Understanding plasmon dispersion in nearly free electron metals: Relevance of exact constraints for exchange-correlation kernels within time-dependent density functional theory

摘要

Small-wave-vector excitations in Coulomb-interacting systems can be decomposed into high-energy collective longitudinal plasmon and low-energy single-electron excitations. At the critical wave vector 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 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 r_s ＞ 1. The RPA and all beyond-RPA methods investigated here result in a wrong infinite plasmon lifetime for a wave vector smaller than the critical one where the plasmon dispersion curve runs into particle-hole excitations. Exchange-correlation kernel corrections to the 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 wave vectors 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 of 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.