Electromagnetic dressing of the electron energy spectrum of Au(111) at high momenta

Light-engineering of quantum materials via electromagnetic dressing is considered an on-demand approach for tailoring electronic band dispersions and even inducing topological phase transitions. For probing such dressed bands, photoemission spectroscopy is an ideal tool, and we employ here a novel experiment based on ultrafast photoemission momentum microscopy. Using this setup, we measure the in-plane momentum-dependent intensity fingerprints of the electromagnetically-dressed sidebands from a Au(111) surface for $s$- and $p$-polarized infrared driving. We find that at metal surfaces, due to screening of the driving laser, the contribution from Floquet-Bloch bands is negligible, and the dressed bands are dominated by the laser-assisted photoelectric effect. Also, we find, from calculations, that in contrast to general expectations, $s$-polarized light can dress free-electron states at large photoelectron momenta. Our results show that the dielectric response of the material must carefully be taken into account when using photoemission for the identification of light-engineered electronic band structures.

Figure 1

Schematics for the electromagnetic dressing with IR light of (a) Bloch bands, yielding Floquet-Bloch bands, and (b) quasifree electrons, leading to LAPE. In both scenarios, sidebands ($n_{\pm 1}$, dashed line) of the main photoemission spectral feature ($n_0$, solid line) are observed in the photoemission experiment. (c) Both processes terminate at the same final state energy, requiring the consideration of scattering amplitude between both processes.

Figure 2

Time-resolved momentum microscopy experiment. In a stroboscopic experiment, we drive the Au(111) crystal with intense IR laser pulses and probe the instantaneous band structure with EUV light. The momentum microscope provides simultaneous access to the kinetic energy ($E_{\mathrm{kin}}$) and full in-plane momentum-resolved ($k_x$ and $k_y$) data sets, as illustrated by the three momentum maps at energies $E-E_F$ of 1.1, 0.5, and $-0.1$ eV. The accessible in-plane momentum range is limited by the photoemission horizon that scales with $k_{xy}\propto \sqrt{E_{\mathrm{kin}}}$. The experimental geometry is sketched in the bottom part. The drive and probe laser pulses impinge nearly collinear onto the surface at an angle of ${22}^{\circ }$ from the surface plane. The coordinate frame of the in-plane electric field ($E_{xy}$, ${\theta }_E$) and momentum ($k_{xy}$, ${\theta }_k$) components is shown in polar coordinates; the out-of-plane components $E_z$ and $k_z$ are normal to the surface. The polarization of the driving light is tuned with a $\lambda /2$ plate and defined by the angle $\varphi$.

Figure 3

[(a) and (b)] Calculated in-plane momentum distributions of the LAPE sideband amplitude $|a_1{|}^2$ after Eq. (3) for $p$- and $s$-polarized light impinging along $k_x$ in an oblique angle of incidence; the white arrow indicates the direction of the in-plane electric field component. Sideband yield can be expected for LAPE in both polarizations. [(c) and (d)] If the in-plane electric field components are screened ($E_{xy}=0$), no sidebands are expected for $s$-polarized light. In $p$-polarized driving, $|a_1{|}^2$ is symmetric around the $k_{xy}=0$. Note that all plots are visualized on the same color scale, in the full accessible photoemission horizon.

Figure 4

(a) ($k_x$, $k_y$)-resolved momentum maps extracted from the three-dimensional momentum microscopy data obtained with $p$-polarized EUV light and $p$- (left column) and $s$- (right column) polarized IR driving light in temporal overlap. The top row shows momentum maps taken close to the Fermi level that we label as the zero-photon-order sideband $n_0$. The high-symmetry points $\overline{\mathrm{\Gamma }}$, $\overline{K}$, $\overline{M}$, and the Shockley surface band (SS) as well as the $sp$-band transitions (sp) are indicated. The black arrow represents the direction of light incidence. The bottom row shows the first-order sideband intensity ($n_1$) around $E-E_F$ = $+1.1$ eV above the Fermi-level for driving with $p$- (left) and $s$-polarized (right) IR light. (b) Systematic evaluation of the momentum integrated intensity of the first-order sideband $n_1$ when rotating from $p$- to $s$-polarized light. The data are well approximated with Eq. (4), implicating that the in-plane electric field components are screened ($E_{xy}=0$). (c) Azimuthal dependence of the sideband intensity of the SS band and the sp-band transition (details on the normalization of the data is provided in the Supplemental Material [18]). The data can be fitted with Eq. (4), indicating that the in-plane component of the electric field is efficiently screened.