Electron temperature dependence of the electron-phonon coupling strength in double-wall carbon nanotubes

We apply Time-Resolved Two-Photon Photoemission spectroscopy to probe the electron-phonon (e-ph) coupling strength in double-wall carbon nanotubes. The e-ph energy transfer rate G(T$_{\mathrm{e}}$, T$_{\mathrm{l}})$ from the electronic system to the lattice depends linearly on the electron (T$_{\mathrm{e}})$ and lattice (T$_{\mathrm{l}})$ temperatures for T$_{\mathrm{e}}$ \textgreater $\Theta_{\mathrm{Debye}}$. Moreover, we numerically solved the Two-Temperature Model. We found: (i) a T$_{\mathrm{e}}$ decay with a 3.5 ps time constant and no significant change in T$_{\mathrm{l}}$; (ii) an e-ph coupling factor of 2 $\times$ 10$^{16}$ W/m$^{3}$; (iii) a mass-enhancement parameter, $\lambda $, of (5.4 $\pm$ 0.9) $\times$ 10$^{-4}$; and (iv) a decay time of the electron energy density to the lattice of 1.34 $\times$ 0.85 ps.