Dark versus blocking states in electronic transport: A Lee-Yang zero analysis of full counting statistics

Electronic transport through nanostructures can be suppressed by coherent population trapping, in which quantum coherence leads to a dark state that decouples from the drain electrode. Finite transport, then, relies on decoherence of the dark state. An alternative scenario for reduced transport is weak coupling of a state, referred to as a blocking state, to the drain. This raises the question of whether and how these two scenarios can be distinguished in the transport features. For the example of electron transport through a carbon nanotube, we analyze the full counting statistics in terms of Lee-Yang zeros and factorial cumulants. This allows us to identify regimes in which the distinction between dark and blocking state is possible and regimes in which this is not the case.