(Color online) (a) Schemes of resonant and nonresonant photoemission channels of intermediate-state excitation observed in 2PPE for Cu(111): (A) resonant transition, (B) virtual-state transition, and (C) nonresonant indirect excitation. The shaded areas denote the bulk band projection along the direction for Cu(111). The solid curves inside the dashed box above the vacuum level EV reflect the measured 2PPE final-state kinetic energies. (b) A zoom-in of the dashed box [compare with Fig. 4(a) below]. (c) EDCs from Cu(111) with hν= 4.29 eV, which provides representative near-resonant and off-resonant conditions. Spectra are shown for k || = −0.18 Å−1 (squares), which corresponds to resonant-photoemission channel A yielding a single peak, and k || = 0 Å−1 (circles), which corresponds to nonresonant photoemission channels B and C yielding two peaks; note that the corresponding C channel shown in (b) is slightly displaced from k || = 0 to distinguish between processes B and C.
(a) Laser intensity dependence of the EDCs of the unresolved n = 0 and n = 1 peaks for near-normal emission from Cu(775) surface (at the photon energy used here, 4.51 eV, the excitation is nearly resonant and the two peaks cannot be fully resolved). The counts are normalized relative to the peak associated with the primary electrons. The down and up arrows indicate the positions of the peak at the lowest and highest intensities used, indicating an observed peak shift of 0.1 eV due to space-charge effects. Inset: Full 2PPE spectrum showing both secondary electrons at low kinetic energies and the primary electrons at kinetic energies near 4 eV. (b) Laser intensity dependence of the integrated (solid triangles) and peak (open triangles) electron counts vs laser intensity. The laser intensity units for (a) and (b) are given in relative units; the highest values of 35 can be roughly calibrated as giving a focused pulse energy of approximately 10 μJ/cm2.
(Color online) Normalized EDC data for (a) 4.66 eV and (b) for 5.02 eV photon energies from Cu(775). The band dispersion for the folded Cu surface state (dashed curves) and n = 1 and n = 2 image states (upper solid curve) are also indicated. An additional, weak intermediate state feature, which arises from transitions between bulk sp states near the L-point, is marked with a dotted curve.
(Color online) Angle-resolved 2PPE (a) from Cu(111) surface for an incident photon energy of 4.29 eV and (b) from Cu(775) for 4.48 eV. Two representative EDCs for (a) Cu(111) corresponding to k || = 0 and −0.18 Å−1 are presented in Fig. 1(c). The dotted curves represent the n = 0 surface-state band dispersion and the solid curves represent the n = 1 image-state band dispersion. The normalized photoemission signal intensity corresponding to the solid curves as a function of momentum is plotted in the lower portion of each figure. Insets: Corresponding calculated 2PPE signals using the measured effective masses.
(Color online) Angle-resolved 2PPE spectra for a series of incident photon energies indicated on the top of each panel on the Cu(775) surface chosen to illustrate the qualitative evolution of the resonances between the backfolded surface state and the n = 1 image state. The resonance points arethen extracted and plotted from more detailed data such as shown in Fig.6(b). The x-axis of each panel corresponds to emission angles in the range θ ∈ [−18°, 14°] as shown in the first panel.
(Color online) Band dispersion data for (a) Cu(111) and (b) Cu(775) using resonant band mapping. The top curves denote the n = 1 intermediate state, while the bottom curves denote the surface state (n = 0). The quadratic curves [(a) and top of (b)] are fits to the data. The fits yield n = 1 effective masses of m* = 1.17 ± 0.10 me and m* = 1.13 ± 0.20 me for the Cu(111) and Cu(775) surfaces, respectively. For Cu(111), m* = 0.40 ± 0.10 me for n = 0; for Cu(775), m* = 0.48 ± 0.30 me .
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