Dielectric Screening in Floquet-Volkov Dressing of Semiconductors

Abstract

Nonequilibrium manipulation of quantum materials via electromagnetic dressing provides an on-demand route to tailoring electronic band structures through Floquet engineering. Time- and angle-resolved photoemission spectroscopy offers a direct means to probe these light-dressed electronic states. In such photoemission experiments, dressing can also occur for quasi-free electrons outside the material, giving rise to Volkov states. In certain cases, strong surface screening reduces the penetration of the driving field into the solid, resulting in Volkov contributions that dominate over Floquet ones. In this work, we systematically investigate the influence of materials' dielectric properties on Floquet-Volkov dressing of semiconductors, focusing on bulk layered van der Waals materials GeS, SnS, and 2H-WSe$_2$. First, by combining a simple model based on Fresnel equations with an electron-scattering description of Volkov amplitudes, we use polarization-dependent Volkov sideband intensities to extract a lower bound for the real part of the materials' dielectric functions, which typically lie between the reported dielectric constants for monolayer and bulk crystals. We demonstrate that increasing the fluence of the pump laser enables the generation of high-order Volkov sidebands which exhibit clear signatures of nonlinear light-matter interactions. Finally, we show that for our experimental geometry, the quasi-transparent nature of semiconductors in below-band-gap driving regime allows the optical pump to propagate within the sample and undergo multiple total internal reflections, producing temporally delayed Volkov replicas in pump-probe measurements via dressing of photoelectrons by evanescent fields. These systematic studies uncover previously unexplored aspects of Floquet-Volkov dressing in solids, highlighting the role of dielectric screening of the driving field.

Figures (7)

• Figure 1: Schematic of the experimental setup.(a) A polarization-tunable infrared (IR) pump (1.2 eV, 135 fs) and a p-polarized extreme ultraviolet (XUV, 21.6 eV) probe pulses are focused on the sample in the interaction chamber of a time-of-flight momentum microscope at an incidence angle $\theta=65^\circ$. We show constant energy contours measured for the semiconductor GeS, for the incidence plane aligned along the mirror plane, integrated over all pump polarizations, at pump-probe temporal overlap, at the energies of the valence band maximum (VBM) and of the first-order sideband ($\mathrm{VBM}+\hbar\omega$). (b) Experimentally measured photoemission intensity from GeS along $k_y$, with the light scattering plane aligned along the armchair direction, summed over all pump polarizations, at pump-probe temporal overlap. (c) Schematic of the crystal structures of GeS, SnS, and 2H-WSe$_2$.
• Figure 2: Simulated polarization-dependent field components for Au(111), GeS and 2H-WSe$_2$ for an incidence angle of 65$^\circ$.(a) Schematic representation of the experimental geometry and of the partially reflected electric field with reference to our axis convention. The two in-plane components are $x$ and $y$. When the pump polarization is completely in-plane (s-polarization), the electric field is along $y$. (b-d) Square of the real part of the electric field ($\Re{(\mathbf{E})}^2$) of Au(111) (orange), GeS (blue), and 2H-WSe$_2$ (green) projected along $z$ (b), $x$ (c), and $y$ (d), calculated through Eq. \ref{['eq:Etot']} as a function of the pump linear polarization angle ($\phi$).
• Figure 3: Momentum-integrated polarization-resolved sideband intensity in GeS.(a) Evolution of the momentum-integrated Volkov intensity with the pump polarization axis angle at a pump fluence of $\sim$1.6 mJ/cm$^2$. The black dots are the experimental data, the blue line is calculated in the fully unscreened case, the red curve is calculated in the fully screened case, and the black line is the result from the fit using Eq. \ref{['eq:alpha_revised']} ($\epsilon=7.8$). (b) Closer view of (a) around the s-polarized pump ($\phi=90^\circ$). The pink dashed line is the polarization-dependent Volkov intensity calculated using the reported value of the dielectric constant for the bulk material ($11<\epsilon_\mathrm{bulk}<15$el-bakkali_layers_2021koc_mechanical_2015arfaoui_optical_2023venghaus_dielectric_1975. Here, the curve is obtained with $\epsilon=12.5$). Similarly, the cyan dashed line is calculated for the monolayer (ML) value ($\epsilon_\mathrm{ML}\sim4$el-bakkali_layers_2021), and the black curve is the result from the fit ($\epsilon=7.8$).
• Figure 4: Polarization-dependent momentum distribution of the Volkov sideband intensity in GeS.(a-d) Momentum-resolved maps of $|\alpha|^2$ calculated using Eq. \ref{['eq:alpha_revised']} and the fitted value of $\epsilon=7.8$ (experimental value of GeS) for (a) $\phi=-45^\circ$, (b) $\phi=0^\circ$ (p-polarized pump), (c) $\phi=+45^\circ$, and (d) $\phi=90^\circ$ (s-polarized pump). The red arrows represent the in-plane direction of polarization of the pump. (e) Polarization-resolved forward/backward asymmetry (i.e., along $k_x$) in the momentum-distribution of the first sideband (black dots are experimental results and the black line is the theoretical result using the fitted value of $\epsilon=7.8$). The asymmetry is defined as the normalized difference between the intensity within the forward and backward regions delimited by the dashed black lines in (a) and (c). (f) Polarization-resolved up/down asymmetry (i.e. along $k_y$) of the momentum distribution of the first sideband (black dots are experimental results and the black line is the theoretical result using the fitted value of $\epsilon=7.8$). The asymmetry is defined as the normalized difference between the top and bottom regions delimited by the dashed black lines in (b) and (d).
• Figure 5: Polarization-dependent momentum distribution of photoemission intensity from the valence band (VB) and first-order sideband of GeS, upon below-band-gap pumping at a pump fluence of $\sim$1.6 mJ/cm$^2$. The red arrows represent the in-plane direction of the pump polarization. (a-b) Experimentally measured momentum distributions of photoemission intensities from valence band ($E=E_\mathrm{VBM}\sim0$ eV) for p- and s-polarized pump, respectively. (c-d) Calculated momentum distribution of photoemission intensities of first-order sidebands obtained from experimental momentum distribution (a) and (b) multiplied by the simulated Volkov sideband intensity using Eq. \ref{['eq:alpha_revised']} (with the fitted value of $\epsilon=7.8$). (e-f) Experimentally measured momentum distributions of photoemission intensities from first-order sidebands (integrated over $1.1~\mathrm{eV}<E<1.3~\mathrm{eV}$) for p- and s-polarized pump, respectively.