Electronic structure effects in spatiotemporally resolved photoemission interferograms of copper surfaces

Attosecond photoelectron spectroscopy allows the observation of electronic processes on attosecond time scales ($1\text{as}={10}^{-18}$ s), as has been demonstrated in proof-of-principle experiments that probe the electronic dynamics in isolated atoms with unprecedented accuracy. Its recent expansion to solid targets is starting to allow the distinction of ultrafast collective electronic processes in matter with added spatial resolution, probing the electronic band structure and dielectric response in nanoplasmonically enhanced light-induced processes of relevance for photocatalysis, optoelectronics, and light harvesting. Based on a quantum-mechanical model for photoelectron emission by an attosecond pulse train from the $d$ band of a Cu(111) surface into a delayed assisting laser pulse, we calculate two-pathway two-photon interferograms as functions of the photoelectron energy and pulse delay. Our results scrutinize the dependence of observable photoelectron interferograms on the electronic structure of and electron transport in the substrate and agree well with experimental spectra and semiclassical Monte Carlo simulations of Lucchini et al. [Phys. Rev. Lett. 115, 137401 (2015)].

Figure 1

(a) RABBITT experimental setup of Lucchini et al. [11]. Linearly $p$ polarized XUV APTs and time-delayed IR pulses are incident at ${75}^{\circ }$ on a Cu(111) surface, while photoelectrons emitted in the reflection plane are detected under $-{30}^{\circ }$ with respect to the surface normal. (b) Same as in panel (a) for ${15}^{\circ }$ pulse incidence and ${30}^{\circ }$ electron detection.

Figure 2

RABBITT interferograms for [(a), (b)] ${75}^{\circ }$ and [(c), (d)] ${15}^{\circ }$ incidence, normalized separately. [(a), (c)] Experiment [11]. [(b), (d)] Theory.

Figure 3

(a) Measured [11] and calculated oscillations in the photoelectron yields integrated over 0.3-eV intervals around ${\mathrm{HH}}_{19}$ and ${\mathrm{SB}}_{20}$ energies for ${75}^{\circ }$ incidence. (b) Fourier transform of panel (a) with frequencies in units of ${\omega }_{IR}$. [(c), (d)] Same as panels (a) and (b) for ${15}^{\circ }$ incidence.

Figure 4

Interfering photoemission pathways leading to $4{\omega }_{IR}$ oscillations in the HH yields in Fig. 3. (a) Two two-IR-photon transitions. [(b), (c)] Zero-IR-photon and a four-IR-photon transitions.

Figure 5

Parameter dependence of delay-integrated yields as functions of the photon energy for single-parameter variations from the best experiment-matching set: $\lambda \left({\varepsilon }_f\right)$ from Ref. [23], $U_0=17.035$ eV, ${\delta }_{IR}=2.25a_s$, and $E_{TB}=E_b=-7.74$ eV. Sensitivity to changes in (a) $\lambda \left({\varepsilon }_f\right)$, (b) $U_0$, (c) ${\delta }_{IR}$, and (d) $E_{TB}$. Experimental yield adapted from Ref. [11].

Figure 6

RABBITT phases ${\varphi }_{2n}^{RAB}$ extracted from our calculated spectra in Fig. 2 in comparison with the experimental and simulated (MC) results from Ref. [11].