A gauge-invariant density matrix approach is presented to describe the non-equilibrium dynamics of multiband superconductors after photo-excitation. The derived gauge-invariant Bloch equations extend the Anderson pseudo-spin precession model by fully incorporating the center-of-mass motion of Cooper pairs. We also describe lightwave propagation effects inside a superconducting film by including the self-consistent interaction of the photo-excited superconducting system with the propagating electromagnetic field inside the superconductor using Maxwell's equations.
Magnetically doped topological insulators (TIs) attract a great deal of interest for both fundamental scientific studies and potential applications. These systems are promising for the realization of quantum anomalous Hall effect, and more generally, for the potentially controllable magnetism, which can underlay many useful technological applications. Here, we reveal the first photoinduced magnetization dynamics in a 40 nm thin film of magnetically doped TIs, CrxBi2-xTe3 with x=0.29 using femtosecond time-resolved magneto-optical Kerr effect (MOKE) spectroscopy. The ultrafast spin dynamics of the sample at low temperature 5 K is characterized by two demagnetization dynamics, attributed to spin-spin (~0.5 ps) and spin-phonon (~10 ps) scatterings, respectively, followed by a slow recovery process with 100s of ps time scale. While it gets faster at elevated temperature and finally vanishes above ~ 90 K, much higher than the reported Curie temperature Tc~23.8 K, due to strong Van Vleck magnetic susceptibility in the magnetically doped TIs system, distinct from the case of GaMnAs. In addition to providing implications for deeper understanding of spin dynamics in magnetically doped TI systems, the study will potentially benefit the development of magnetic TIs-based spintronic devices.
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