The best thermoelectrics revisited in the quantum limit 

Sifan Ding, Xiaobin Chen, Yong Xu & Wenhui Duan

npj Computational Materials 9: 189 (2023)

doi.org/10.1038/s41524-023-01141-1

Published online: 14 Oct 2023

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热电器件: zT最高能有多少？

半个世纪以来，高热电因子（zT）的热电材料的搜寻吸引了人们极大的关注。关于最优热电转换效率的问题，人们认为在1996年时已经被Mahan和Sofo等人从理论上解决了。该研究发现Mahan等人原始的推导是有漏洞的，他们得到的Mahan-Sofo极限并不总能给出最大的热电优值。来自清华大学的徐勇教授和哈工大（深圳）陈晓彬副教授等人，重新研究了最优热电的问题，在 Landauer-Büttiker的理论框架下利用变分法证明了最优的透射概率应该是厢型(boxcar)函数，而不是Mahan等人一开始提出的delta函数型，相应得到的量子极限下的热电优值可高于Mahan-Sofo极限。该研究提出可以利用拓扑材料来实现最优热电所需要的透射概率——拓扑材料的边缘态受对称性保护，可通过引入缺陷与无序来破坏体态的电子输运，而保留不受一般缺陷与无序影响的边缘态的透射，从而得到厢型的透射概率。该研究得出了量子极限下热电优值的理论上限，对未来热电领域的发展有重要意义。

Editorial Summary

Thermoelectrics: How much is the highest zT?

The search for materials with a high thermoelectric figure of merit (zT) has attracted lots of attention for centuries. It is believed that the classical problem of best thermoelectrics was solved by Mahan and Sofo in 1996. This work reveals a loophole in the original derivation of Mahan's work, which cannot guarantee the best thermoelectrics. Coming from the Department of Physics, Tsinghua University and Harbin Institute of Technology, Prof. Yong Xu, Xiaobin Chen, et al. revisit the problem of best thermoelectrics by using the calculus of variations under the Landauer-Buttiker formulism. They point out that the best transmission probability should be the boxcar function instead of the delta function and that the best zT far exceeds the Mahan-Sofo limit. Furthermore, this work proposes to utilize topological materials for achieving the desired boxcar-type transmission probability. As is well known, defects and disorders affect the bulk states but do not impact the topological edge states, which are usually protected by symmetries. This work defines the upper limit of thermoelectrics in the quantum limit, which is fundamentally significant to the future development of thermoelectrics.