Band-Resolved Double Photoemission Spectroscopy on Correlated Valence Electron Pairs in Metals

Correlated valence electrons in Ag and Cu are investigated using double photoemission spectroscopy driven by a high-order harmonic light source. Electron pairs consisting of two $d$ electrons as well as pairs with one $sp$ and one $d$ electron are resolved in the two-dimensional energy spectrum. Surprisingly, the intensity ratio of $sp\text{−}d$ to $d\text{−}d$ pairs from Ag is 3 times higher than in the self-convoluted density of states. Our results directly show the band-resolved configurations of electron pairs in solids and emphasize a band-dependent picture for electron correlation even in these paradigmatic metals.

Figure 1

(a) Histogram of two-electron photoemission coincidence events (raw data) on Ag(001) at $h\nu =32.3\mathrm{eV}$. The setup is shown schematically in the inset. (b) Raw and scaled background (bg) $E_{\text{sum}}$ spectra.

Figure 2

(a) DPE data at $h\nu =32.3\mathrm{eV}$ on Ag(001). (b) $E_{\text{sum}}$ spectrum from (a) integrated over $E_{\text{diff}}=\pm 1\mathrm{eV}$. (c) The same as (b) for $h\nu =25.1\mathrm{eV}$. (d) DOS of Ag [13] with DPE processes. $E_V$ labels the vacuum level.

Figure 3

Comparison of DPE spectra with the self-convoluted DOS adapted from Powell (cDOS) [22]. The constituents of electron pairs are labeled near the upper scale. (a) DPE spectra of Ag(001) at $h\nu =32.3(25.1)\mathrm{eV}$ with empty (solid) symbols from Figs. 2 and 2. The threefold higher intensity of $sp\text{−}d$ pairs compared to cDOS is highlighted. (b) DPE spectrum of Cu(111) with $h\nu =32.3\mathrm{eV}$ integrated over all $E_{\text{diff}}$ for better statistics.

Figure 4

$E_{\text{diff}}$ spectra for (a) Ag(001) and (b) Cu(111) with empty (solid) symbols for $h\nu =32.3(25.1)\mathrm{eV}$. Each spectrum is integrated over $E_{B,\text{sum}}=\pm 2\mathrm{eV}$ for Ag and $\pm 1\mathrm{eV}$ for Cu centered at the indicated pair binding energy region in Figs. 2 and 3. The $d\text{−}d\text{−}{d}^{*}$ spectra are centered at $E_{B,\text{sum}}^{d\text{−}d\text{−}{d}^{*}}-2\mathrm{eV}$, and the Cu $sp\text{−}sp$ spectra at $E_{B,\text{sum}}$ around 1.4 eV. For comparison, the $sp\text{−}d$ pairs from Ag and the $d\text{−}d$ pairs from Cu at $h\nu =25.1\mathrm{eV}$ are scaled by a factor of 0.7.