Propagation Characteristics of Electrostatic Surface Plasma Waves at the Spin-Polarized Quantum Plasma–Vacuum Interface

Abstract

This investigation explores the characteristics of electrostatic surface plasma waves within the framework of a spin-polarized quantum plasma. Utilizing the spin-polarized quantum hydrodynamic model and incorporating essential elements like Fermi pressure and Bohm potential, we derive the dispersion relation governing surface plasma waves at a plasma–vacuum interface. Through Fourier decomposition of the hydrodynamic model, we establish the dispersion relation that outlines the behavior of surface plasmons under conditions of small amplitude. Quantum effects, encompassing degenerate pressure, and Bohm potential are considered with specific attention given to the spin polarization effect, treating spin up, and spin down electrons as distinct species. The resulting dispersion relation demonstrates that, regardless of the degree of spin matching, Bohm potential significantly alters the phase speed in the limit of a large wave vector. Increasing spin mismatch in the quantum plasma leads to a decrease in the phase speed of the surface mode for a fixed value of the plasmonic coupling parameter $H$. Our findings bear relevance to graphene-based plasmonic systems, aligning with some of the observations reported in Gao et al. (2013) and Guo et al. (2019).