Peltier effect: From linear to nonlinear
Authors: Yang Zhen , Zhu Can , Ke Ya-Jiao , He Xiong , Luo Feng , Wang Jian , Wang Jia-Fu , Sun Zhi-Gang ,   State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China,   College of Science, Wuhan University of Technology, Wuhan 430070, China,   Wuhan National High Magnetic Field Center, Huazhong University of Science and Technology, Wuhan 430074, China
Published: January 2021

Thermoelectric refrigeration technology is an environment-friendly refrigeration technology with broad application prospects. The Peltier effect plays a central role in the thermoelectric refrigeration process, however, the Peltier coefficient is difficult to measure. So in the actual application process, first, the Seebeck coefficient is usually obtained, and then the Peltier coefficient is achieved by the Kelvin's second relation indirectly. It should be noted that the Kelvin's second relation is obtained under linear conditions (Ohm's law, Fourier's law, etc.), while in practice, nonlinear current-voltage relationships (Schottky junction, pn junction, etc.) and nonlinear heat transport relations are common. And quantum effect plays a leading role in the nano-scaled region, then the Peltier effect must consider the influence of nonlinearity, and the applicability of the Kelvin's second relation must also be reconsidered. This paper first summarizes the theoretical derivation of Peltier coefficient and the Kelvin’s second relation by different methods, then discusses the hypothetical conditions used in the derivation process, and points out that the Kelvin’s second relation can be established only under the hypothetical linear conditions. Then, several experimental methods of determining the Peltier coefficient are summarized. It is found that there are still many problems encountered in the measurement of Peltier coefficient, and the Kelvin’s second relation has not been proved accurately by practical experiments. Various side effects (Fourier effect, Thomson effect, Joule effect and Seebeck effect) in the measurement process affect the temperature distribution of the system directly or indirectly, making it difficult to measure Peltier heat. After that, the theoretical work of nonlinear Peltier effect is briefly introduced. In the process of thermal transport and electrical transport on a microscopic scale, quantum effect plays a leading role, and the nonlinear part of the Peltier coefficient gradually emerges. These studies show the cognition of researchers that the Peltier effect gradually changes from linear to nonlinear. The nonlinear Peltier effect not only exists objectively, but also is very important in the practical applications. However, the current research on the nonlinear Peltier effect is still at the theoretical level, and there is almost no experimental work. Finally, we discuss the research strategy and feasible research direction of Peltier effect under nonlinear conditions. An integrated study of the relationship among various heterojunction band structures, interface properties and interface effects is helpful in comprehensively understanding the Peltier effect. With the continuous improvement of experimental conditions and theoretical research, the study of nonlinear Peltier effect is expected to realize a new breakthrough.