Band structure and excitonic properties of WSe2 in the isolated monolayer limit in an all-electron approach

We present a study of the electronic band structure and optical absorption spectrum of monolayer ${\mathrm{WSe}}_{2}$ using an all-electron quasiparticle self-consistent $GW$ approach, $\mathrm{QS}G\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{W}$, in which the screened Coulomb interaction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{W}$ is calculated including ladder diagrams representing the electron-hole interaction. The Bethe-Salpeter equation is used to calculate both the screened Coulomb interaction $\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{W}$ in the quasiparticle band structure and the imaginary part of the macroscopic dielectric function. The convergence of the quasiparticle band gap and lowest exciton peak position is studied as a function of the separation of the monolayers when using periodic boundary conditions. The quasiparticle gap is found to vary as $1/d$ with $d$ the size of the vacuum separation, while the lowest excitonic peak reaches convergence much faster. The nature of the exciton spectrum is analyzed and shows several peaks below the quasiparticle gap when a sufficient number of $\mathbf{k}$ points is used. The results are found to be in good agreement with previous theoretical and experimental studies after adding spin-orbit coupling corrections and can be explained in the context of the Wannier-Mott theory adapted to two dimensions.