Momentum-resolved observation of ultrafast interlayer charge transfer between the topmost layers of $\mathrm{Mo}{\mathrm{S}}_2$

We report on the direct observation of electron transfer between the surface and the second layer of the prototypical transition-metal dichalcogenide $2\mathrm{H}\text{−}\mathrm{Mo}{\mathrm{S}}_2$. We are able to disentangle the excitation and the transfer process in our measurement. Thereby, we determine both the momentum location and the duration of the electron transfer between the first two layers. Our $GW$-based tight-binding calculations reveal that the band gap in the surface layer is considerably larger than in deeper layers and that the coupling between surface and deeper layers is strongly momentum-dependent throughout the Brillouin zone. At the conduction-band minimum $\overline{\mathrm{\Sigma }}$ we find strong coupling, which explains the ultrafast interlayer charge transfer observed in our experiment at this location.

Figure 1

Scheme of the experiment. Electrons are excited by tunable visible pump pulses and probed by XUV photons. Emitted electrons are detected in a hemispherical electron analyzer along $\overline{\mathrm{\Sigma }}\text{−}\overline{K}$. Only electrons from the surface layer contribute to the 2PPE signal. The layer-dependent size of the band gap, indicated by different colors of the $K$ valleys, allows us to excite the system within different layers by tuning the pump-pulse photon energy, and to study electron transfer between layers. (a) Excitation above or close to the surface layer gap. Electrons within each layer are excited at $\overline{K}$ and transferred to $\overline{\mathrm{\Sigma }}$ within 5 fs. (b) Excitation between surface and second layer gap. Only electrons in deeper layers are excited at $\overline{K}$, and the transfer between layers at this momentum location is suppressed due to the larger gap and weak coupling. After the fast transfer to $\overline{\mathrm{\Sigma }}$ within deeper layers, electrons are transferred to the surface layer due to the strong coupling at $\overline{\mathrm{\Sigma }}$.

Figure 2

Dynamics and energetic positions of excited electrons in the surface layer. Energy-momentum maps of the initial stages of electron excitation around $\overline{K}$ for a pump photon energy (a) above the surface layer band gap and (b) below the surface layer gap for different pump-probe delays $\mathrm{\Delta }t$. In the case of above surface layer band-gap excitation, an electron population localized at $\overline{K}$ is clearly visible around temporal overlap, which significantly decreases for larger delays but never vanishes in our observed time interval. In contrast, for pump photon energies below the surface layer band gap, only a faint replica of the valence band is observed around temporal overlap, which we attribute to nonresonant photoemission. (c),(d) Comparison of the 2PPE signal within the complete momentum range of the experiment for the temporal overlap and for long delays. A population at both high symmetry points is clearly visible already around temporal overlap in the case of high excitation energies (c), whereas only the conduction-band minimum at $\overline{\mathrm{\Sigma }}$ is populated for low excitation energies (d). Dashed lines indicate the excitation threshold for the surface layer (valence-band maximum $+$ pump photon energy).

Figure 3

(a) Energy-momentum map of the valence band and populated conduction band. The unoccupied part is integrated over delays $\mathrm{\Delta }t>150$ fs, where we observe no significant change in the population. (b) The energy distribution curve is a projection $\pm 0.03$ Å around $\overline{K}$. From fits to the EDC we extract a surface layer band gap at $\overline{K}$ of 1.97 eV. (c) Band structure (around $\overline{K}$) calculated for a slab of 40-layer $\mathrm{Mo}{\mathrm{S}}_2$ using conventional TB and our TB-QP approach. (d) Schematic energy level diagram of the calculated bands (TB-QP) at $\overline{K}$. The surface layer is largely decoupled from the other layers of the slab and has the largest band gap (2.39 eV). The band gaps of the other layers, which are summarized as bulk, are smaller and range from 2.30 to 2.19 eV. The extracted band gaps illustrate that the surface layer is decoupled from lower-lying layers.

Figure 4

(a) Time evolution of the 2PPE signal at $\overline{K}$ for excitation energies above (yellow) and below (red) the surface layer gap. Solid lines are fits from a dynamical model of 2PPE intensities. (b) Time evolution of the 2PPE signal at $\overline{\mathrm{\Sigma }}$ for the same excitation energies as in (a). A rate equation model (solid lines) resulting in an electron transfer time between layers of 17 fs gives remarkable agreement with the experimental data points. (c) Conduction-band coupling between the surface layer and all other layers of bulklike $\mathrm{Mo}{\mathrm{S}}_2$ (slab of 40 layers). The coupling is calculated within our TB-QP approach on a $24\times 24\times 1k$-space grid between all subbands of the two lowest conduction bands.