Trapping of Image-Potential Resonances on a Free-Electron-like Surface

Image-potential states have been studied by two-photon photoemission for the surface of Al(100) where the whole series is energetically degenerate with free-electron-like bulk states. In contrast with expectations, the series of resonances is not smeared out to one broad structure as a result of a strong coupling to the bulk continuum. Instead, the first resonance ($n=1$) is found to be suppressed, and the resonances with quantum numbers $n=2,3,4,5$ are resolved as individual peaks in the time-resolved spectra. Both effects are suggested to be a consequence of resonance trapping.

Figure 1

(a) Schematic drawing of the electronic structure of Al(100) and the 2PPE excitation scheme. Grey shaded areas denote projected bulk bands [30], parabolic lines the Shockley surface state (SS) and the first two image-potential resonances ($n=1$, $n=2$). (b),(c) 2PPE spectra recorded with different delay times between the UV excitation and the IR probe pulses. Lorentzian lines and arrows indicate the contributions of individual resonances to the total spectra. As distinct from the resonances, the feature marked (*) is excited by IR and probed by UV pulses. The energy scale in (b) is not applicable to this 2PPE process. The feature (*) originates from an intermediate state 0.9 eV above the Fermi level (see text).

Figure 2

Energy positions of image-potential resonances as functions of quantum numbers $n$. The experimental values (filled circles) were determined by fitting Lorentzian line shapes to several 2PPE spectra (5–13 for each $n$). The error bars indicate the uncertainties of determining these peak positions relative to each other and do not include a possible overall shift of the energy scale by $\pm 50\mathrm{meV}$ from the error of the sample work function.

Figure 3

Density of states calculated for a discrete Rydberg series $-0.85\mathrm{eV}/n^2$ coupled to an unstructured continuum. The coupling strength is indicated in terms of the width ${\Gamma }_1$ of the $(n=1)$ resonance (see text). It increases in steps of 0.05 eV from top to bottom.

Figure 4

2PPE intensity from Al(100) as a function of delay time between UV pump and IR probe pulses corresponding to different intermediate state energies (filled circles) and results of corresponding density matrix simulations for different coupling strength (lines). The data have been normalized for equal maximum intensity and offset for clarity.