  Direct thermal-to-electric energy converters typically operate in the linear
regime, where the ratio of actual maximum power relative to the ideal maximum
power, the so-called fill factor (FF), is 0.25. By increasing the FF one can
potentially increase maximum power by up to four times, but this is only
possible in the nonlinear regime of transport and has previously rarely been
considered. Here we show, based on fundamental symmetry considerations, that
the leading order non-linear terms that can increase the FF require devices
with broken spatial symmetry. To experimentally demonstrate such a system, we
study nonlinear, thermoelectric transport across an asymmetric energy barrier
epitaxially defined in a single semiconductor nanowire. We find in both
experiment and theory that we can increase the FF above the linear-response
limit of 0.25, accompanied by a drastic increase in short circuit current,
open-circuit voltage and maximum power. Our results show that geometric
symmetry breaking combined with the design of nonlinear behaviour represent a
design strategy for increasing the performance of thermal-to-electric energy
converters such as in hot-carrier photovoltaics, thermophotovoltaics or in
anisotropic thermoelectric materials.
