Optimal thermoelectric figure of merit of a molecular junction

We show that a molecular junction can give large values of the thermoelectric figure of merit $ZT$, and so 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 non-zero. 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 $ZT\sim(\tilde{G}_{th}^{ph})^{-1/2}$, where $\tilde{G}_{th}^{ph}$ is the phonon thermal conductance divided by the thermal conductance quantum.