  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.
