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Comparison of GW band structure to semi-empirical approach for an FeSe monolayer

We present the G$_0$W$_0$ band structure, core levels, and deformation potential of monolayer FeSe in the paramagnetic phase based on a starting mean field of the Kohn Sham density functional theory (DFT) with the PBE functional. We find the GW correction increases the bandwidth of the states forming the $M$ pocket near the Fermi energy, while leaving the $Γ$ pocket roughly unchanged. We then compare the G$_0$W$_0$ quasiparticle band energies with the band structure from a simple empirical +A approach, which was recently proposed to capture the renormalization of the electron-phonon interaction going beyond DFT in FeSe, when used as a starting point in density functional perturbation theory (DFPT). We show that this empirical correction succeeds in approximating the GW non-local and dynamical self energy in monolayer FeSe and reproduces the GW band structure near the Fermi surface, the core energy levels, and the deformation potential (electron-phonon coupling).