Full counting statistics of super-Poissonian shot noise in multilevel quantum dots

We examine the full counting statistics of quantum dots, which display super-Poissonian shot noise. By an extension to a generic situation with many excited states we identify the underlying transport process. The statistics is a sum of independent Poissonian processes of bunches of different sizes, which leads to the enhanced noise. The obtained results could be useful in determining transport characteristics in molecules and large quantum dots, since the noise (and higher cumulants) allow us to identify the internal level structure, which is not visible in the average current.

Figure 1

(Color online) (a) Two-terminal quantum dot with two levels. The tunneling rate from the lower level to the left lead is thermally activated due to the finite occupation of the left lead. All other tunneling processes have much larger rates. Coulomb charging allows only one of the levels to be occupied. (b) The same with $N_{+}$ upper levels and $N_{-}$ lower levels. (c) Transport cycles leading to super-Poissonian shot noise. With a small tunneling rate $x{\Gamma }_L$ a cycle is initiated by an electron tunneling from the dot to the left lead, followed by $n$ cycles $(n=0,1,2,\dots )$ of tunneling through the upper level with probability $1∕2$. Finally the process is stopped by a tunneling event from the right terminal to the lower level with probability $1∕2$. In total $n+1$ charges are transfered in a cycle with a rate $x{\Gamma }_L{(1∕2)}^{n+1}$, which explains the super-Poissonian noise and all other transport characteristics.