Full counting statistics of a chaotic cavity with asymmetric leads

TL;DR

This paper derives an exact formula for the full counting statistics of charge transport in a chaotic cavity with asymmetric leads, revealing unique behavior of higher-order cumulants at high biases.

Contribution

It provides the first exact cumulant generating function for a chaotic cavity with asymmetric leads using Keldysh-Green functions, highlighting novel cumulant behavior.

Findings

Third cumulant changes sign at high biases in asymmetric cavities.

Third cumulant approaches a voltage-independent constant in symmetric cavities.

Derived formula determines all-order cumulants of current noise.

Abstract

We study the statistics of charge transport in a chaotic cavity attached to external reservoirs by two openings of different size which transmit non-equal number of quantum channels. An exact formula for the cumulant generating function has been derived by means of the Keldysh-Green function technique within the circuit theory of mesoscopic transport. The derived formula determines the full counting statistics of charge transport, i.e., the probability distribution and all-order cumulants of current noise. It is found that, for asymmetric cavities, in contrast to other mesoscopic systems, the third-order cumulant changes the sign at high biases. This effect is attributed to the skewness of the distribution of transmission eigenvalues with respect to forward/backward scattering. For a symmetric cavity we find that the third cumulant approaches a voltage-independent constant proportional to the temperature and the number of quantum channels in the leads.