ExperimentalE(k→)dispersions for the Zn3dstates: Evidence for itinerant character

Abstract

Using angle-resolved photoemission from Zn (0001) we observe that the Zn $3d$ states exhibit energy-band dispersion (0.17 eV from ${\Gamma }_6^{+}$ to ${\Gamma }_5^{-}$ for the upper $d$ band) and $k$-dependent polarization selection rules. The $d$ bands are centered at 10 eV below the Fermi energy $E_F$ and are 1.0 eV wide (${\Gamma }_4^{-}$ to ${\Gamma }_5^{-}$). In contrast, ab initio band calculations using a Hedin-Lundqvist potential yield $d$ bands centered at ∼8.3 eV below $E_F$ that are 1.5 eV wide and disperse by 0.33 eV, thus indicating the significance of self-energy corrections for these deep-lying narrow bands. Upon empirically correcting the $d$-band position by adjusting the exchange parameter $\alpha$ in a nonrelativistic $X\alpha$ calculation, the calculated bandwidth (1.0 eV) and dispersion are also in agreement with experiment. Experimental critical points are (energies relative to $E_F$): ${\Gamma }_5^{-}=-9.60\mathrm{}$ eV, ${\Gamma }_6^{+}=-9.77\mathrm{}$ eV, ${\Gamma }_6^{-}=-10.05\mathrm{}$ eV, - 10.30 eV, ${\Gamma }_5^{+}=-10.05\mathrm{}$ eV, - 10.31 eV, ${\Gamma }_4^{-}=-10.62\mathrm{}$ eV. The observed initial-state lifetime broadening (full width of half maximum) is 0.3 eV at the top of the $d$ bands and 0.5 eV at the bottom of the $d$ bands.