lifetime of Charge Carriers in Multiwalled Nanotubes

The nature of low-energy excitations in multiwalled nanotubes (MWNTs) is investigated by means of two-color time-resolved photoemission. A careful analysis of the ballistic transport, secondary excitations, and band structure effects was employed in order to extract single electron lifetimes from the observed relaxation trend. It is demonstrated that in the vicinity of the Fermi level the energy dependence of $e\mathrm{\text{−}}e$ scattering times is inversely proportional to approximately the square of the excitation energy. This result provides strong evidence that electron transport in MWNTs exhibits a Fermi-liquid behavior, indicating that long-range $e\mathrm{\text{−}}e$ interaction along the tube vanishes due to screening.

Figure 1

The two-photon photoemission signal as a function of the pump-probe delay (cross-correlation trace) recorded for the conduction electrons at $E-E_F=170\pm 20\mathrm{m}\mathrm{e}\mathrm{V}$. The experimental data are fitted with a biexponential curve utilizing the slow, ${\tau }_{e\mathrm{\text{−}}e}$, and fast, ${\tau }_{e\mathrm{\text{−}}\mathrm{p}\mathrm{h}}$, decay components (see text).

Figure 2

(a) Energy bands in the vicinity of $E_F$, calculated for a (110, 110) SWNT. (b) Spectrum of $e\mathrm{\text{−}}h$ pair excitations, illustrating the energy-momentum constraints on electronic decay from the least energetic state labeled (1). (c),(d) The available phase space for an electron decay from the initial state labeled (1) is illustrated through the overlap of the $e\mathrm{\text{−}}h$ pair spectrum with energy-loss spectra.

Figure 3

Energy dependence of the excited electron lifetimes. (a) Close to $E_F$, the electron relaxation trend exhibits a FLT-like power-law energy dependence [see (b)]. However, for electron excitations that energetically exceed the first VHS, $E\ge E_{\mathrm{V}\mathrm{H}\mathrm{S}}\approx 70\mathrm{m}\mathrm{e}\mathrm{V}$, the lifetime energy dependence is anomalous, $\tau \propto (E-E_F{)}^1$. Inset (b) “zooms in” on the energy interval, where the measured electron lifetimes are inversely proportional to approximately the square of the excitation energy. Estimated location of the first VHS in a (110, 110) SWNT (sharp peak near 70 meV), which, in the case a MWNT, containing a collection of different SWNT shells, becomes inhomogeneously broadened.