Title: Revealing the Coulomb interaction strength in a cuprate superconductor,
Abstract: We study optimally doped
Bi$_{2}$Sr$_{2}$Ca$_{0.92}$Y$_{0.08}$Cu$_{2}$O$_{8+\delta}$ (Bi2212) using
angle-resolved two-photon photoemission spectroscopy. Three spectral features
are resolved near 1.5, 2.7, and 3.6 eV above the Fermi level. By tuning the
photon energy, we determine that the 2.7-eV feature arises predominantly from
unoccupied states. The 1.5- and 3.6-eV features reflect unoccupied states whose
spectral intensities are strongly modulated by the corresponding occupied
states. These unoccupied states are consistent with the prediction from a
cluster perturbation theory based on the single-band Hubbard model. Through
this comparison, a Coulomb interaction strength U of 2.7 eV is extracted. Our
study complements equilibrium photoemission spectroscopy and provides a direct
spectroscopic measurement of the unoccupied states in cuprates. The determined
Coulomb U indicates that the charge-transfer gap of optimally doped Bi2212 is
1.1 eV.