Airy-gas plasmons

The Airy gas, which is the simplest edge electron gas, became an important model system for the exchange-correlation and kinetic energy functional development of the ground-state density functional theory. In this work, we compute the random phase approximation (RPA) and the adiabatic local density approximation (ALDA) Airy-gas density response functions, using the exact one-particle orbitals and eigenvalues. From the dynamical response function, we study several properties of the Airy-gas model, such as the Airy loss-function, the induced density, the Airy-plasmon full width at half maximum, the screened interaction, and the stopping power, providing a systematic study of these properties with respect to the slope of the effective linear potential 𝐹 that can be considered the main variable of any metal surface. For instance, using the peaks of the loss function, we extract the Airy-gas plasmon energy dispersion, and we perform a careful analysis of the Airy-gas plasmons at various slopes of the effective linear potential. We find similar features with the real metal surfaces, such as the long-wavelength Airy-plasmon coefficient is negative and very sensitive to the slope value 𝐹, while the short-wavelength Airy-plasmon coefficient is almost independent on 𝐹. Overall, we show that the slope 𝐹 plays a crucial role for the surface plasmons and their related properties.