Thermoelectric energy converters under a trade-off figure of merit with broken time-reversal symmetry

We study the performance of a three-terminal thermoelectric device such as heat engine and refrigerator with broken time-reversal symmetry by applying the unified trade-off figure of merit ($\dot{\Omega}$ criterion) which accounts for both useful energy and losses. For heat engine, we find that a thermoelectric device working under the maximum $\dot{\Omega}$ criterion gives a significantly better performance than a device working at maximum power output. Within the framework of linear irreversible thermodynamics such a direct comparison is not possible for refrigerators, however, our study indicates that, for refrigerator, the maximum cooling load gives a better performance than the maximum $\dot{\Omega}$ criterion for a larger asymmetry. Our results can be useful to choose a suitable optimization criterion for operating a real thermoelectric device with broken time-reversal symmetry.