Electron spill-out effects in plasmon excitations by fast electrons

Area of Science:

• Condensed Matter Physics
• Surface Science
• Computational Physics

Background:

• Understanding electron dynamics at interfaces is crucial for materials science.
• Existing models like the Specular Reflection Model (SRM) have limitations in describing diffuse interfaces.
• Electron density spill-out effects at metal surfaces require sophisticated theoretical treatment.

Purpose of the Study:

• To develop a non-retarded hydrodynamic approach for electron-metal-vacuum interface interactions.
• To investigate the energy loss spectrum (EELS) of fast electrons traversing such interfaces.
• To analyze the impact of interface diffuseness and electron density spill-out on surface plasmon dispersion.

Main Methods:

• A non-retarded hydrodynamic formalism using a dispersive bulk dielectric function.
• Self-consistent calculation of induced charge density.
• Application to electron energy loss spectroscopy (EELS) at metal-vacuum interfaces.
• Modeling electron density spill-out using Lang-Kohn density.

Main Results:

• Analytical expressions for loss probability equivalent to SRM for sharp interfaces.
• Demonstration of electron density spill-out effects on longitudinal and transverse momentum transfer.
• Observed significantly weaker surface plasmon dispersion compared to SRM predictions.
• Validation of findings with existing theoretical and experimental data.

Conclusions:

• The developed hydrodynamic approach provides a robust framework for studying electron-interface interactions.
• Interface profile and electron density spill-out are critical factors influencing surface plasmon behavior.
• The model offers potential for extending studies to more complex interfaces, such as transition metals and insulators.