Optimal thermoelectric figure of merit of a molecular junction

Abstract

We show that a molecular junction can give large values of the thermoelectric figure of merit $ZT$, and so it could be used as a solid-state energy-conversion device that operates close to the Carnot efficiency. The mechanism is similar to the Mahan-Sofo model for bulk thermoelectrics---the Lorenz number goes to zero violating the Wiedemann-Franz law while the thermopower remains nonzero. The molecular state through which charge is transported must be weakly coupled to the leads, and the energy level of the state must be of order ${k}_{B}T$ away from the Fermi energy of the leads. In practice, the figure of merit is limited by the phonon thermal conductance; we show that the largest possible $ZT\ensuremath{\sim}{({\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{\text{th}}^{\text{ph}})}^{\ensuremath{-}1/2}$, where ${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{G}}_{\text{th}}^{\text{ph}}$ is the phonon thermal conductance divided by the thermal conductance quantum.