Exact Coulomb cutoff technique for supercell calculations in two dimensions

TL;DR

This paper introduces a reciprocal space Coulomb cutoff method for two-dimensional systems, reducing computational effort and improving accuracy in supercell calculations by effectively screening spurious interactions.

Contribution

It extends a previous 3D Coulomb cutoff technique to 2D systems, enabling more accurate and efficient supercell calculations for reduced periodicity systems.

Findings

Significantly improves calculation accuracy for 2D systems.

Reduces computational effort in supercell simulations.

Effective screening of spurious interactions in reduced periodicity systems.

Abstract

We present a reciprocal space technique for the calculation of the Coulomb integral in two dimensions in systems with reduced periodicity, i.e., finite systems, or systems that are periodic only in one dimension. The technique consists in cutting off the long-range part of the interaction by modifying the expression for the Coulomb operator in reciprocal space. The physical result amounts in an effective screening of the spurious interactions originated by the presence of ghost periodic replicas of the system. This work extends a previous report [C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006)], where three-dimensional systems were considered. We show that the use of the cutoffs dramatically enhances the accuracy of the calculations for a given supercell size, and it allows to describe two-dimensional systems of reduced periodicity with substantially less computational effort. In particular, we consider semiconductor quantum-dot arrays having potential applications in quantum information technology.