Spin and valley control of free carriers in single-layer ${\mathrm{WS}}_2$

The semiconducting single-layer transition-metal dichalcogenides have been identified as ideal materials for accessing and manipulating spin- and valley-quantum numbers due to a set of favorable optical selection rules in these materials. Here, we apply time- and angle-resolved photoemission spectroscopy to directly probe optically excited free carriers in the electronic band structure of a high quality single layer (SL) of ${\mathrm{WS}}_2$ grown on Ag(111). We present a momentum-resolved analysis of the optically generated free hole density around the valence band maximum of SL ${\mathrm{WS}}_2$ for linearly and circularly polarized optical excitations. We observe that the excited free holes are valley polarized within the upper spin-split branch of the valence band, which implies that the photon energy and polarization of the excitation permit selective excitations of free electron-hole pairs with a given spin and within a single valley.

Figure 1

(a) ARPES spectrum of ${\mathrm{WS}}_2$ taken before optical excitation. The BZ in the inset shows the measurement direction via the dashed line. (b) Difference between the peak excitation spectrum obtained with an $s$-polarized pump pulse at a photon energy of 2.05 eV and the equilibrium spectrum in (a). The sketch presents the resonant excitation at the VBM and CBM. (c) Time dependent intensity difference (markers) summed over the dashed boxed regions on the CBM and VBM, respectively, in (b). Overlaid thick lines are fits to a function consisting of an exponential rising edge and a single exponential decay with time constant $\tau$. (d) Integrated EDCs at equilibrium (Eq.) and peak excitation (Exc.) along with their difference (Diff.) for the corresponding data in (b). The integration was carried out over the VBM and CBM in the momentum range from 1.15 to 1.45 ${\AA }^{-1}$. Gaussian fits of the peaks in the difference are shown along with estimates of the transition energies in eV (error bars are $\pm 0.05$ eV).

Figure 2

(a),(b) Selection rules for transitions from the upper VB to the CBM in the $\overline{K}$ and ${\overline{K}}^{\prime }$ valleys. (c) BZ orientations and selection rules for the two possible domain orientations probed in this work. (d),(e) Difference signal for optical pumping with (d) ${\sigma }^{-}$ and (e) ${\sigma }^{+}$ circular polarization and a photon energy of 2.05 eV. (f) EDCs of the difference integrated over the VBM and CBM regions for the data in (d) and (e).

Figure 3

(a) EDCs extracted over the VBM and fitted with two Lorentzian line shapes on a parabolic background. Each EDC is binned over a range of $\pm 0.02$ ${\AA }^{-1}$. (b) Example EDC fit for equilibrium (Eq.) and optically excited (Exc.) data with plots of the individual Lorentzian components. (c) Measured spectrum used for the EDC analysis in (a). (d) Reconstruction of the spectrum using the fitted EDCs. (e),(f) Difference (Diff.) spectra corresponding to the data and fit in (c) and (d). The spectrum analyzed here was measured with an $s$-polarized optical excitation at a photon energy of 2.05 eV [see also Fig. 1].

Figure 4

(a)–(d) Number of holes $N_h$ per momentum state (markers) and distribution function fits (curves) for [(a),(b)] $s$-polarized optical pumping and [(c),(d)] circularly polarized optical pumping with a photon energy of 2.05 eV. The hole number was extracted using the analysis procedure in Fig. 3 for [(a),(c)] the upper VB and [(b),(d)] the lower VB. The calculated hole density $n_h$ per valley is provided in each panel. The insets of the ${\mathrm{WS}}_2$ band diagrams present the possible transitions for the optical excitation conditions in each panel.