Direct Determination of Lifetime and Energy Dispersion for the EmptyΔ1Conduction Band of Copper

Abstract

We present an accurate determination of the energy dispersion ($E$ vs $k$) and the first direct determination of the energy-dependent lifetime $\Gamma \mathrm{}\left(E\right)\mathrm{}$ of well-defined excited Bloch states in a crystal. Using angle-resolved photoemission for Cu(100), we find that the lifetime broadening increases from $\Gamma =1.2\mathrm{}$ eV (6 × ${10}^{-16\mathrm{}}$ sec) to 1.8 eV (4 × ${10}^{-16\mathrm{}}$ sec) for ${\Delta }_1$ conduction-band states ranging 10.5 to 13.5 eV above the Fermi level. The measured dispersion (∼2% accuracy) shows a reduced effective mass ($\frac{m^{*}}{m_0}=0.90-0.94\mathrm{}$) which is related to self-energy effects.