3 years ago

An Analytical Dynamical Response Theory for Bounded Medium Without Additional Boundary Conditions: A Unified View of Dispersive and Non-Dispersive Models.

Hai-Yao Deng

In the present work, we derive a dynamical response theory for semi-infinite materials without the widely-used auxiliary boundary conditions. The theory is generic with its basic structure totally independent of the particulars of electron dynamics, be they local or nonlocal. Analytical expressions are then obtained of the charge density-density response function. It is shown that this function is naturally parsed into two parts, one of which represents primarily a bulk property while the other a pure surface property. We then apply the theory to common electron dynamics models and provide a unified view of their underlying propositions. 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 further employ the response function to evaluate the 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. 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. Our work solves a fundamental problem in condensed matter physics and surface science and is expected to find broad applications.

Publisher URL: http://arxiv.org/abs/1806.08308

DOI: arXiv:1806.08308v4

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