Theory of quasiparticle energies: Band gaps and excitation spectra in solids

Abstract

A first-principles theory for the band gaps and electronic excitation energies in crystals is described. Optical and photoemission spectra are properly interpreted as transitions between quasiparticle states of the many-electron system. The theory requires adequate treatment of the Coulomb interaction between the electrons, including exchange and dynamical correlation effects. The nonlocal energy-dependent electron self-energy operator is evaluated from first principles using the full dielectric matrix and the dressed Green's function. Quasiparticle energies for materials covering a wide range of metallicity and ionicity are presented. With no empirical input, the calculated band gaps, optical transition energies, and band dispersions are all within a few percent of experimental values. For semiconductors and insulators, we find that local field effects in the screening of the Coulomb interaction and dynamical renormalization are both crucial for accurate results. The present method also extends beyond the case of bulk crystals, e.g., to surfaces. Results on the surface state energies of the Ge (111): As and S(111):As surface are discussed and compared with experiment.