Single-particle excitation of core states in epitaxial silicene

Recent studies of core-level x-ray photoelectron spectroscopy (XPS) spectra of silicene on ZrB2(0001) were found to be inconsistent with the density of states (DOS) of a planar-like structure that has been proposed as the ground state by density functional theory (DFT). To resolve the discrepancy, a reexamination of the XPS spectra and direct theoretical access of accurate single-particle excitation energies are desired. By analyzing the XPS data using symmetric Voigt functions, different binding energies and their sequence of Si 2p orbitals can be assigned from previously reported ones where asymmetric pseudo-Voigt functions are adopted. Theoretically, we have adopted an approach developed very recently, which follows the sophisticated Delta self-consistent field (Delta SCF) methods, to study the single-particle excitation of core states. In the calculations, each single-particle energy and the renormalized core-hole charge density are calculated straightforwardly via two SCF calculations. By comparing the results, the theoretical core-level absolute binding energies including the splitting due to spin-orbit coupling are in good agreement with the observed high-resolution XPS spectra. The good agreement not only resolves the puzzling discrepancy between experiment and theory (DOS) but also advocates the success of DFT in describing many-body interactions of electrons at the surface.