Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces

Abstract

We present an implementation of the linear density response function within the projectoraugmented wave (PAW) method with applications to the linear optical and dielectric properties of both solids, surfaces, and interfaces. The response function is represented in plane waves while the single-particle eigenstates can be expanded on a real space grid or in atomic orbital basis for increased efficiency. The exchange-correlation kernel is treated at the level of the adiabatic local density approximation (ALDA) and crystal local field effects are included. The calculated static and dynamical dielectric functions of Si, C, SiC, AlP and GaAs compare well with previous calculations. While optical properties of semiconductors, in particular excitonic effects, are generally not well described by ALDA, we obtain excellent agreement with experiments for the surface loss function of graphene and the Mg(0001) surface with plasmon energies deviating by less than 0.2 eV. Finally, the method is applied to study the influence of substrates on the plasmon excitations in graphene.

Optical properties of bulk semiconductors and graphene/boron nitride: The Bethe-Salpeter equation with derivative discontinuity-corrected density functional energies

“…The overestimation is enhanced by inclusion of the ALDA kernel (the second row for each semiconductor), in agreement with previous studies. 30 The GLLBSC without the discontinuity increase the band gaps relative to the LDA and consequently reduces the dielectric function toward the experimental value. The inclusion of the discontinuity further opens up the gap and the corresponding dielectric constants (third column) systematically underestimate the experimental values.…”

“…The quantity n nk,n k+q (G) ≡ ψ nk |e −i(q+G)·r |ψ n k+q (5) is referred to as the charge density matrix. 30 In the long wavelength limit, that is, for q → 0, and for n = n , application of the k · p perturbation theory 35 yields the important identity…”

“…A detailed description of the evaluation of the charge density matrix and the ALDA xc kernel within the PAW formalism can be found in Ref. 30.…”

“…The use of k-point symmetry for obtaining the wave functions at k points outside the irreducible Brillouin zone has been described in a previous paper. 30 In the following we describe how symmetry considerations can be used to reduce the q-point sum.…”

“…Considering both bulk and low-dimensional systems we find that the accuracy of the GLLBSC-BSE approach is comparable to the GW-BSE approach. All the methods are implemented in the GPAW code, [28][29][30] an electronic structure package based on the projector augmented wave methodology. 31,32 For the bulk systems Si, C, InP, MgO, GaAs, and LiF, we find that the fundamental gaps and static dielectric constants calculated with GLLBSC compare well with experimental data.…”