二维薛定谔型量子材料的扩展爱因斯坦扩散迁移率方程
Extended Einstein diffusion-mobility equation for two-dimensional Schrödinger-type quantum materials
摘要：
本文给出了从分子到材料的二维薛定谔型输运系统的扩散迁移率的精确解析方程。这种薛定谔系统中的电子态密度属于二维非相对论载流子动力学。我们将高斯函数应用到载流子密度的推导中，从而推导出一般费米系统和简并费米系统的电子可压缩性和扩散迁移率。这个模型最初是从广义爱因斯坦关系发展而来的，同时考虑了多体相互作用的热力学效应。相互作用的影响包括通过不完美的费米气体熵函数。我们的扩展模型解释了在宽的温度范围内，无序系统中热力学和电子学对扩散迁移率的协同作用。使用早期的实验和理论结果，我们已经证明了我们的扩展爱因斯坦模型的有效性，不同的二维简并系统。结果验证了原来的爱因斯坦方程在一定的温度和化学势值为不同的高斯方差。除了这些组合之外，还观察到偏差。在很低的温度下，扩散迁移率仅取决于化学势，这是理想量子材料的扩展爱因斯坦方程。
英文摘要：
We present the exact analytical equation of diffusion-mobility for two-dimensional (2D) Schrödinger type transport systems, from molecules to materials. The density of electronic states in such Schrödinger systems pertains to the 2D non-relativistic carrier dynamics. We implement the Gaussian function into carrier density derivation; accordingly we develop the electronic compressibility and diffusion-mobility for both the generic and the degenerate Fermi systems. This model is originally developed from generalized Einstein relation, along with concern about the thermodynamic effects on many-body interactions. The effect of interactions is included through the imperfect Fermi-gas entropy function. Our extended model explains the cooperative behavior of thermal and electronic counterparts on diffusion-mobility in disordered systems at wide temperature range. Using earlier experimental and theoretical results, we have shown the validity of our extended Einstein model for different 2D degenerate systems. The results validate the original Einstein equation at certain sets of temperature and chemical potential values for different Gaussian variances. Beyond those combinations, the deviation is observed. At very low temperature, the diffusion-mobility depends only on chemical potential, which is the extended Einstein equation for ideal quantum materials.
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