Energy Band Structure of Multistream Quantum Electron System

TL;DR

This paper develops a quantum multistream model to analyze the electronic band structure of plasmonic excitations in streaming electron gases, revealing energy gaps due to mode coupling and collective interactions.

Contribution

It introduces a novel quantum multistream approach to calculate energy band structures in plasmonic systems, including effects of virtual streams and electron-lattice interactions.

Findings

Energy bands separated by gaps due to velocity filaments and mode coupling.

Band gap size maximizes at the first Brillouin zone boundary near metallic densities.

Energy band structure is a universal feature of coupled quantum multistream systems.

Abstract

In this paper, using the quantum multistream model, we develop a method to study the electronic band structure of plasmonic excitations in streaming electron gas with arbitrary degree of degeneracy. The multifluid quantum hydrodynamic model is used to obtain $N$-coupled pseudoforce differential equation system from which the energy band structure of plasmonic excitations is calculated. It is shown that inevitable appearance of energy bands separated by gaps can be due to discrete velocity filaments and their electrostatic mode coupling in the electron gas. Current model also provides an alternative description of collisionless damping and phase mixing, i.e., collective scattering phenomenon within the energy band gaps due to mode coupling between wave-like and particle-like oscillations. The quantum multistream model is further generalized to include virtual streams which is used to calculate the electronic band structure of one-dimensional plasmonic crystals. It is remarked that, unlike the empty lattice approximation in free electron model, energy band gaps exist in plasmon excitations due to the collective electrostatic interactions between electrons. It is also shown that the plasmonic band gap size at first Brillouin zone boundary maximizes at the reciprocal lattice vector, $G$, close to metallic densities. Furthermore, the electron-lattice binding and electron-phonon coupling strength effects on the electronic band structure are discussed. It is remarked that inevitable formation of energy band structure is a general characteristics of various electromagnetically and gravitationally coupled quantum multistream systems.