WSe $_2$的带拟合和基于Wannier的模型构建的比较
Comparison of band-fitting and Wannier-based model construction for WSe$_2$
摘要：
过渡金属二硫属化物材料$MX_2 (M=Mo,W;X=S,Se)$由于其新颖的二维结构，具有优异的光学和输运性能而受到广泛的研究。从计算的角度来看，密度泛函理论模拟在这些系统中表现得非常好，是预测和补充实验结果的不可或缺的工具。然而，由于时间和长度尺度，即使是最有效的DFT实现可以达到今天，这种方法受到严格的限制，以处理有限的温度模拟或电子晶格耦合时，研究激发态：所需的单位细胞研究，例如，系统的热波动或大极化子将需要一个大的计算能力。多尺度技术，如最近提出的第二原理密度泛函理论，可以超越这些限制，但需要在调查中的系统的紧密结合模型的建设。在这项工作中，我们比较了两种这样的方法来构建WSe $_2$的频带。特别地，我们比较了（i）Wannier模型构建的结果与（ii）Liu及其同事的能带拟合方法，其中价带顶部和导带底部由三个对称的带建模，主要具有钨$d_{z^2}$，$d_{xy}$和$d_{x^2-y^2}$特征。我们的研究结果强调了这两种方法之间的差异，以及带拟合模型的构建如何导致高估了紧束缚表示中实空间基础的本地化。
英文摘要：
Transition metal dichalcogenide materials $MX_2 (M=Mo,W;X=S,Se)$ are being thoroughly studied due to their novel two-dimensional structure, that is associated with exceptional optical and transport properties. From a computational point of view, Density Functional Theory simulations perform very well in these systems and are an indispensable tool to predict and complement experimental results. However, due to the time and length scales where even the most efficient DFT implementations can reach today, this methodology suffers of stringent limitations to deal with finite temperature simulations or electron-lattice coupling when studying excitation states: the unit cells required to study, for instance, systems with thermal fluctuations or large polarons would require a large computational power. Multi-scale techniques, like the recently proposed Second Principles Density Functional Theory, can go beyond these limitations but require the construction of tight-binding models for the systems under investigation. In this work, we compare two such methods to construct the bands of WSe$_2$. In particular, we compare the result of (i) Wannier-based model construction with (ii) the band fitting method of Liu and co-workers where the top of the valence band and the bottom of the conduction band are modeled by three bands symmetrized to have mainly Tungsten $d_{z^2}$, $d_{xy}$ and $d_{x^2-y^2}$ character. Our results emphasize the differences between these two approaches and how band-fitting model construction leads to an overestimation of the localization of the real-space basis in a tight-binding representation.
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