Multiphoton $k$-resolved photoemission from gold surface states with 800-nm femtosecond laser pulses

We measure direct multiphoton photoemission of the Au(111) surface state with 800-nm laser pulses. We observe the parabolic dispersion in the angular distribution of photoelectrons having absorbed between four and seven photons. The ${\mathbf{k}}_{\parallel }$ dispersion we measure can be explained in terms of Shockley-state replicas, with a nascent hot electrons distribution at ${\mathbf{k}}_{\parallel }$ above the Fermi level. Moderate laser power densities, of the order of $100\mathrm{GW}/\mathrm{cm}{}^2$, resulted in large electron yields, indicating the importance of multiphoton excitations to define the electronic and magnetic properties of matter in the first hundred femtoseconds after laser excitation.

Figure 1

Left: Angular resolved photoelectron spectroscopy of the Au(111) surface state measured around normal emission with 60 eV synchrotron radiation (top) and 800-nm femtosecond laser pulses (bottom). Dotted lines represent the parabolic angular dispersion of the Rashba split surface states with $m^{*}=0.26m_e$ and the relative final-state energy. Final-state energies corresponding to the absorption of four, five, six, and seven 800-nm photons from the Fermi level are shown by the horizontal ticks on the right axis. Right: Schematic processes for multiphoton absorption from the surface state (solid line) of Au(111). The shaded area represents surface-projected bulk states.

Figure 2

Primary photoemission intensity obtained experimentally within $1^{\circ }$ of the $\Gamma$ direction (open circles), after subtracting the background. The solid (red) curve is the model theoretical prediction (see text). Inset: Original data and subtracted background.

Figure 3

Left: Angular resolved photoelectron spectroscopy of the Au(111) surface state measured rotating the sample normal by $5{}^{\circ }$ away from the analyzer axis. The dashed and solid lines represent the parabolic angular dispersion of the Rashba split surface states with $m^{*}=0.26m_e$ and $m^{*}=1m_e$, respectively. Right: Photoemission spectra integrated over $1{}^{\circ }$ around $\Gamma$ measured for 120 GW/cm${}^2$ [rightmost (red) curve] and 60 GW/cm${}^2$ (black curve). The leftmost, thin solid (blue) curve represents the symmetric line shape measured at 60 eV photon energy.

Figure 4

Details of the field-free model Hamiltonian. The eigenvalues show the presence of a surface state within the gap, as in real Au(111). The Fermi level was taken as the 0 of the energy scale. Inset: (Bottom) Periodic potential modeling the linear chain of atoms and (top) wave function of the symmetric surface state.

Figure 5

Left: Computed surface band structure on the first layer of a Au(111)-$\left(1\times 1\right)$ slab. Right: Density of states (DOS) at the $\Gamma$ point projected on the surface Au atom for the $22\times \sqrt{3}$ surface reconstruction, summing contributions from ${\mathbf{k}}_{\parallel }$ points which fold into the BZ center (represented by filled circles in the inset). Inset: BZ of the pristine (hexagon) and reconstructed (thin rectangle) Au(111) surface.