无序晶体输运系数的第一性原理研究II
Disordered Crystals from First Principles II: Transport Coefficients
摘要：
这是有限温度下晶体中电子输运的第一性原理计算基础项目的第二部分，旨在建立一个预测性第一性原理平台，该平台将从头算分子动力学（AIMD）和有限温度Kubo公式与热无序结晶相的耗散相结合。后者被编码在遍历动力系统$(Ω,\mathbb G,{\rm d}\mathbb P)$中，其中$Ω$是原子自由度的配置空间，$\mathbb G$是作用于$Ω$的空间群，而${\rm d}\mathbb P$是相对于$\mathbb G$作用的遍历吉布斯测度。我们首先演示了如何通过连续科恩-沙姆理论的离散原子轨道为基础的形式主义，而不打破物理观测值w.r.t.的协方差。$(Ω,\mathbb G,{\rm d}\mathbb P)$。然后，我们展示了如何实现的Kubo公式，调查其自平均属性，并推导出一个最佳的有限体积approximates. We还描述了一个数值创新，使AIMD模拟与较长的轨道和详细说明我们的模拟的细节。最后，我们给出了不同温度下晶体硅输运系数的数值计算结果。
英文摘要：
This is the second part of a project on the foundations of first-principle calculations of the electron transport in crystals at finite temperatures, aiming at a predictive first-principles platform that combines ab-initio molecular dynamics (AIMD) and a finite-temperature Kubo-formula with dissipation for thermally disordered crystalline phases. The latter are encoded in an ergodic dynamical system $(Ω,\mathbb G,{\rm d}\mathbb P)$, where $Ω$ is the configuration space of the atomic degrees of freedom, $\mathbb G$ is the space group acting on $Ω$ and ${\rm d}\mathbb P$ is the ergodic Gibbs measure relative to the $\mathbb G$-action. We first demonstrate how to pass from the continuum Kohn-Sham theory to a discrete atomic-orbitals based formalism without breaking the covariance of the physical observables w.r.t. $(Ω,\mathbb G,{\rm d}\mathbb P)$. Then we show how to implement the Kubo-formula, investigate its self-averaging property and derive an optimal finite-volume approximation for it. We also describe a numerical innovation that made possible AIMD simulations with longer orbits and elaborate on the details of our simulations. Lastly, we present numerical results on the transport coefficients of crystal silicon at different temperatures.
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