Finite-size effects in a nanotube connected to leads:: Super- and sub-Poissonian noise

The injection of electrons in the bulk of a carbon nanotube which is connected to ideal Fermi-liquid leads is considered. While the presence of the leads gives a cancellation of the noise cross correlations, the autocorrelation noise has a Fano factor which deviates strongly from the Schottky behavior at voltages where finite-size effects are expected. Indeed, as the voltage is increased from zero, the noise is first super-Poissonian, then sub-Poissonian, and eventually it reaches the Schottky limit. These finite-size effects are also tested using a diagnosis of photoassisted transport, where a small ac modulation is superposed onto the dc bias voltage between the injection tip and the nanotube. When finite-size effects are at play, we obtain a stepwise behavior for the noise derivative, as expected for normal-metal systems, whereas in the absence of finite-size effects, due to the presence of Coulomb interactions, a smoothed staircase is observed. The present work shows that it is possible to explore finite-size effects in nanotube transport via a zero-frequency noise measurement.