Enhancement of thermoelectric efficiency and violation of the Wiedemann-Franz law due to Fano effect

We consider the thermoelectric properties of a double-quantum-dot molecule coupled in parallel to metal electrodes with a magnetic flux threading the ring. By means of the Sommerfeld expansion we obtain analytical expressions for the electric and thermal conductances, thermopower and figure of merit for arbitrary values of the magnetic flux. We neglect electronic correlations. The Fano antiresonances in transmission demand that terms usually discarded in the Sommerfeld expansion are taken into account. We also explore the behavior of the Lorenz ratio L=\kappa/\sigma T, where \kappa\ and \sigma\ are the thermal and electrical conductances and T the absolute temperature, and we discuss the reasons why the Wiedemann-Franz law fails in presence of Fano antiresonances.