超过渐近极限的二维和一维电子气的精确“精确交换”势
Exact "exact exchange" potential of two- and one-dimensional electron gases beyond the asymptotic limit
摘要：
电子在邻近固体表面或低维系统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是重要的。在这里，我们确定附近的二维和一维电子气（EG）的潜力，这样做的分析在密度泛函理论（DFT）的确切交换的水平。我们发现，在$r_\perp\gg k_F^{-1}$，其中$r_\perp$是距离EG和$k_F$是费米半径，潜在的服从已经知道的渐近$-e^2/r_\perp$，而在$r_\perp \lesssim k_F^{-1}$，但{ \em仍然在真空中}，定性和定量的偏差的交换势从渐近定律发生。激发到低位像态的运动场属于后一种状态，导致与里德堡系列的显著偏离。在一般情况下，我们的分析交换势建立基准的数值方法在低维科学，DFT是迄今为止最常见的工具。
英文摘要：
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 nano-science. 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 $r_\perp\gg k_F^{-1}$, where $r_\perp$ is the distance from the EG and $k_F$ is the Fermi radius, the potential obeys the already known asymptotic $-e^2/r_\perp$, while at $r_\perp \lesssim k_F^{-1}$, but {\em 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.
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