Origin of photoemission final-state effects in Bi 2 Sr 2 CaCu 2 O 8 by very-low-energy electron diffraction

Very-low-energy electron diffraction with a support of full-potential band calculations is used to achieve the energy positions, dispersions, lifetimes, and Fourier compositions of the photoemission final states in ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8}$ at excitation energies below 45 eV. We find (1) highly structured final states that explain the dramatic photon energy dependences in photoemission; (2) a photoelectron lifetime decrease above 30 eV, resulting in increased damping of these dependences; (3) an intense $c(2\ifmmode\times\else\texttimes\fi{}2)$ diffraction below 25 eV, which reveals a significant extrinsic contribution to the shadow Fermi surface due to final-state diffraction. In a perspective, the experimental final states can be utilized to tune the photoemission experiment on specific valence states or Fermi surface replicas.