理解近自由电子金属中的等离子体激元色散：与时间相关的密度泛函理论中新型交换相关核的精确约束的相关性
Understanding plasmon dispersion in nearly-free-electron metals: the relevance of exact constraints for novel exchange-correlation kernels within time-dependent density functional theory
摘要：
库仑相互作用系统中的小波矢激发可以分解为高能纵向等离子体激元和低能单电子激发。在等离子体激元分支与单电子激发区域合并的临界波矢和相应频率处，等离子体激元的集体能量耗散成单电子-空穴激发。Jeltron模型提供了接近自由电子极限的金属的电子能量损失谱（EELS）的合理描述。随机相位近似（RPA）在高密度极限下是精确的，但即使对于rs > 1的密度，也可以合理地捕获等离子体色散。RPA和所有超越RPA的方法在这里调查，导致一个错误的无限等离子体激元寿命的波矢量小于临界的等离子体激元色散曲线进入粒子空穴激发。交换相关核修正RPA修改等离子体色散曲线。然而，在前面研究的内核的结构和形式上有很大的差异。我们目前的工作介绍了最近的模型交换只和交换相关内核，并讨论了一些确切的约束在内核的建设的相关性。我们表明，由于等离子体色散采样的波矢量的范围小于相关能量采样的范围，不同的内核可以使相关能量的强差异和弱差异的等离子体色散。这项工作完成了我们的理解等离子体激元分散在现实的金属，如Cs，其中已观察到负等离子体激元分散。我们发现只有积极的等离子体激元色散在jeletion的密度为Cs。
英文摘要：
Small-wavevector excitations in Coulomb-interacting systems can be decomposed into the high-energy collective longitudinal plasmon and the low-energy single-electron excitations. At the critical wavevector and corresponding frequency where the plasmon branch merges with the single-electron excitation region, the collective energy of the plasmon dissipates into single electron-hole excitations. The jellium model provides a reasonable description of the electron-energy-loss spectrum (EELS) of metals close to the free-electron limit. The random phase approximation (RPA) is exact in the high-density limit but can capture the plasmonic dispersion reasonably even for densities with rs > 1. RPA and all beyond-RPA methods investigated here, result in a wrong infinite plasmon lifetime for a wavevector smaller than the critical one where the plasmon dispersion curve runs into particle-hole excitations. Exchange-correlation kernel corrections to RPA modify the plasmon dispersion curve. There is however a large difference in the construction and form of the kernels investigated earlier. Our current work introduces recent model exchange-only and exchange-correlation kernels and discusses the relevance of some exact constraints in the construction of the kernel. We show that, because the plasmon dispersion samples a range of wavevectors smaller than the range sampled by the correlation energy, different kernels can make a strong difference for the correlation energy and a weak difference for the plasmon dispersion. This work completes our understanding about the plasmon dispersion in realistic metals, such as Cs, where a negative plasmon dispersion has been observed. We find only positive plasmon dispersion in jellium at the density for Cs.
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