论文标题
电子的动态介电函数和声子从电子中与2D Dirac Crystals中的声音子密切相关的电子能源
Dynamic dielectric function and phonon self-energy from electrons strongly correlated with acoustic phonons in 2D Dirac crystals
论文作者
论文摘要
二维（2D）狄拉克晶体的独特结构，具有线性在Brillouin-Zone边界的接近性和费米能量的近距离结构，会产生异常情况，其中已知小型Fermi-Energy扰动可严格影响该系统的电子相关晶格。 Fermi-surface嵌套（FSN）条件通过电子形成相互作用确定这种影响，需要对晶体的响应函数$（χ）$（χ）$的准确估计，这是任何温度值的声子波形Q的函数。到目前为止，由于相对容易地符合Q-独立型振动的计算频率，因此仅在介电响应函数$χ（Q，ω）$χ（Q，ω）$方面进行了$χ（Q）$的$χ（Q）$ $（Q）$，仅在介电响应函数$χ（Q，ω）$方面进行了。但是，元模型与不断存在的声音子（$ω$确实取决于Q且因此具有分散性）的模型对于理解许多关键的晶体特性至关重要。缺乏这种模型通常会导致假设这些系统中的介电响应函数$χ（q）$可以从自由电子行为中理解。在这里，我们表明，与自由电子系统不同的是，使用Lindhard模型从2D Dirac晶体中计算出的$χ（Q）$，在FSN条件下显示出尖端。 $ \ frac {\partialχ} {\ partial q} $的强大可变性在有限的温度下也持续存在，而在动态情况下，即使声音的速度很小，$χ（q）$也可能倾向于无穷大。我们的发现对电子声音声子相互作用和传输属性（例如声子线宽度）的含义也将被讨论。
The unique structure of two-dimensional (2D) Dirac crystals, with electronic bands linear in the proximity of the Brillouin-zone boundary and the Fermi energy, creates anomalous situations where small Fermi-energy perturbations are known to critically affect the electron-related lattice properties of the system. The Fermi-surface nesting (FSN) conditions determining such effects via electron-phonon interaction, require accurate estimates of the crystal's response function $(χ)$ as a function of the phonon wavevector q for any values of temperature. Numerous analytical estimates of $χ(q)$ for 2D Dirac crystals beyond the Thomas-Fermi approximation have been so far carried out only in terms of dielectric response function $χ(q,ω)$, for photon and optical-phonon perturbations, due to relative ease of incorporating a q-independent oscillation frequency in their calculation. However, models accounting for Dirac-electron interaction with ever-existing acoustic phonons, for which $ω$ does depend on q and is therefore dispersive, are essential to understand many critical crystal properties. The lack of such models has often led to assume that the dielectric response function $χ(q)$ in these systems can be understood from free-electron behavior. Here, we show that, different from free-electron systems, $χ(q)$ calculated from acoustic phonons in 2D Dirac crystals using the Lindhard model, exhibits a cuspidal point at the FSN condition. Strong variability of $\frac{\partialχ}{\partial q}$ persists also at finite temperatures, while $χ(q)$ may tend to infinity in the dynamic case even where the speed of sound is small, albeit nonnegligible, over the Dirac-electron Fermi velocity. The implications of our findings for electron-acoustic phonon interaction and transport properties such as the phonon line width derived from the phonon self energy will also be discussed.
