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

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 semilocal 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., Kekulé distortion.