Direct time-domain observation of attosecond final-state lifetimes in photoemission from solids

Abstract

Attosecond spectroscopic techniques have made it possible to measure differences in transport times for photoelectrons from localized core levels and delocalized valence bands in solids. We report the application of attosecond pulse trains to directly and unambiguously measure the difference in lifetimes between photoelectrons born into free electron-like states and those excited into unoccupied excited states in the band structure of nickel (111). An enormous increase in lifetime of 212 ± 30 attoseconds occurs when the final state coincides with a short-lived excited state. Moreover, a strong dependence of this lifetime on emission angle is directly related to the final-state band dispersion as a function of electron transverse momentum. This finding underscores the importance of the material band structure in determining photoelectron lifetimes and corresponding electron escape depths.

Fig. 1.. Photoemission time delay on and off a resonance in the band structure.

(A) Using high-order harmonics, different photoelectron final states can be accessed, corresponding to free electron–like states or excited states in the band structure. The damping length of the final-state wave function inside the crystal is increased when the transition coincides with a final-state resonance. (B) Static ARPES excited by s-polarized HHG. The energy resolution is ~0.3 eV, which is sufficient to distinguish photoemissions from two initial bands (${\Lambda }_3^{\alpha }$ and ${\Lambda }_3^{\beta }$). (C) Photoemission time delays from laser-dressed harmonic sidebands for s- and p-polarized HHG for noble gas targets. A notable delay is introduced at sideband SB16, attributable to the >200-as lifetime of the excited state in the material band structure.

Fig. 2.. Final-state resonance in photoemission from Ni(111).

(A) EDC curves excited by s- (red) and p-polarized (blue) HHG in a normal emission geometry (integrated ~ ±2° around the Γ point). The position of the Fermi level (black dashed line) is determined from the laser photon energy (~1.6 eV) and analyzer work function (4.25 eV). The orange dashed line shows the shift of the high-energy peak with HHG photon energy, emphasizing the contribution of bulk band transitions. The intensity of the ${\Lambda }_3^{\beta }$ band clearly shows a spectral resonance at ~24 eV. (B) Band structure along the Γ-L direction (normal to the surface) extracted from our data (open symbols) compared with results of previous experiments (30) (solid lines) and DFT calculations (dashed lines). A free-electron final state in a constant inner potential (30) is assumed and is used to map the electron momentum normal to the sample surface k_⊥. The final-state resonance observed in (A) corresponds to a direct transition from the ${\Lambda }_3^{\beta }$ initial band to the ${\Lambda }_1^{\mathrm{B}}$ final band, as highlighted by the blue arrow.

Fig. 3.. Direct time-domain measurement of the final-state lifetime.

(A) Photoemission time delays ${\tau }_{\text{PE}}({\Lambda }_3^{\beta })-{\tau }_{\text{PE}}({\Lambda }_3^{\alpha })$ and ${\tau }_{\text{PE}}({\Lambda }_1)-{\tau }_{\text{PE}}({\Lambda }_3^{\alpha })$ as a function of photon energy, clearly showing an increase in lifetime (by 212 ± 30 as) when the final state corresponds to a short-lived excited state in the band structure. Error bars represent SD of time delays extracted from more than 200 individual scans. The red solid line is a Lorentzian curve with the same linewidth as in (B). (B) Spectral intensity of the ${\Lambda }_3^{\beta }$ initial band as a function of photon energy. The blue point (14th order) is obtained from HHG driven by 390-nm laser field. Error bars represent the fitting uncertainties of the photoelectron yield from individual photoelectron spectra that were used to extract each point (see supplementary materials). The pink line represents a Lorentzian fit, yielding a linewidth of γ = 3.68 eV. (C) Two-dimensional map of photoelectron yields as a function of photoelectron energy and pump-probe time delay τ_d, excited by s-polarized HHG. To enhance the color contrast, 90% of the ground-state spectrum is subtracted to visualize the interferogram. The relative delays between photoelectrons from the ${\Lambda }_3^{\alpha }$ and ${\Lambda }_3^{\beta }$ initial bands are manifested as a large offset in oscillations in the sidebands (white dashed boxes). A zoom-in view in both energy and time delay at the resonant energy is plotted in fig. S5D. Right panel: 1D lineouts for ${\Lambda }_3^{\alpha }$ and ${\Lambda }_3^{\beta }$ initial bands in the corresponding regions. (D) Results of 1D semiclassical simulations. Relative to photoelectrons emitted from 2 Å below the surface, those emitted from 10 Å below the surface are delayed by 267 as. Inset: Profile of the dressing field strength normal to the surface (E_z) across the interface.

Fig. 4.. Angle-dependent photoemission time delays.

(A) Angle-dependent photoemission time delay ${\tau }_{\text{PE}}({\Lambda }_3^{\beta },\theta )-{\tau }_{\text{PE}}({\Lambda }_3^{\alpha },\theta )$ for SB16 and SB14 obtained using s-polarized HHG. The experimental data are points; the solid lines are a fit to the final-state band structure obtained from our model and DFT calculations (see supplementary materials). Error bars represent SD of the time delays extracted from more than 200 individual scans. (B) Typical RABBITT interferograms for SB16 with emission angles [(a) and (b)] labeled in (A). The offset in oscillations is highlighted with white dashed boxes. (C) Illustration of direct transitions in the $\overline{\Gamma }-\overline{\mathsf{K}}$ direction for SB14 and SB16. Because different photon energies are used for these two sidebands, different k_⊥ along the Γ-L direction are assigned according to the band-mapping results in Fig. 2B. The initial and final bands are highlighted by thick solid lines; the binding energy of the initial band (purple) is corrected according to the binding energy obtained in our experiments. Transitions corresponding to sideband photon energies are labeled as dashed arrows. Inset: Experimental geometry. IR and HHG beams are focused onto a Ni(111) surface at a 45° incident angle; θ is assigned to the emission angle of photoelectrons relative to the sample normal direction (z) along the $\overline{\Gamma }-\overline{\mathsf{K}}$ direction.