Density functional calculations of atomic structure, charging effect, and static dielectric constant of two-dimensional systems based on B-splines

Abstract

We have implemented a total-energy minimization scheme to allow for relaxation of atomic positions in density functional calculations for two-dimensional (2D) materials using a mixed basis set. The basis functions consist of products of 2D plane waves in the plane of the material and localized B-splines along the perpendicular direction. By using the mixed basis approach (MBA), we have studied the atomic relaxation and charge polarization of 2D systems under an applied electric field. In contrast to the conventional super-cell approach (SCA) which adopts repeated slabs sandwiched between vacuum regions, MBA makes no requirement of compensating background charge for treating electrically charged 2D systems due to carrier injection. With MBA we can avoid using a periodic sawtooth potential for systems under the applied field as commonly adopted in SCA. Furthermore, we introduced a simple method to determine the out-of-plane dielectric constants of 2D materials without the ambiguity of defining their effective thickness. This is achieved by calculating the linear response in charge polarization to the applied field. Selected 2D systems, including graphene and transition-metal dichalcogenides are tested. Our MBA results are consistent with previous SCA calculations when both approaches are equally applicable. However, for charged systems with high carrier density, we find significant deviation from SCA results obtained by imposing artificial charge neutrality condition.