We report a general macroscopic theory for the electrodynamic response of semi-infinite metals (SIMs). The theory includes the hitherto overlooked capacitive effects due to the finite spatial extension of a surface. The basic structure of this theory is independent of the particulars of electron dynamics. Analytical expressions have been obtained of the charge density-density response function, which is naturally parsed into two parts. One of them represents a bulk property while the other a pure surface property. We apply the theory to study the responses according to several electronic dynamics models and provide a unified view of their validity and limitations. The models studied include the local dielectric model (DM), the dispersive hydrodynamic model (HDM) and specular reflection model (SRM), as well as the less common semi-classical model (SCM) based on Boltzmann's transport equation. We show that, in terms of their basic equations, the SRM is an extension of the HDM, just as the HDM is an extension of the DM. The SCM improves over the SRM critically through the inclusion of translation symmetry breaking and surface roughness effects. We then employ the response function to evaluate the so-called dynamical structure factor, which plays an important role in particle scattering. As expected, this factor reveals a peak due to the excitation of surface plasma waves (SPWs). Surprisingly, however, the peak is shown to be considerably sharper in the SCM than in other models, indicating an incipient instability of the system according to this model. We also study the distribution of charges induced by a charged particle grazing over a SIM surface at constant speed. This distribution is shown to contain model-specific features that are of immediate experimental interest.

中文翻译：

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有界金属的电动响应理论：表面电容效应

我们报告了半无限金属 (SIM) 的电动力学响应的一般宏观理论。该理论包括迄今为止由于表面的有限空间延伸而被忽视的电容效应。该理论的基本结构独立于电子动力学的细节。得到了电荷密度-密度响应函数的解析表达式，自然解析为两部分。其中一个代表整体性质，而另一个代表纯表面性质。我们应用该理论根据几种电子动力学模型研究响应，并对其有效性和局限性提供统一的观点。研究的模型包括局部介电模型 (DM)、色散流体动力学模型 (HDM) 和镜面反射模型 (SRM)，以及不太常见的基于玻尔兹曼输运方程的半经典模型 (SCM)。我们表明，就它们的基本方程而言，SRM 是 HDM 的扩展，就像 HDM 是 DM 的扩展一样。通过包含平移对称性破坏和表面粗糙度效应，SCM 对 SRM 进行了重大改进。然后我们使用响应函数来评估所谓的动态结构因子，它在粒子散射中起着重要作用。正如预期的那样，由于表面等离子体波 (SPW) 的激发，该因素显示出一个峰值。然而，令人惊讶的是，SCM 中的峰值显示出比其他模型中的更尖锐，表明根据该模型，系统处于初期不稳定性。我们还研究了带电粒子以恒定速度掠过 SIM 表面引起的电荷分布。该分布显示包含具有直接实验兴趣的模型特定特征。