Oscillating factorial cumulants in counting statistics are due to interactions

Abstract

We discuss our recent theoretical proposal to detect interactions in the electron transport through a nano-scale system by measuring high-order factorial cumulants of the full counting statistics. Our proposal is based on theoretical studies which have demonstrated that the zeros of the generating function for the full counting statistics are always real and negative for non-interacting electrons in a two-terminal scattering setup. As we have shown, this implies that the factorial cumulants do not oscillate as functions of any system parameter. Interactions, however, can cause the zeros to move away from the negative real axis into the complex plane. This transition is clearly visible in the factorial cumulants which start oscillating. We illustrate our findings with a model of transport through a two-level Coulomb blockade quantum dot, which we analyze both for finite times and in the long-time limit, and we discuss possible experimental implementations to test our predictions.