Counting statistics of dark-state transport through a carbon nanotube quantum dot

In a recent experiment [A. Donarini et al., Nat. Commun. 10, 381 (2019)], electronic transport through a carbon nanotube quantum dot was observed to be suppressed by the formation of a quantum-coherent ``dark state.'' In this paper we consider theoretically the counting statistics and waiting-time distribution of this dark-state-limited transport. We show that the statistics are characterized by giant super-Poissonian Fano factors and long-tailed waiting-time distributions, both of which are signatures of the bistability and extreme electron bunching caused by the dark state.