Low-dimensional electronic systems in thermoelectrics have the potential to achieve high thermalto-electric energy conversion efficiency. A key measure of performance is the efficiency when the device is operated under maximum power conditions. Here we study the efficiency at maximum power of three low-dimensional, thermoelectric systems: a zero-dimensional quantum dot (QD) with a Lorentzian transmission resonance of finite width, a one-dimensional (1D) ballistic conductor, and a thermionic (TI) power generator formed by a two-dimensional energy barrier. In all three systems, the efficiency at maximum power is independent of temperature, and in each case a careful tuning of relevant energies is required to achieve maximal performance. We find that quantum dots perform relatively poorly under maximum power conditions, with relatively low efficiency and small power throughput. Ideal one-dimensional conductors offer the highest efficiency at maximum power (36% of the Carnot efficiency). Whether 1D or TI systems achieve the larger maximum power output depends on temperature and area filling factor. These results are also discussed in the context of the traditional figure of merit ZT .

Quantum dots are model systems for quantum thermoelectric behavior because of their ability to control and measure the effects of electron-energy filtering and quantum confinement on thermoelectric properties. Interestingly, nonlinear thermoelectric properties of such small systems can modify the efficiency of thermoelectric power conversion. Using quantum 7 These authors contributed equally to this work. 8

Quantum dots are an important model system for thermoelectric phenomena, and may be used to enhance the thermal-to-electric energy conversion efficiency in functional materials, by tuning the Fermi energy relative to the dots' transmission resonances. It is therefore important to obtain a detailed understanding of a quantum dot's thermopower as a function of the Fermi energy. However, so far it has proven difficult to take the effects of interactions into account in the interpretation of experimental data. In this paper, we present detailed measurements of the thermopower of quantum dots defined in heterostructure nanowires. We show that the thermopower lineshape is described well by a Landauer-type transport model that uses as its input experimental values of the dot conductance, which contains information about interaction effects. 6

When a quantum dot is subjected to a thermal gradient, the temperature of electrons entering the dot can be determined from the dot's thermocurrent if the conductance spectrum and background temperature are known. We demonstrate this technique by measuring the temperature difference across a 15 nm quantum dot embedded in a nanowire. This technique can be used when the dot's energy states are separated by many kT and will enable future quantitative investigations of electron-phonon interaction, nonlinear thermoelectric effects, and the efficiency of thermoelectric energy conversion in quantum dots.