Effect of ladder diagrams on optical absorption spectra in a quasiparticle self-consistent <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi mathvariant="italic">GW</mml:mi></mml:math> framework

Abstract

We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent $\mathit{GW}$ method [Phys. Rev. B 76, 165106 (2007)] for the electronic structure with the solution of the ladder approximation to the Bethe-Salpeter equation for the macroscopic dielectric function. The solution of the Bethe-Salpeter equation has been implemented within an all-electron framework, using a linear muffin-tin orbital basis set, with the contribution from the nonlocal self-energy to the transition dipole moments (in the optical limit) evaluated explicitly. This approach addresses those systems whose electronic structure is poorly described within the standard perturbative $\mathit{GW}$ approaches with density-functional theory calculations as a starting point. The merits of this approach have been exemplified by calculating optical absorption spectra of a strongly correlated transition metal oxide, NiO, and a narrow gap semiconductor, Ge. In both cases, the calculated spectrum is in good agreement with the experiment. It is also shown that for systems whose electronic structure is well-described within the standard perturbative $\mathit{GW}$, such as Si, LiF, and $h\text{\ensuremath{-}}\mathrm{BN}$, the performance of the present approach is in general comparable to the standard $\mathit{GW}$ plus Bethe-Salpeter equation. It is argued that both vertex corrections to the electronic screening and the electron-phonon interaction are responsible for the observed systematic overestimation of the fundamental band gap and spectrum onset.