Nonequilibrium Band Mapping of Unoccupied Bulk States Below the Vacuum Level by Two-Photon Photoemission

We demonstrate two-photon photoemission (2PPE) to map a bulk unoccupied band, \textit{viz.} the Cu \textit{sp}-band 0 to 1 eV below the vacuum level, in the vicinity of the L point. This short-lived bulk band is seen due to the strong optical pump rate, and the observed transition energies and their dispersion with photon energy, are in excellent agreement with tight-binding band-structure calculations. A careful analysis of the 2PPE spectra permits unambiguous assignment of the transitions. The variation of the 2PPE final-state energy with photon energy has a measured slope of $\sim $1.64, in contrast with values 1 or 2 observed for 2PPE from two-dimensional states, i.e., image and surface states.