The best thermoelectrics revisited in the quantum limit

The classical problem of best thermoelectrics, which was believed originally solved by Mahan and Sofo [Proc. Natl. Acad. Sci. USA 93, 7436 (1996)], is revisited and discussed in the quantum limit. We express the thermoelectric figure of merit (zT) as a functional of electronic transmission probability T by the Landauer-Buttiker formalism, which is able to deal with thermoelectric transport ranging from ballistic to diffusive regimes. We also propose to apply the calculus of variations to search for the optimal T giving the maximal zT. Our study reveals that the optimal transmission probability T is a boxcar function instead of a delta function proposed by Mahan and Sofo, leading to zT exceeding the well-known Mahan-Sofo limit. Furthermore, we suggest realizing the optimal T in topological material systems. Our work defines the theoretical upper limit for quantum thermoelectrics, which is of fundamental significance to the future development of thermoelectrics.

Automated summary

This study revisits the classical problem of best thermoelectrics and discusses it in the quantum limit. By expressing the thermoelectric figure of merit as a functional of electronic transmission probability T and applying the calculus of variations, the optimal transmission probability is found to exceed the Mahan-Sofo limit. Additionally, the study suggests realizing the optimal transmission probability in topological material systems, defining the theoretical upper limit for quantum thermoelectrics and contributing to the future development of thermoelectrics.