Subcycle control of valley-selective excitation via dynamical Franz-Keldysh effect in WSe$_2$ monolayer

This study performed first-principles calculations based on the time-dependent density functional theory to control the valley degree of freedom relating to the dynamical Franz-Keldysh effect (DFKE) in a monolayer of transition metal dichalcogenide. By mimicking the attosecond transient absorption spectroscopy, we performed numerical pump-probe experiments to observe DFKE around the $K$ or $K'$ valley in WSe$_2$ monolayer with a linearly-polarized pump field and a circularly-polarized probe pulse. We found that the circularly-polarized probe pulse with a given helicity can selectively observe the transient conductivity modulated by DFKE in each valley. The transient conductivity and excitation probability around each valley oscillate with the pump field frequency $\Omega$. The phases of the $\Omega$ oscillation for the $K$ and $K'$ valleys are opposite to each other. Furthermore, the pump-driven DFKE alters the absorption rate of WSe$_2$ monolayer and yields the valley-dependent $\Omega$ oscillation of the electron excitation induced by the pump plus probe field. With a simplified two-band model, we identified the $\Omega$ oscillation of the off-diagonal conductivity caused by the band asymmetry around the valleys as the physical mechanism responsible for the valley-selective DFKE.