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We study the thermoelectric coefficients of a multi-level quantum dot (QD)weakly coupled to two electron reservoirs in the Coulomb blockade regime.Detailed calculations and analytical expressions of the power factor and thefigure of merit are presented. We restrict our interest to the limit where theenergy separation between successive energy levels is much larger than thethermal energy (i.e., the quantum limit) and we report a giant enhancement ofthe figure of merit due to the violation of the Wiedemann-Franz law whenphonons are frozen. We point out the similarity of the electronic and thephonon contribution to the thermal conductance for zero dimensional electronsand phonons. Both contributions show an activated behavior. Our findingssuggest that the control of the electron and phonon confinement effects canlead to nanostructures with improved thermoelectric properties.

Thermoelectric properties of a weakly coupled quantum dot: enhanced thermoelectric efficiency