Stable plasmon excitations in quantum nanowires

Abstract

Stable electrostatic plasmon excitations due to propagation of Gaussian electron pulses are studied in a cylindrical nanowire of radius “a” and length “L”. For this purpose, we consider conduction electrons that follow the quantum hydrodynamical model to account for quantum statistics, quantum diffraction, and exchange-correlation effects in the presence of classical static ions. The use of the well-known Fourier transform technique and the Trivelpiece-Gould configuration leads to the generalized dispersion for plasmons with finite mode quantization effects via the radial and azimuthal mode indices, as well with quantum settings. The excitations of plasmon wakefield appear when the electron beam propagates with a constant velocity along the axial direction of nanowires. The stability conditions are also analyzed for the existence of wakefield excitations by solving three important inequalities using typical parameters of gold nanowires. The results may prove useful for understanding the plasmon excitations in quantum nanowires, where electrons can be trapped and accelerated in the wakefield to emit radiation in the extreme-ultraviolet range.