Non-linear thermoelectricity in disordered nanowires

We consider non-linear thermoelectric transport in an effectively one-dimensional disordered semiconductor nanowire connected to a pair of three-dimensional perfectly conducting semi-infinite leads, where the impurity band of the disordered wire can be shifted relative to the conduction band of the leads by applying a gate voltage. We show how the gate voltage can be tuned to optimize a unique interplay between the microscopic parameters characterizing the transmission of electrons through the nanowire and the thermodynamic parameters that characterize the Fermi functions in the leads. Assuming a Lorentzian distribution of disorder in the wire, we calculate the full non-linear thermodynamic efficiency $\eta$ as well as the power output $P$. We show that for a fixed set of microscopic and thermodynamic parameters $\eta$ can be increased from zero to $\eta > 0.5 \eta_c$, where $\eta_c$ is the Carnot efficiency, by simply changing the gate voltage. The power output $P$ can then be scaled by connecting many wires in parallel.