Anisotropic Stark shift, field-induced dissociation, and electroabsorption of excitons in phosphorene

TL;DR

This study investigates how excitons in phosphorene respond to electric fields, revealing strong directional dependence in Stark shifts, dissociation, and polarizability, with analytical models confirming the anisotropic effects.

Contribution

It provides the first analytical approximation for anisotropic electric-field-induced dissociation rates in phosphorene, extending previous isotropic models.

Findings

Dissociation rates decrease significantly when rotating the electric field from armchair to zigzag directions.

Large anisotropy observed in exciton polarizability tensor components.

Isotropic interaction potential approximates anisotropic potential well, attributing anisotropy mainly to effective mass direction dependence.

Abstract

We compute binding energies, Stark shifts, electric-field-induced dissociation rates, and the Franz-Keldysh effect for excitons in phosphorene in various dielectric surroundings. All three effects show a pronounced dependence on the direction of the in-plane electric field, with the dissociation rates in particular decreasing by several orders of magnitude upon rotating the electric field from the armchair to the zigzag axis. To better understand the numerical dissociation rates, we derive an analytical approximation to the anisotropic rates induced by weak electric fields, thereby generalizing the previously obtained result for isotropic two-dimensional semiconductors. This approximation is shown to be valid in the weak-field limit by comparing it to the exact rates. The anisotropy is also apparent in the large difference between armchair and zigzag components of the exciton polarizability tensor, which we compute for the five lowest lying states. As expected, we also find much more pronounced Stark shifts in either the armchair or zigzag direction, depending on the symmetry of the state in question. Finally, an isotropic interaction potential is shown to be an excellent approximation to a more accurate anisotropic interaction derived from the Poisson equation, confirming that the anisotropy of phosphorene is largely due to the direction dependence of the effective masses.