Effective mass theory for the anisotropic exciton in 2D crystals: Application to phosphorene

TL;DR

This paper develops an analytical model for the anisotropic exciton in 2D materials, specifically applied to phosphorene, providing results that closely match numerical calculations and experimental data.

Contribution

It introduces a new analytical approach for calculating exciton binding energies in anisotropic 2D crystals, validated against numerical solutions and applied to phosphorene.

Findings

Analytical expressions closely match numerical solutions.

Results agree with recent experimental measurements.

Method effectively captures anisotropic screening effects.

Abstract

We present a theoretical study of the exciton binding energy for anisotropic two-dimensional crystals. We obtain analytical expressions from variational wave functions in different limits of the screening length to exciton size ratio and compare them with numerical solutions, both variational and exact. As an example, we apply these results to phosphorene, a monolayer of black phosphorous. Aided by density functional theory calculations for the evaluation of the two-dimensional polarizability, our analytical solution for the exciton binding energy gives a result which is very close to the numerical ones and, in turn, is comparable to the experimental value, as recently reported.