  The bottleneck in modern thermoelectric power generation and cooling is the
low energy conversion efficiency of thermoelectric materials. The detrimental
effects of lattice phonons on performance can be mitigated, but achieving a
high thermoelectric power factor remains a major problem because the Seebeck
coefficient and electrical conductivity cannot be jointly increased. The
conducting electron gas in thermoelectric materials is the actual working fluid
that performs the energy conversion, so its properties determine the maximum
efficiency that can theoretically be achieved. By relating the thermoelastic
properties of the electronic working fluid to its transport properties
(considering noninteracting electron systems), we show why the performance of
conventional semiconductor materials is doomed to remain low. Analyzing the
temperature dependence of the power factor theoretically in 2D systems and
experimentally in a thin film, we find that in the fluctuation regimes of an
electronic phase transition, the thermoelectric power factor can significantly
increase owing to the increased compressibility of the electron gas. We also
calculate the ideal thermoelectric conversion efficiency in noninteracting
electron systems across a wide temperature range neglecting phonon effects and
dissipative coupling to the heat source and sink. Our results show that driving
the electronic system to the vicinity of a phase transition can indeed be an
innovative route to strong performance enhancement, but at the cost of an
extremely narrow temperature range for the use of such materials, which in turn
precludes potential development for the desired wide range of thermoelectric
energy conversion applications.
