Density-functional approach to the band gaps of finite and periodic two-dimensional systems

TL;DR

This paper introduces a density-functional theory approach for accurately calculating the fundamental band gaps of finite and periodic 2D electronic systems, with computational efficiency comparable to standard methods.

Contribution

It develops a new orbital-dependent exchange potential model that improves gap predictions in 2D systems without increasing computational cost.

Findings

Accurate band gap calculations for 2D quantum dots.

Effective modeling of band structure tuning in artificial graphene.

Comparable computational cost to standard total energy calculations.

Abstract

We present an approach based on density-functional theory for the calculation of fundamental gaps of both finite and periodic two-dimensional (2D) electronic systems. The computational cost of our approach is comparable to that of total energy calculations performed via standard semi-local forms. We achieve this by replacing the 2D local density approximation with a more sophisticated -- yet computationally simple -- orbital-dependent modeling of the exchange potential within the procedure by Guandalini et al. [Phys. Rev. B 99, 125140 (2019)]. We showcase promising results for semiconductor 2D quantum dots and artificial graphene systems, where the band structure can be tuned through, e.g., Kekul\'e distortion.