# Wavefunction of Plasmon Excitations with Space Charge Effects

## TL;DR

This paper derives an analytic wavefunction for plasmon excitations in a 1D electron gas influenced by various space charge distributions, revealing shielding effects and impurity impacts relevant to nanotechnology and plasmonics.

## Contribution

It provides a generalized closed-form analytic expression for the wavefunction of collective excitations considering arbitrary space charge distributions, extending prior models.

## Key findings

- Two parallel Dirac charge sheets shield interior plasmon excitations.
- Weak impurity layers disrupt the crystal's electrostatic periodicity.
- Analytic models applicable to nanotechnology and plasmonics development.

## Abstract

The one dimensional (1D) driven quantum coupled pseudoforce system governing the dynamics of collective Langmuir electron oscillations is used in order to investigate the effects of variety of space charge distributions on plasmon excitations of a nearly free electron gas with arbitrary degree of degeneracy and electron fluid temperature. A generalized closed form analytic expression for the grand wavefunction of collective excitations in presence of an arbitrary space charge distribution is presented based on the stationary solutions of the driven coupled pseudoforce system which has been derived from the Schr\"{o}dinger-Poisson model. The wavefunction and electrostatic potential profiles for some especial cases such as the Heaviside charge distribution, Dirac charge sheet, impurity charge sheet in 1D plasmonic lattice and the Kroning-Penney Dirac charge distributions with particular applications in plasmonics and condensed matter physics is investigated in this paper. It is remarkably found that two parallel Dirac charged sheets completely shield all interior plasmon excitations with any given energy value from outside electrostatic fields and charge densities. It is also found that the presence of even a weakly charged impurity layer within a perfect 1D plasmonic crystal profoundly destroys the periodic electrostatic field of the crystal lattice, hence, the Bloch character of the wavefunction considered in band gap theory of solids. Current investigation of electron excitations in arbitrary degenerate electron gas in the presence of static charge distributions may be used to develop analytic models for a variety of real physical situations. It also helps in further developments of the rapidly growing fields of nanotechnology and plasmonics.