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

We present an implementation of the linear density response function within the projector-augmented 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 the Mg(0001) surface with plasmon energies deviating by less than 0.2 eV. Finally, we apply the method to study the influence of substrates on the plasmon excitations in graphene. On SiC(0001), the long wavelength $π$ plasmons are significantly damped although their energies remain almost unaltered. On Al(111) the $π$ plasmon is completely quenched due to the coupling to the metal surface plasmon.