Electron-phonon coupling in single walled carbon nanotubes determined by shot noise

We have measured shot noise in metallic single-walled carbon nanotubes of length L=1 $\mu$m and have found strong suppression of noise with increasing voltage. We conclude that the coupling of electron and phonon baths at temperatures $T_e$ and $T_{ph}$ is described at intermediate bias (20 mV $<$ \vv $\lesssim $ 200 mV) by heat flow equation $P=\Sigma L (T_e^3-T_{ph}^3)$ where $\Sigma \sim 3 \cdot 10^{-9}$ W/mK$^3$ due to electron interaction with acoustic phonons, while at higher voltages optical phonon - electron interaction leads to $P =\kappa_{op} L [N (T_e)-N(T_{ph})]$ where $N(T)= 1/(\exp(\hbar\Omega/k_BT)-1)$ with optical phonons energy $\hbar \Omega$ and $\kappa_{op}=2 \cdot 10^{2}$ W/m.