Femtosecond valley polarization and topological resonances in transition metal dichalcogenides

We theoretically introduce the fundamentally fastest induction of a significant population and valley polarization in a monolayer of a transition metal dichalcogenide (i.e., ${\mathrm{MoS}}_2$ and ${\mathrm{WS}}_2$). This may be extended to other two-dimensional materials with the same symmetry. This valley polarization can be written and read out by a pulse consisting of just a single optical oscillation with a duration of a few femtoseconds and an amplitude of $\sim 0.25\mathrm{V}/\text{Å}$. Under these conditions, we predict an effect of topological resonance, which is due to the Bloch motion of electrons in the reciprocal space where electron population textures are formed due to non-Abelian Berry curvature. The predicted phenomena can be applied for information storage and processing in PHz-band optoelectronics.

Figure 1

Residual CB population $N_{\mathrm{CB}}^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ for monolayer ${\mathrm{MoS}}_2$ in the extended zone picture. The red solid line shows the first Brillouin zone boundary with $K,K^{\prime }$ points indicated. The amplitude of the optical field is $F_0=0.25$ V ${\AA }^{-1}$. (a) Wave form $\mathbf{F}\left(t\right)$ for a right-handed circularly polarized pulse. (b) The same as (a) but for a left-handed circularly polarized pulse [$\mathcal{T}$ reversed to that in (a)]. (c) Residual population of spin-up electrons $N_{\mathrm{CB}\uparrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ for a right-handed pulse. (d) The same as (c) $N_{\mathrm{CB}\uparrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ but for a left-handed pulse. (e) Residual population of spin-down electrons $N_{\mathrm{CB}\downarrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ for a right-handed pulse. (f) The same as (e) $N_{\mathrm{CB}\downarrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ but for a left-handed pulse.

Figure 2

Residual CB populations $N_{\mathrm{CB}}^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ for monolayer ${\mathrm{WS}}_2$ after a right-handed circularly polarized pulse. Note that the corresponding distributions for a left-handed pulses are related to these by the $\mathcal{T}$ symmetry similar to Fig. 1. The red solid line shows the Brillouin zone boundary. Amplitude of the applied field is $F_0=0.25$ V ${\AA }^{-1}$. (a) Population $N_{\mathrm{CB}\downarrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$ for spin-up electrons. (b) The same as (a) but for spin-down electrons $N_{\mathrm{CB}\uparrow }^{\left(\mathrm{res}\right)}\left(\mathbf{k}\right)$.

Figure 3

For a chiral left-handed pulse, Bloch trajectories $\mathbf{k}(\mathbf{q},t)$ in the $K^{\prime }$ valley and topological phase ${\varphi }_{cv}^{\left(\mathrm{T}\right)}(\mathbf{q},t)$ for transitions $v\to c$ between bands forming the band gaps at the $K$ and $K^{\prime }$ points. (a) Separatrix for the pulse used is shown by the black line. Electron Bloch trajectory $\mathbf{k}(\mathbf{q},t)$ is shown for an initial point $\mathbf{q}$ outside the separatrix. The $K^{\prime }$ point is denoted by a solid dot and the Berry connection is denoted by a green “whirl” where the chirality is indicated by arrows. (b) The same as (a) but for $\mathbf{q}$ inside the separatrix. (c) Topological phase ${\varphi }_{cv}^{\left(\mathrm{T}\right)}(\mathbf{q},t)$ on the Bloch trajectory for the $K$ point and $\mathbf{q}$ outside of the separatrix (red line) and inside the separatrix (blue line). (d) The same as (c) but for the $K^{\prime }$ point.