Spectral properties of quasiparticles in silicon: A test of many-body theory

The spectral function $A(\mathit{q},\omega )$ of silicon has been measured along a number of symmetry directions using high-energy high-resolution electron momentum spectroscopy. It is compared with first-principles calculations based on the interacting one-electron Green’s function which is evaluated in the $\mathrm{GW}$ and the cumulant expansion approximations. Positions of the quasiparticle peaks (dispersion), their widths (lifetimes), and the extensive satellite structures are measured over a broad range of energies and momenta. The band dispersions are well described by both calculations, but the satellite predicted by the $\mathrm{GW}$ calculation is not observed. Unlike the $\mathrm{GW}$ calculation, the cumulant expansion calculation gives a significantly better description of the shape and momentum dependence of the satellite structure, presenting a promising approach for studying high-energy excitations.