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Exact exact-exchange potential of two- and one-dimensional electron gases beyond the asymptotic limit

机译:超过渐近极限的二维和一维电子气体的精确精确交换势

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摘要

The exchange-correlation potential experienced by an electron in the free space adjacent to a solid surface or to a low-dimensional system defines the fundamental image states and is generally important in surface and nanoscience. Here we determine the potential near the two- and one-dimensional electron gases (EG), doing this analytically at the level of the exact exchange of the density-functional theory (DFT). We find that, at r_⊥ >> k_F~(-1), where r_⊥ is the distance from the EG and k_F is the Fermi radius, the potential obeys the already known asymptotic -e~2/r_⊥, while at r_⊥ approx< k_F~(-1), but still in vacuum, qualitative and quantitative deviations of the exchange potential from the asymptotic law occur. The playground of the excitations to the low-lying image states falls into the latter regime, causing significant departure from the Rydberg series. In general, our analytical exchange potentials establish benchmarks for numerical approaches in the low-dimensional science, where DFT is by far the most common tool.
机译:电子在与固体表面或低维系统相邻的自由空间中所经历的交换相关势定义了基本的图像状态,并且在表面和纳米科学中通常很重要。在这里,我们确定二维和一维电子气(EG)附近的电势,并在密度泛函理论(DFT)的精确交换一级进行分析。我们发现,在r_⊥>> k_F〜(-1)处,其中r_⊥是距EG的距离,而k_F是费米半径,该势能服从已知的渐近-e〜2 /r_⊥,而在r_ ⊥约<k_F〜(-1),但仍处于真空状态,交换势与渐近定律发生质和量的偏差。低层图像状态激发的运动场属于后一种状态,从而大大偏离了里德伯格级数。通常,我们的分析交换潜力为低维科学中的数字方法建立了基准,而DFT是迄今为止最常用的工具。

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  • 来源
    《Physical review》 |2016年第19期|195432.1-195432.9|共9页
  • 作者

    Vladimir U. Nazarov;

  • 作者单位

    Research Center for Applied Sciences, Academia Sinica, Taipei 11529, Taiwan;

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  • 原文格式 PDF
  • 正文语种 eng
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