Quantum Level Instability of Transverse Excitation in Electron Flow

Abstract

In current research, we use the effective Schrödinger-Poisson model to study a new kind of quantum-level instability in an infinite-wall slab electron flow. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the linear transverse collective excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular drift. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to mutual interactions between single electron oscillations, analogous to the problem of a particle in a box, and collective Langmuir oscillations, which are modulated over single electron quantum state. We also report the transverse excitation instability of plasmon energy level in electron slab flow due to the interplay between the wave-like dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability in terms of different aspects of the many-electron system. Such a quantum-level instability may have important applications in characteristic behavior of plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid may also have broad applications in nanoscale quantum device calibration and quantum measurements.