Npj Comput. Mater.:热电材料 zT到底能到多高?
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Fig. 1 Comparison of the maximum zT of a step-function transmission function with a delta-function one
Fig. 2 Optimal transmission probability and zT
来自清华大学物理系的徐勇教授以及哈工大(深圳)陈晓彬副教授等人,重新研究了最优热电这个经典问题。他们发现Mahan等人原始的推导中存在漏洞,相应得到的Mahan-Sofo极限并不总能给出最优的热电性能。在量子极限下,通过Landauer-Büttiker的理论框架并利用变分法来优化热电优值,他们证明了最优的透射概率函数是厢型(boxcar)函数,而不是Mahan等人一开始提出的函数,相应得到的热电优值可高于Mahan-Sofo极限。
Fig. 3 Variation of zT with the width of the transport window in a 1D chain model
此外,他们还提出可以利用拓扑材料来实现最优热电所要求的透射行为: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。
这个工作得出了量子热电的理论上限并提出了实现热电上限性能可以用的材料,有望促进未来热电领域的新发展。该文近期发表于npj Computational Materials 9: 189(2023),英文标题与摘要如下,点击左下角“阅读原文”可以自由获取论文PDF。
Fig. 4 Scenarios for achieving the best zT in topological materials
The best thermoelectrics revisited in the quantum limit
Sifan Ding, Xiaobin Chen, Yong Xu & Wenhui Duan
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-Büttiker 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.
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