Comment on "Linear Scaling of the Exciton Binding Energy versus the Band Gap of Two-Dimensional Materials"

TL;DR

This paper challenges the universal linear relation between exciton binding energy and band gap in quasi-2D materials, showing deviations at small gaps and proposing a model that accounts for nonlocal screening effects.

Contribution

It demonstrates that the linear Eb vs. Eg relation breaks down at small band gaps and introduces a model incorporating nonlocal screening effects for accurate exciton description.

Findings

Linear relation holds at large band gaps.

Deviations occur at small band gaps (<0.3 eV).

Nonlocal screening effects are essential for small-gap materials.

Abstract

In a recent letter [J. -H. Choi et al. Phys. Rev. Lett. 115, 066403 (2015)], a universal linear relation between the binding energy Eb of exciton and the band gap Eg is found in different quasi-2D semiconductors. However, when one extrapolates the straight line to Eg=0, a positive Eb is obtained. This means that a stable exciton exists in a metal (Eg=0), or in other words, the excitation energy is negative. Therefore, for quasi-2D semiconductors with small band gap, Eb vs. Eg must deviate from the straight line suggested in the Letter. We performed similar GW+BSE calculation as the Letter for compressed phosphorene and stretched graphene. At larger band gap, our data fall in the same straight lien as the Letter. But for the quasi-2D semiconductors with small band gap, the Eb vs. Eg curve approaches to zero. A simple model based on local instantaneous screened interaction gives reasonable agreement with the more rigorous calculations. For the quasi-2D semiconductors with diminishing gap Eg<0.3eV, due to the nonlocal retarded effect induced by the strong screening in the small gap materials, one has to use 2-time transition amplitude (Bethe-Salpeter wave function) to describe exciton.