# Theory of Plasmons for Two-Dimensional Materials in the Random Phase Approximation

## Abstract

**:**

## 1. Introduction

## 2. Theory of Two-Dimensional Plasmons

#### 2.1. Derivation of 2D Plasmon Theory from the 3D One

#### 2.2. Planar and Edge Plasmons

#### 2.2.1. Planar Plasmon

#### 2.2.2. Edge Plasmon

#### 2.3. Light Emission from Edge Plasmon in Nanodisk

#### 2.4. Plasmons in Uniform 2D and 3D Weyl Fermions

_{2}Ir

_{2}O

_{7}, satisfy the following 3D Weyl equation [24]:

## 3. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

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Dimension | Bulk/Planar | Surface/Edge | |
---|---|---|---|

Schrödinger | 3D | ${\left({n}_{3D}\right)}^{1/2}$ | ${\left({n}_{3D}\right)}^{1/2}$ |

fermion | 2D | ${\left({n}_{2D}\right)}^{1/2}\sqrt{k}$ | ${\left({n}_{2D}\right)}^{1/2}/\sqrt{a}$ |

Weyl | 3D | ${\left({n}_{3D}\right)}^{1/3}$ | ${\left({n}_{3D}\right)}^{1/3}$ |

fermion | 2D | ${\left({n}_{2D}\right)}^{1/4}\sqrt{k}$ [23] | ${\left({n}_{2D}\right)}^{1/4}/\sqrt{a}$ [9] |

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Ichikawa, M.
Theory of Plasmons for Two-Dimensional Materials in the Random Phase Approximation. *Condens. Matter* **2016**, *1*, 9.
https://doi.org/10.3390/condmat1010009

**AMA Style**

Ichikawa M.
Theory of Plasmons for Two-Dimensional Materials in the Random Phase Approximation. *Condensed Matter*. 2016; 1(1):9.
https://doi.org/10.3390/condmat1010009

**Chicago/Turabian Style**

Ichikawa, Masakazu.
2016. "Theory of Plasmons for Two-Dimensional Materials in the Random Phase Approximation" *Condensed Matter* 1, no. 1: 9.
https://doi.org/10.3390/condmat1010009