Symmetry properties of attosecond transient absorption spectroscopy in crystalline dielectrics

We theoretically investigate a relation between the crystalline symmetry and the transient modulation of optical properties of crystalline dielectrics in pump-probe measurements using intense pump and attosecond probe fields. When the photon energy of the pump field is much below the bandgap energy, the modulation of the optical conductivity is caused by the intraband electronic motion, that is, the dynamical Franz-Keldysh effect. We analytically investigate symmetry properties of the modulated optical conductivity utilizing the Houston function and derive a formula that relates the temporal oscillation in the absorption with the transformation properties of the modulated optical conductivity. To verify the validity of the formula, we perform real-time first-principles calculations based on the time-dependent density functional theory for a pump-probe process taking 4H-SiC crystal as an example.