AI 中文总结
本研究开发基于黎曼ζ函数级数的全阶莫特方法，将其应用于石墨烯光热电器件，得到热电参数闭式表达式，揭示塞贝克系数上限、维德曼-弗兰兹定律违反等特性，提供了超越低温近似的分析方法。
AI 中文摘要
标准莫特公式被广泛用于描述热电输运，但当温度远小于费米能时，其精度会降低。本研究利用黎曼ζ函数级数，开发了莫特方法的全阶扩展形式。研究表明，当输运函数为多项式时，该级数在有限项后终止，可在模型内给出精确结果。我们将该方法应用于采用二次电导率模型的石墨烯光热电器件，得到了塞贝克系数、洛伦兹比和电子品质因子的闭式表达式。分析显示，塞贝克系数会达到最大值而非无限增大，且在较高温度下，维德曼-弗兰兹定律会被显著违反。此外，我们发现无序会降低热电性能，在洁净石墨烯模型中，电子品质因子存在上限，最后还探讨了辐射热输运对品质因子的影响。这些结果为研究石墨烯热电输运提供了一种超越常规低温莫特近似的简单分析方法。
英文摘要
The standard Mott formula is widely used to describe thermoelectric transport, but it becomes less accurate when the temperature is not much smaller than the Fermi energy. In this work, we develop an all-orders extension of the Mott approach using a series of Riemann zeta functions. We show that when the transport function is a polynomial, the series ends after a finite number of terms, giving exact results within the model. We apply this method to graphene photothermoelectric devices using a quadratic conductivity model. The results provide closed-form expressions for the Seebeck coefficient, Lorenz ratio, and electronic figure of merit. The analysis shows that the Seebeck coefficient reaches a maximum instead of increasing indefinitely, while the Wiedemann-Franz law can be significantly violated at higher temperatures. We also find that disorder reduces the thermoelectric performance and that the electronic figure of merit has an upper limit in the clean graphene model. Finally, we discuss the effect of radiative heat transport on the figure of merit. These results provide a simple analytical way to study graphene thermoelectric transport beyond the usual low-temperature Mott approximation.
Comments29 pages, 4 figures, 5 tables
