Enhanced thermoelectric coupling near electronic phase transition: The role of fluctuation Cooper pairs

Thermoelectric energy conversion is a direct but low-efficiency process, which precludes the development of long-awaited wide-scale applications. As a breakthrough permitting a drastic performance increase is seemingly out of reach, we fully reconsider the problem of thermoelectric coupling enhancement. The corner stone of our approach is the observation that heat engines are particularly efficient when their operation involves a phase transition of their working fluid. We derive and compute the thermoelastic coefficients of various systems, including Bose and Fermi gases, and fluctuation Cooper pairs. Combination of these coefficients yields the definition of the thermodynamic figure of merit, the divergence of which at $finite$ temperature indicates that conditions are fulfilled for the best possible use of the thermoelectric working fluid. Here, this situation occurs in the fluctuation regime only, as a consequence of the increased compressibility of the working fluid near its phase transition. Our results and analysis clearly show that efforts in the field of thermoelectricity can now be productively directed towards systems where electronic phase transitions are possible.