# Anisotropic plasmons, excitons and electron energy loss spectroscopy of phosphorene

## TL;DR

This study investigates the anisotropic electron energy loss spectrum of monolayer phosphorene using ab-initio calculations, revealing anisotropic excitonic and plasmon peaks, and how doping affects intraband plasmon behavior.

## Contribution

It provides a detailed theoretical analysis of anisotropic plasmons and excitons in phosphorene, including the effects of doping and effective mass ratios, using advanced ab-initio methods.

## Key findings

- Anisotropic excitonic peaks near the bandgap in phosphorene.
- Doping introduces intraband plasmon peaks within the bandgap.
- Intraband plasmon dispersion follows a sqrt(q) behavior with anisotropic characteristics.

## Abstract

In this article, we explore the anisotropic electron energy loss spectrum (EELS) in monolayer phosphorene based on ab-initio time dependent density functional theory calculations. Similar to black phosphorous, the EELS of undoped monolayer phosphorene is characterized by anisotropic excitonic peaks for energies in vicinity of the bandgap, and by interband plasmon peaks for higher energies. On doping, an additional intraband plasmon peak also appears for energies within the bandgap. Similar to other two dimensional systems, the intraband plasmon peak disperses as $\omega_{\rm pl} \propto \sqrt{q}$ in both the zigzag and armchair directions in the long wavelength limit, and deviates for larger wavevectors. The anisotropy of the long wavelength plasmon intraband dispersion is found to be inversely proportional to the square root of the ratio of the effective masses: $\omega_{\rm pl}(q \hat{y})/\omega_{\rm pl}(q \hat{x}) = \sqrt{m_x/m_y}$.