Heat-charge mixed noise and thermoelectric efficiency fluctuations

The close relationship between the noise and the thermoelectric conversion is studied in a quantum dot using a quantum approach based on the non-equilibrium Green function technique. We show that both the figure of merit and the efficiency can be written in term of noise and we highlight the central role played by the correlator between the charge current and the heat current that we call the mixed noise. After giving the expression of this quantity as an integral over energy, we calculate it, first in the linear response regime, next in the limit of small transmission through the barriers (Schottky regime) and finally in the intermediate regime. We discuss the notion of efficiency fluctuations and we also see here that the mixed noise comes into play.