Efficient scheme for GW quasiparticle band-structure calculations with applications to bulk Si and to the Si(001)-(2×1) surface

Abstract

We report an efficient scheme for evaluating the quasiparticle corrections to local-density-approximation (LDA) band structures within the GW approximation. In this scheme, the GW self-energy corrections are evaluated in a sufficiently flexible Gaussian orbital basis set instead of using plane-wave Fourier representations of the relevant two-point functions. It turns out that this set has to include orbitals up to f-type symmetry, when in the LDA calculations Gaussian orbitals up to d-type symmetry are needed for convergence. For bulk Si, both schemes yield virtually identical quasiparticle band structures and the demand on computer time is roughly the same. For the Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) surface, the GW Gaussian orbital scheme is a factor of 5 faster. In our calculations for Si(001)-(2\ifmmode\times\else\texttimes\fi{}1) the dynamic dielectric matrix is obtained by applying a plasmon-pole approximation. The static dielectric matrix of the Si(001) surface is fully calculated within the random phase approximation (RPA). In addition, we have performed quasiparticle surface band-structure calculations employing two model dielectric matrices. Our respective results are compared with those obtained employing the full RPA dielectric matrix as well as with results of previous calculations by other authors which were based on model dielectric matrices.